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The analysis of slant-from-texture in early vision Aks, Deborah J. 1993

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THE ANALYSIS OF SLANT-FROM-TEXTURE IN EARLY VISIONbyDeborah J. AksUniversity of British ColumbiaB.A., The State University Center of New York at Binghamton, 1984M.A., The University of British Columbia, 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIES(Department of Psychology)We accept this^is as conforming to the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1993© Deborah J. AksIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department of 1°- 4 IJ7C 6:)yThe University of British ColumbiaVancouver, CanadaDate /7 41/40d- /”.3DE-6 (2/88)AbstractA considerable amount of research exists on the subjective perception of three-dimensional structure from texture gradients. The present set of experiments extendsthese tests of phenomenal perception by examining the underlying processes used ininterpreting slant-from-texture. The first two experiments show that measures ofsubjective perception predict speeded performance in a visual search task, and that themediating representation relies on an assumption of projective size (i.e., discriminating thesize of the target is difficult when the short target is far or the long target is near). Thethird experiment shows that sensitivity to apparent depth in the texture display is presenteven in rapid and parallel search conditions where early vision is known to operate. Thefourth experiment assesses the relative contribution of two dominant dimensions of thetexture gradient -- "perspective" (i.e., a radial pattern) and "compression" (i.e., aforeshortened pattern). Both dimensions are detected by early vision as signals forapparent depth. The fmal experiment examines how early vision codes these twodimensions. Sternberg's (1969) Additive Factors Method (AFM) is used to assessseparability of encoding, and Blalock's path analysis (1962, 1985) is used to examine theorder of encoding. AFM shows that perspective and compression have independentinfluences on search performance in the most rapid search conditions, but that theirinteraction increases as search slows. The path analysis shows further that when bothtexture dimensions are available, perspective exerts a more immediate and perhaps even anexclusive influence on performance. These findings support the view that perspective andcompression are coded separately at the earliest stages of visual processing and share acommon code only later in visual processing.Slant - from - textureiiiTable of ContentsTitle Page^Abstract iiTables of Contents ^ iiiList of Tables viiList of Figures viiiAcknowledgments^Chapter 1Slant-from-Texture 1Overview^ 4Texture gradients 4Perceptual use of texture gradient information^ 7Empirical tests. ^ 8Chapter 2Separating the process from the product^ 11Do subjective measures predict speeded performance? 14The visual search task^ 15Experiment 1Slant-from-texture influences on visual search^ 17Method^ 18Subjects 18Stimuli and Procedure^ 18Results^ 21Display size effects 25Central location effects^ 25Location and testing order 26Discussion^ 26Experiment 2Separating top-to-bottom from apparent-distance effects^ 27Method^ 28Subjects 28Stimuli and Procedure^ 28Slant - from - textureivResults^ 28Location effects in the control condition^ 32Display size effects^ 32Testing order 33Discussion^ 33Chapter 3How early are the slant-from-texture influences?^ 35A two stage model of vision^ 35Encoding slant-from-textureEarly or late? 37RT Slope performance^ 38Projective size or apparent proximity?^ 38Summary^ 41Experiment 3Slant-from-texture influences in early vision^ 41Method^ 42Subjects 42Stimuli and Procedure ^ 42Results^ 46Threshold for preattentive vision. 46Visual search on textured surfaces.^ 46Display size and apparent depth. 48Additional influences^ 51Practice. ^ 51Top - bottom search biases 51Left - right search bias. ^ 53Item Orientation 54Size - depth consistency. 56Discussion^ 57Item grouping?^ 57Search biases 58Implications. 58Slant - from - textureChapter 4An examination of the texture gradient dimensions^ 61Monocular Depth Cues^ 61Decomposing the texture gradient. 62Relative contribution to subjective perception^ 65Experiment 4Influences from dimensions^ 67Method^ 68ResultsPerspective & Compression Combined^ 69Item orientation. ^ 72Perspective Results 72Display size and apparent depth^ 75Performance difference across backgrounds. 75Item orientation.^ 77Additional location influences^ 78Summary of perspective effects 78Compression Results^ 78Performance difference across backgrounds.^ 79Item orientation. 81Additional influences^ 81Summary of compression effects^ 81Discussion^ 82Chapter 5^ 86How does our visual system combine the dimensions?^ 86-A test of additivity^ 88Method^ 90Results 91Contrast test of Additivity.^ 94Processing speed and additivity^ 96Item orientation. ^ 96Speed of Processing, additivity, and item orientation^ 99Discussion^ 100Processing sequence. ^ 104Slant - from - textureviMethod^ 104Results  105Discussion 109General Discussion^  111Implications for theories of early vision.^  112Implications for theories of surface perception.  114Early vision and surface perception.  116References^  118Appendix A 129Slant - from - textureviiList of TablesTable 1: Standard Error of the Mean (SEM) for RT and percentage of errors inExperiment 1.^ 23Table 2: Standard Error of the Mean (SEM) for RT and percentage of errors inExperiment 2.^ 31Table 3: Mean correct reaction time and percentage of errors in Experiment 3 --Combined Gradients^ 47Table 4: Mean correct reaction time and percentage of errors in Experiment 3 --Top-Bottom Analysis^ 52Table 5: Mean correct reaction time and percentage of errors in Experiment 4 --Perspective Gradient ^ 76Table 6: Mean correct reaction time and percentage of errors in Experiment 4 --Compression Gradient ^ 80Table 7: Inter-correlation and partial correlations across texture gradientconditions^ 106Slant - from - textureviiiList of FiguresFigure 1: Picture containing slant-from-texture. ^ 2Figure 2: Construction of a texture gradient. 3Figure 3: Trigonometric function relating surface texture to slant angle ^ 5Figure 4: Visual search displays...^ 20Figure 5: Experiment 1 results -- Mean correct RT and Percent Errors. ^ 22Fig rte: Experiment 2 results -- Mean correct RT and Percent Errors. ^ 30Figure 7: Experiment 2 RT Slope performance.^ 39figura: Combined texture gradient background used in Experiment 3. ^ 43Figure 9: Full set of search items used to assess thresholds for early vision. ^ 44Figure 10: Experiment 3 results -- Mean correct RT and Percent Errors. ^ 49Figure 11: Experiment 3 results separated across item orientation. 55Eigum12: Perspective, compression and combined gradient search displays.Figure 12a: Vertical items.^ 63Figure 12b: Horizontal items. 64Eigatia: Mean RT difference and Percent Error difference across slant and controlbackground for Perspective, Compression and Combined gradient targettrials in Experiment 4.Figure 13a: Short target trials. ^ 70Figure 13b: Long target trials.  ^ 71Figure 14: Mean RT and percent error difference separated across item orientation.Figure 14a: Short target trials^ 73Figure 14b: Long target trials.  ^ 74Figure 15: RT slopes for Perspective, Compression and Combined conditions. ^ 83Slant - from - textureixFigure 16: Additivity test using orthogonal variation of texture dimensions separatedacross size-depth consistency.Figure 16a: Consistent conditions^ 92Figure 16b: Inconsistent conditions 93Figure 17: Contrast scores -- Mean difference in RT and percent error across alltexture (perspective and compression) present and absent trials^ 95Figure 18: Additivity results separated across item orientation.Figure 18a: Vertical items ^ 97Figure 18b: Horizontal items.^ 98Figure 19: Contrast scores separated across item orientation.Figure 19a: Short target trials^  100Figure 19b: Long target trials.  101Figure 20: Path representation of texture processing^ 107Slant - from - texturexAcknowledgmentsI extend great thanks to all of the following people who helped me through quite ajourney -- Jim for teaching new and inspiring approaches to old perceptual problems andfor the tremendous contributions to the Slant-from-texture research; Stan for providingcreative ideas, a wealth of illusions and endless challenges throughout my graduate career;Janet , Rob and Rod for keen insight on important issues in my thesis and muchappreciated encouragement; Dimitri for superb editorial contributions; Roger fortrigonometric expertise; Chris for Reason from around the globe; my family for endlessemotional support -- Mom for reminding me of the applied, the virtual and the real worlds;Dad for reminding me of the sailing and scuba worlds; my sibs -- Judy, Steve and Lori --for being my friends; my friends -- Jill, Kelly, David, Sarah, Ed, Shuji and all the folksfrom the Vision lab & the Big Apple -- for being so supportive. And last but not least...Mohamad for his omnipresence.Chapter 1: Slant-from-TextureWhen viewing a picture of a textured surface, such as the snow-rippled mountainin Figure 1, observers typically report an impression of a slanted surface receding intothe distance. This is true regardless of the fact that a two-dimensional (2-D) image cannever completely specify a surface in depth. How do we perceive depth from an imagethat is constrained to two dimensions? One potential solution is that our visual systemuses geometric rules to interpret 2-D images as projections from real objects in the world(i.e., Brunelleschi; 1413, cited in Kemp, 1978). Such a strategy would imply that ourvisual system assumes a single vantage point, and uses rules of linear perspective wheninterpreting line drawings. This may mean that vision interprets the vanishing points ina 2-D image as distance points in the 3-D world and uses this information to determinegeometric relationships of objects in space. A detailed description of ways in which wemay solve this correspondence problem between the image and the scene is presentedfollowing a brief discussion of the projective distortion in the texture gradient and anoverview of the present studies.^Insert Figure 1^When light from a slanted surface is projected onto an image plane, uniformsurface texture is distorted in the image to form a texture gradient as shown in Figure 2.In a flat textured surface, the horizontal and vertical dimensions of texture elementsdiminish gradually in size as the slant angle increases away from the observer. Thesystematic variation of texture due to changes in distance and slant provides importantinformation about the 3-D properties of an object relative to an observer. The relativedistance information specified by texture gradients will be referred to as slant-from-texture throughout the thesis. There is also information about the magnitude anddirection that a surface dips away from the frontal plane but these are of secondaryimportance in this study of apparent depth perception.^Insert Figure 2^Figure 1. Picture of mountain glacier as an example of a textured surface receding into the distance. Horizontal andvertical distortions of the snow ripples in the image indicate information about surface slant.Center of Projectionr<0Line of SightProjecting RaysFigure 2. Representation of light from a flat - slanted surface being projected onto an image plane showing how uniformsurface texture is distorted in the image to form a texture gradient. The horizontal and vertical dimensions of textureelements in the image diminish gradually in size as the slant angle of the floor increases away from the viewer.Slant - from - texture4OverviewThe perception of slant-from-texture was investigated in a series of visual searchexperiments with the goal of answering the following questions. First, do tests ofsubjective perception and rules of projective geometry predict visual search performancein slant-from-texture displays? Second, which visual systems are influenced by slant-from-texture: early or late? Third, which dimensions of the texture gradient influencevisual search, and does the literature on subjective perception predict the relativeimportance of these dimensions in search performance? Fourth, which dimensions canbe detected in parallel in visual search? The fmal section examines how the visualsystem combines the dimensions of the texture gradient to elicit an impression of slant.Implications for underlying representations and processes are discussed.Texture gradients A considerable amount of work has been devoted to mathematical andgeometrical proofs relating surface slant of objects to texture gradients in images (i.e.,Cutting and Millard, 1984; Dunn, 1986; Flock, 1964; 1965; Kantani, 1984; Marr, 1982;Pizlo & Rosenfeld; 1992; Purdy, 1960; Stevens, 1981; 1983a; 1983b; Witkin, 1981).Cutting and Millard's (1984) trigonometric functions representing the perspective andcompression aspects of texture are shown in Figure 3. To use these equations inextracting slant-from-texture, assumptions about texture regularity, texture elementspacing, and surface planarity are required (e.g., texture elements are assumed to beregular in size, uniform in spacing, and flush against a flat surface). Given theseconstraints, corresponding rules can be used to describe how the visual systeminterprets texture gradients as having slant and distance information.^Insert Figure 3^J.J. Gibson (1950a; 1950b; 1979) is credited as the first researcher to testwhether texture is mathematically and psychologically sufficient as a stimulus for depthe - eye heightd - distanceto - texture elementr radius of elementC - compressionP perspectiveSurfaceEocdc7) C = arctan [ (d+r)/e] - arctan [ (d-r)/e] = a l - a21/2P = 2* arctan [r/ (d2 + e2 )]^= 2bSlant = 8 = arc Cos (C/P)Figure 3. Cutting and Millard's (1984) trigonometric functions representing the perspective and compression aspects ofthe surface texture and their relationship to surface slant.eSlant - from - texture6perception. A computational analysis by Purdy (1960) demonstrated that four variationsamong optical texture elements were equally informative: gradients of size,compression, convergence, and density. In each case, the slant of a planar surface isspecified by the arccot (Glk) where G is the gradient and k is a constant specific to thetype of gradient. Purdy's equations, although they accurately describe gradientinformation, do not separate out additional information present in the gradient that maymore accurately be used by the human visual system to judge the slant of surfaces.Recognizing the insufficiency of these gradient solutions, Stevens (1981) arguesinstead that the visual system uses separate dimensions of surface texture to estimatedistance (element width), and orientation (element height / width). This approacheliminates the confound of distance and orientation information, which when combinedcan lead to erroneous judgments of slant. More precise estimates of surface slant areobtained by separating orientation into tilt and slant components, and mapping themdirectly onto object orientation and distance. In Stevens' framework, tilt (i.e., thedirection in which the surface recedes) is easy to determine from a texture gradient, butslant (i.e., the amount which the surface recedes) is difficult to find. Tilt is reliablydetermined by first detecting the direction with the least variation in texture spacing --this is the line that passes through equal image heights of the texture elements, and isequidistant from the viewer. The direction perpendicular to this line is the surface tilt.The rules for determining slant, however, change dramatically depending uponthe properties of the surface texture. For a flat surface with regular texture elements(i.e., tiled floor), Slant = arccos (element height /element width). For a surface withprotruding elements (i.e., grass), Slant = arcsin (element height /element width).Steven's work explicitly shows that the calculation of slant, unlike tilt, is unreliableacross a variety of surfaces. He shows that the number of possible mathematicalSlant - from - texture.^7functions increases with each additional exception to the "flat and uniformly texturedstandards".Stevens (1983) suggests a rule based on the initial determination of tilt. This rulerelies on use of a texture dimension that is equidistant from the viewer and which is atright angles to the axis of tilt (See tilt calculation). Stevens refers to this dimension as thecharacteristic dimension (CD), and as shown in Chapter 4, it eliminates the need for anassumption of texture elements resting flat on a surface. Thus, the CD is simply afunction of the distance from the viewer and, as demonstrated later, is equivalent to aprimary dimension of the texture gradient (i.e., perspective). From this source ofinformation, slant can be calculated by determining the gradient (G) of CD's using theequation: Slant = arctan (G (CD) / CD ).The simplest and most general description of the reliable relationship betweentexture size and distance is based on the fundamental property of projective geometry that"far objects project smaller images on the retina than close objects of the same size".Projective size can also be described as the relative changes in the visual angle of imageelements, defined as the arctan (h / d) where h is the height of the focal stimulus and d isthe distance from the observer to the stimulus. This relationship, however, has at leastone limitation -- its imprecision. Unlike the other equations which provide absolute slantinformation, projective size only provides relative distance information. Reliance solelyon principles of projective geometry, a somewhat gross measure of distance, is plausiblein light of evidence (some of which is summarized below) that humans are better atestimating relative rather than absolute distance.Perceptual use of texture gradient informationHaving established the sufficiency of texture gradients to specify distance andslant information (given the noted assumptions), our next concern is whether or notperceivers use this information. This question is far from new. This controversial issueSlant - from - texture8has been debated among perceptual researchers since the middle of the nineteenthcentury when Helmholtz argued that some laws of physical optics are manifest inunconscious processes of shape constancy (1868/1968). Similar claims includeGibson's belief in the direct perception of projective invariants (1950, 1979), Rock'sview that the visual system is guided by implicit knowledge of projective laws (1983),and Ullman's claim that vision transforms polar (i.e., projective) representations intoparallel (i.e., non-projective) ones (1979). Even though these theories differ in thecomputations and depth information used, they all share the view that vision is sensitiveto some form of projective information.Empirical tests. Gibson (1950a; 1950b) was among the first to test the human ability to usetexture to judge slant. Subjects matched the slant of textured surfaces, represented inphotographs taken from varying viewpoints, by a corresponding inclination of the palmof their hands. Not surprisingly, the patterns of optical texture in the photographsproduced responses consistent with an interpretation of a physical surface oriented indepth. However, there was a systematic tendency to underestimate the actual slant -- aneffect that was greater for texture patterns that were irregular Subsequent studiesshowed that although subjects were not so good at judging absolute slant, they werequite good at judging differences in slant (Attneave, 1972; Beck & Gibson, 1955;Braunstein & Payne, 1969; Clark, Smith, & Rabe, 1955; Epstein, Bontrager, & Park,1962; Flock, Graves, Tenney, & Stephenson, 1967; Freeman, 1966; Gillman, 1970;Olson, 1974; Perrone, 1980; Phillips, 1970; and Rosinski & Levine, 1976).Research also showed that relative depth judgments increase in magnitude withincreases in simulated depth in texture gradient displays (Stevens,1981; Todd &Akerstrom, 1987; Vickers, 1971). In Vickers' study, subjects' thresholds of perceiveddepth were derived from a method of limits procedure where subjects uncovered theSlant - from - texture9patterns, line by line, until they "received an impression of depth". Immediatelyafterwards, the pattern was completely exposed, and subjects were asked to bring theslide down from the top until the "impression of depth disappeared". Anotherexperiment in this study, made use of a method of matching and adjustment, wherebysubjects indicated the degree of perceived slant by adjusting a corresponding 3-D plane.Similar to Gibson's earlier palm board procedure (1950a), Vickers' study showed thatslant and depth impressions become stronger as the number and degree of depth cuesincrease.Another experimental technique compared subjects' responses to objects thatcontain perspective information to those without. The amount of available projectiveinformation can be changed simply by manipulating the distance between an object andan image. When the projection onto the image plane is at infinity and therefore parallel,the resulting representation is known as parallel, orthographic (Cutting, 1986), orobject-centered (Marr, 1982). When the projection onto the image plane is less thaninfinity and converges, the resulting form is polar, projective (Cutting, 1986), orviewer-centered (Marr, 1982). The exclusive use of orthographic projection in studiesof object perception has been criticized on the grounds that most objects under ourscrutiny are relatively near to us (Cutting & Millard, 1984). While perspectiveprojection captures these variations in nearness, orthographic projection simulatesinfinite viewing distance, a situation approximated only when looking throughtelescopes at small, distant objects. Thus, in this respect orthographic projection is"unnatural".Studies that compare subjects' judgments of drawings that either are viewer-centered or object-centered, have shown that we do in fact use projective information inmaking judgments about the distance and slant of particular objects represented inimages (Bengston, Stergios, Ward, & Jester, 1980; Cutting, 1987; Doesschette, 1964;Slant - from - texture10Gibson, 1979; Hagen, 1980; Johannson & Borjesson, 1980; McGreevy & Ellis, 1986;Nicholls & Kennedy; 1991; Rosinski, Mulholland, Degelman, Farber, 1980). Forexample, Bengston et al (1980) showed that changing the vantage point affects theperception of distance in accordance with projective geometry. Similarly, Rosinski etal, (1980) tested the effects of vantage point changes on perceived slant. These studiesshow that the accuracy of distance and slant judgments declines when subjects arepositioned at a view other than the depicted vantage point, thus showing our sensitivityto some projective information.However, there are other studies showing human robustness to deviations fromthe intended vantage point that counter this view. If we are sensitive to projectiveinformation we should be able to detect deviations from it; but subjects in variousexperiments were unable to detect these deviations (Farber & Rosinski, 1978;Goldstein, 1987; Rosinski et al, 1980). The apparent contradiction of having bothsensitivity to projective aspects of an image and robustness to their distortions can bereconciled by any one of three alternative explanations. First, 2-D information fromeither a surrounding frame or binocular disparity can inform us about the depictedvantage point (Goldstein, 1987). Second, many perspective distortions areindiscriminable from one another (Cutting, 1987). Third, there is evidence that we cancompensate for changes in viewing perspective and therefore we may respondindependently of viewpoint even though we initially registered viewer-centeredinformation (Hagen, 1980; Perkins, 1973; Pirenne, 1970). Given these accounts of therobustness of perspective, the previously noted tests show that the final human perceptuses perspective information in a texture gradient to judge slant or distance.Slant - from - texture11Chapter 2:Separating the process from the productIn the review of the literature on 3-D perception in Chapter 1, there was nomention of perceptual processes; responses were simply related to subjectiveimpressions of depth or slant. However, researchers tend to describe this work asthough they tested some cognitive or perceptual process (Braunstein, 1976; Stevens,1981). The danger in extrapolating the results of subjective reports to underlyingprocesses is clearly demonstrated in cases where prior knowledge has been found to beindependent of automatic perceptual judgments (Beck, 1966; 1982; Garner, Hake, &Eriksen, 1956; Gillam, 1970; Hochberg, 1956). In Gillam's study, for example,subjects who reported seeing slant performed no differently on a slant matching taskfrom subjects who reported not seeing slant. Similarly, subjects in Beck's study (1966,1982) showed an incongruity between their judgments of element dissimilarity andtexture segmentation. Although a tilted T is judged to be more similar to an upright Tthan is an L, when repeated to form textures, subjects automatically group Ls withupright Ts, rather than with tilted Ts. While line slope is the more important propertyfor textural segmentation, line arrangement is the more salient property for similarityjudgments. Both Beck's and Gillam's experiments warn of generalizing findings fromverbal reports to performance under stress of time or accuracy. Different factors andperceptual processes may influence rapidly-made versus contemplative decisions.The few experiments that are an exception to the large number of studiesemploying depth or slant ratings include speeded performance tests (Bennett & Warren;1993; Leibowitz & Bourne, 1956; Pringle & Uhlarik, 1982; Smets & Stappers; 1990;Uhlarik, Pringle, Jordan, & Misceo; 1980), and tests that manipulate attention (Epstein& Babler; 1989, 1990; Epstein, Babler, & Bownds, 1992; Epstein & Broota, 1986;Epstein & Lovitts; 1985). These are the only documented psychophysical studies, toSlant - from - texture12date, studying the visual process(es) involved in the perception of depth fromperspective information. In Epstein & Broota (1985), subjects compared the size ofobjective and projective representations of objects to previously encountered figures.Shapes rotated in depth were presented in conditions that differed in the amount ofattention directed to the matching task. In trials where subjects' attention was fullydevoted to the task, they chose the objective alternative as a match for the standard.However, in trials where attention was diverted to an odd-even discrimination task,subjects chose the projective alternative. Epstein and Broota use these findings asevidence for two operations being used in size-distance processing (See also Epstein &Lovitts; 1985). First, there are automatic processes that register projective size andshape, and second, there is an attentive process that integrates those outputs into anobject-centered description. Additional tests of this theoretical account (Epstein &Babler; 1989; 1990; Epstein, Babler, & Bownds, 1992) are presented in Chapters 2 and5.Rival accounts show that the allocation of attention influences the effectiveness ofdepth cues (Coren & Porac, 1983; Gogel, 1967; Gogel, Loomis, Newman, & Sharkey,1985; Gogel & Tietz, 1976; Peterson, 1986; Shulman, 1991a; 1991b; Tsal, 1984).However, these studies use illusion magnitude assessments that do not isolate depthinformation from alternative mechanisms known to mediate illusions (i.e., test andinducing element confusion, element averaging, size-contrast). Therefore, the extent towhich these findings generalize specifically to the perception of depth is unknown.Further ambiguity as to the object specified by the image is introduced by theimpoverished nature of the stimuli in these and all of Epstein's studies (i.e., availabilityof only edge or isolated line information). By contrast, a textured surface tends toprovide information about surface material, slant, curvature, as well as edges. Thespeeded performance tasks noted above come the closest to assessing underlying visualSlant - from - texture13processes involved in the interpretation of textured surfaces. Pringle and Uhlarik(1982) and Bennett and Warren (1993) used a simultaneous matching RT task todetermine if shape (and size) recognition depended on environmental or retinal size.They used a display containing a textured hallway in the background to manipulate thesetwo representations of size. Display exposures which were terminated by subjects'responses ranged between 1100 and 1500 cosec. Both environmental and retinalinformation contributed to matching performance. The primary interest of these studieswas to assess underlying representations as indicated by their environmental/retinalmanipulation and to determine if size-scaling utilized a similar process to the one used inmental rotation (i.e., Larsen & Bundeson, 1978; Rock & Linnett, 1993). Use ofrelatively brief exposure manipulations and indirect assessments of perceived distancevia shape matching ensured that they were measuring performance based on depthperception rather than subjective impressions. However, since exposure durationranged between 1100 and 1500 msec, these effects are still likely to be mediated byattention. (Pringle and Uhlarik found similar effects for RTs which ranged between 900and 4000 msec.) Nevertheless, these studies do show that subjects interpret apparentdepth from texture gradient information within 1500 msec on a task that directly testsperformance speed rather than phenomenal depth perception.Stevens (personal communication) and Smets and Stappers (1990) attempted tofurther isolate early apparent depth processing by limiting exposure duration to texturegradient displays. Stevens has studied the task of quantitatively matching depthbetween random dot stereograms and monocular renderings of surfaces depicted by agrid of contours. In one set of conditions, the random dot stereogram depicted agaussian form in depth (viewed such that the bump protrudes in stereo depth towardsthe viewer). An exposure of 100 msec, was sufficient to allow subjects to match byadjusting the amplitude of the subsequently viewed stereoscopic gaussian with theSlant - from - texture14apparent depth of the monocular gaussian. In the reverse situation, as little as 70 msecof presentation of the monocular depiction gave sufficient 3-D information for subjectsto accurately match the two gaussians.Smets and Stappers (1990) also tested (100 msec) brief exposure to a textureddisplay, but here the subjects' task was to detect a texture element oriented opposite tothe underlying texture gradient. Detection depended on disrupting the texture gradientpattern and was interpreted as evidence for early processing of the high-order relationinformation (i.e., first or second derivatives) present in a texture gradient as opposed tothe reliance of early perception on simple local features (2-D orientation). However,Smets and Stappers did not adequately separate these two forms of information. Theuse of a gradient of items as both the search items and surrounding context resulted inan inadequate control for local differences in 2-D orientation. Consequently, their effectmay have been mediated either by simple orientation discriminations between the targetand background lines or by 3-D slant information.The present study avoids this methodological confound by using search items thatare manipulated separately from the slanted context and that are constant in size across thegradient. A second improvement includes varying the number of elements in the visualsearch display. By relating response times to the size of display we can make strongerinferences about the nature of visual processing, as described in Chapters 3 and 4.Do subjective measures of slant-from-texturepredict speeded performance?The first objective of the present study is to determine if slant-from-texture caninfluence visual search performance. The subjective rating literature assures us thatgeometric projective rules are used at least in a number of subjective rating tasks (SeeChapter 1). Since the majority of these experiments allow unlimited time for subjects torespond, the consequence may be that these tests have measured only the output ofSlant - from - texture15perceptual processing. Such testing may not reflect our more immediate andspontaneous visual processes. Only the few noted experiments restrict stimulusexposure typically to about 100 msec to test depth perception. However, many aresubject to confounding influences (Epstein, Babler, & Bownds, 1992; Epstein &Broota, 1986; Epstein & Lovitts; 1985), or remain vague about underlying processes(Epstein & Babler, 1989; 1990; Smets & Stappers, 1990). Therefore, it remainsunclear how soon projective rules are spontaneously used in visual processing and howwe should characterize such processes.The visual search taskIn the visual search experiments presented here, one critical experimentalmanipulation was search for an item on an apparently slanted surface as compared withsearch for an item on a control surface containing no slant. The slanted surface wasdepicted at an angle of 77° from the viewer's frontal plane, and the control surface wasparallel to the viewer's frontal plane as is shown in Figure 4. Subjects were required tosearch for an item that was unique in size (i.e., short target among long distractors orlong target among short distractors), and located on one of the two surfaces ( 77° or 0°).The prediction that visual processing of these items is influenced by apparent depthinformation from a texture gradient will be supported if search performance on thecontrol surface differs from search on a slanted surface in a manner consistent with thedepicted depth information.The pattern of the effect is predicted most simply by the projective size relation --an item in the distance appears retinally smaller than the same item up close. Therefore,visual search is expected to be easier when the long target is far, and harder when it isnear. The inverse performance is expected for the short target -- search will be easywhen the short target is near and difficult when it is far. Such a contextual influencefrom the background texture gradient will counter the prevailing view that rapid visualSlant - from - texture16processing depends only on simple image features such as length, orientation, and color(See Chapters 3 and 5).Take note that the texture gradient studied here differs from the depthinformation used in most of the previously noted experiments (i.e., Epstein & Babler;1989, 1990; Epstein, Babler, & Bownds, 1992; Epstein & Broota, 1986; Epstein &Lovitts; 1985), as well as conventional visual search studies (Treisman & Gormican,1988). Epstein et al manipulated the presence of depth information in an object; heredepth information is manipulated in a surface against which the objects are arranged.Nevertheless, Epstein, Babler and Bownds (1992) point out the importance of havingsearch items presented in an arrangement that fosters an impression of a surface. Intheir study, subjects were much faster in detecting a rotated target among frontal-paralleldistractors as compared with detecting a frontal-parallel target among rotated distractors.This performance asymmetry reflects the greater signal-to-noise ratio elicited by aninterpretation of a continuous surface of non-rotated distractors being disrupted by arotated target. The relevance of this finding to the present study is that it shows theimportance of background coherence. Perhaps search would be just as rapid in the caseof detecting a frontal-parallel target among rotated distractors if rotated distractor items,as a group, shared a common vanishing point.Another reason to present perspective information in the form of a surface ratherthan as a small object is to show realistic and discernible convergence. Realisticconvergence occurs when the distance from the center of projection to the surface (SeeFigure 2) allows between 30° to 60° of the scene to be shown (Cutting, 1986; 1987;Sedgwick, 1986; 1987). Often a surface (or a region of the surface) will fit this range,whereas a small item like those used in visual search experiments, typically takes up "only a few degrees. If the width of the scene is too narrow (< 30°), the depth ofperspective becomes flattened, and if it is too wide (> 60°), the perspective appearsSlant - from - texture17exaggerated (Walters & Bromham; 1970). Placing the image plane between the centerof projection (i.e., reducing the projected image to < 30°) is sufficient as long as therelative convergence remains the same. Pilot testing indicated that at least 5° of visualangle is required for convergence of edges on an object to be detected. This constraintwas satisfied in this study by using a representation of a 45° textured surface reduced33% to match the size of the computer screen (14° by 19° of visual angle).To summarize, the rationale for placing perspective information in a surfacerather than in the search items includes: (1) Using the texture gradient as the backgroundhelps avoid the potential confounds that occurred in Smets and Stappers' study fromusing a gradient of distractors; (2) A textured surface is likely to foster more backgroundcoherence; (3) The 30° to 60° "realistic convergence" range constraint is satisfied; (4)Subjects are able to resolve the converging line information.As noted earlier, evidence for depth processing in visual search will be based oninfluences from size and location. Obtaining any of the predicted effects (i.e., moredifficult search when the short target is far or the long target is near) will show that visualsearch is sensitive to 3-D information and the mediating mechanism accordingly scalesfor projective size.Experiment 1:Slant-from-texture influences on visual searchThis first experiment used the size discrimination task described above wheresearch items were presented on a textured pattern spanning the entire display screen. Thetwo-by-two design consisted of a slant versus control condition, and a long target - shortdistractor condition versus a short target - long distractor condition. Search items weredepictions of realistic cylinders that appeared to rest on the underlying slanted surface.Realistic object-like items were selected because simple line items resemblingthose used by Treisman and Gormican (1988) had unreliable effects across locations inSlant - from - texture18pilot testing. The textured surface may have only elicited undifferentiated noise in slantand control conditions. The simple line search items may have also allowed subjects toignore the background information since it had the appearance of being independent ofthe search task. In order to increase the likelihood that search strategies would beinfluenced by the surrounding context in a manner consistent with the depicted depthinformation, more object-like items were presented on the display surface.MethodSubjects. Eleven members of the University community participated in two 60-minute sessions to complete eight conditions of the visual search experiment. Eachcondition consisted of 3 sets of 60 trials. Nine subjects had no experience with visualsearch tasks. The remaining two were experienced with the task but did not havespecific experience with the search items or the background texture used here. Subjectage ranged from 17 to 33 years; eight were female and three male. All subjects hadnormal or corrected to normal vision.Stimuli and Procedure.  Display presentation and data collection were controlledby a Macintosh computer using the MacLab program (Costin, 1988). The subjects' taskwas to search for a target item among 2, 6, or 10 items. All of the search items werecylinder-like in appearance and were randomly distributed on a 19°X 14° display screen.Targets differed from distractors only in size and were present on a random one-half ofthe trials.Targets had an overall image extent of 1.35 X 1.0 cm, subtending 1.5 x 1.1°.The cylinder's width and wall height were 1.0 cm in the image. Distractors in the firsttwo conditions had an overall extent of 1.7 X 1.2 cm, subtending 1.8 x 1.2°. Thedistractor cylinders' width and wall height were 1.1 cm. Distractors in the second twoconditions had an overall extent of 1.2 X .9 cm, subtending 1.4 x 1.03°, and a cylinderwall height and width of .9 cm. In each of the blocks, targets were presented four timesSlant - from - texture19in each of the three locations: upper, middle, and lower visual fields. Search items wereinitially selected from a set of cylinders that were placed along the line of sight of a 77°slanted surface that contained a systematic texture similar to the one shown in Figure 4.Distractors in the first slant and control conditions were larger than the target by twotexture element steps toward the viewer, while distractors in the second two conditionswere smaller by an equivalent two steps away from the viewer (and target) .^Insert Figure 4 ^Textured surfaces used in the visual search displays were generated by theDynaperspective Design and Modeling program (Tatsumi & Okamura; 1988). Thedisplay screen located 50 cm from the viewer, contained regularly textured surfaces thatappeared to be 80 cm in front of the viewer (apparently 30 cm behind the computerscreen and spanning 45° of visual angle). The control grid was a regular two-dimensional grid containing .9 x .9 cm grid elements on the computer display and hadno slant relative to the viewer's frontal plane. The texture gradient used in theExperimental condition was a depiction of the control grid slanted at a 77° angle as isshown in Figure 4. The gradient was oriented vertically with the densely spaced textureelements depicting far located at the top of the screen, and the more diffusely spacedelements depicting near at the bottom. The gradient consisted of horizontal componentswhich ranged from 1.1 to 2.5 cm from the top to the bottom of the screen, with a meanwidth of 1.7 cm. The gradient also consisted of vertical components which ranged 0.25to 1.5 cm from the screen's top to its bottom, with a mean height of .7 cm. All textureoutlines were black (12.2 cd/m2) and all backgrounds were white (158.9 cd/m 2).Figure 4 shows a sample display where the task is to search for a short cylinder againsta background of longer cylinders.Each trial began with a fixation symbol lit for 500 ms, followed by the displaywhich remained visible until the subject responded. Target presence and absence were20Slant - from - textureFigure 4. The texture gradient used in visual search conditions was a depiction of avertical and horizontal grid slanted at a 77° angle with densely spaced textureelements depicting far, and more diffusely spaced elements depicting near.Cylinder items resting on the textured surface were used as the target and distractoritems in the search task.Slant - from - texture21reported by pressing one of two response keys. Accuracy feedback was presented inthe form of a beep on incorrect trials. Subjects were instructed to maintain fixationthroughout the trial sequence, to respond as rapidly as possible, and to keep errors at aminimum.ResultsMean correct response time (RT) and percentage of errors for target present trialsare shown in Figure 5; standard errors of the means are shown in Table 1. Target absenttrials were not examined in detail since they could not be differentiated by location. Thesensitivity of present trials is described below in a comparison of performance across thelocations of the slant and control conditions. Reported statistics are based on the overallANOVAs which include the two level factor of target presence and the three level factorof target location.^Insert Figure 5 & Table 1^Overall, search was more difficult when the short target was in the top-farlocation relative to the middle and bottom-near locations of the slanted display (RT anderrors: Fisher's LSD tests, II< .01). Mean RT was 386 msec slower and errors were27% greater when the short target was far (mean RT = 1230 msec, mean error = 36%)relative to when it was near (mean RT = 844 msec, mean error = 9%).As expected, the inverse trend occurred when subjects searched for a long targetagainst short distractors. Search was more difficult when the long target was in thebottom-near location relative to the middle and top-far locations (RT and errors: Fisher'sLSD  tests, 12 < .001). Mean RT was 387 msec slower and there were 33% more errorswhen the long target was near (mean RT = 1220 msec, mean error = 43%), than when itwas far (mean RT = 833 msec, mean error = 9%).Surprisingly, slightly worse performance occurred when the short target was atthe top of the control condition (RT: Fisher's LSD tests, 12 < .05; errors: Fisher's LSD■-•. 140°`C.)cUrl 1200.•—•• 1000Ea4E-I 800- NNN,  6102Top Mid Bottom Top Mid BottomNear40 -Slanted Background^Control BackgroundTarget TargetShort^Long^Short^LongTarget LocationFigure 5. Mean correct reaction time and percentage of errors for target present trials of Experiment 1. Two search items(short and long) were examined against two backgrounds (slant and control) and three display sizes (two, six and ten).Critical comparisons are between locations in the slant background (far, middle and near), and the control condition (top,middle and bottom). SEMs are reported in Table 1.Slant - from - textureTable 1^ 23Standard Error of the Mean (SEM) in Experiment,'RT (msec) ^Errors(%)Display Apparent Slant^Control^Slant^ControlSili^LotionSat SatShoo TargetSat Sal2 Far 86 70 7.3 2.8Mid 56 54 5.4 5.2Near 54 48 4.9 9.36 Far 101 121 6.1 2.0Mid 71 46 4.1 4.5Near 43 33 5.5 7.110 Far 119 114 7.6 4.8Mid 97 91 0.0 0.1Near 57 50 5.7 5.2Long Target2 Far 33 33 6.5 2.8Mid 27 41 4.3 2.8Near 77 55 2.5 5.16 Far 64 25 5.8 3.9Mid 56 35 3.3 2.7Near 101 67 2.6 5.910 Far 66 35 8.0 6.0Mid 80 49 0.3 0.1Near 126  83 3.3 5.9Slant - from - texture24tests 12 < .001) and the long target was at the bottom of the control condition (RT:Fisher's LSD tests, 12 < .001; errors: Fisher's LSD  tests g < .001). RT was 145 msecslower with 15% more errors when the short target was at the top of the display (meanRT = 1011 msec; mean error =18%) relative to the bottom (mean RT = 866 msec; meanerror = 4%), and RT was 122 msec slower with 14 % fewer errors when the long targetwas on the top (mean RT = 840 msec, mean % error = 8%) relative to the bottom of thedisplay (mean RT = 961 msec; mean error = 22%).Although these location effects in the control condition were half the magnitudeof those in the slant condition they were significant on the noted pairwise comparisons.This inverse relationship between short and long target performance in the slant andcontrol conditions was also confirmed by the significant interaction between targetlocation and target size for RT, F(2,20) = 40.0, 12 < .001; and errors, F(2,20) = 21.1, 12< .001.However, the stronger interaction between target size and target location in theslant condition relative to the control condition was supported by a significant 3-wayinteraction between background, target location, and target size (RT: F(2,20) = 14.1, 12< .01; errors: F(2,20) = 19.1, 12 < .001), and a significant 4-way interaction betweenbackground, target location, target size and target presence (RT): E(2,20) = 17.6,12 <.001; errors: E(2,20) = 7.2,12 < .01). The latter interaction simply indicates thatapparent location effects were found only in target present trials.Sensitivity to differences in target location for target present trials is furtherreflected in target presence interaction with target location (RT: E(2,20) = 8.6,2 < .01;errors: E(2,20) = 11.4, IL< .001), target size (RT: E(2,20) = 8.2, 12 < .05), and size andlocation (3-way ANOVA -- RT: F(2,20) = 37.0, 12 < .001; errors: E(2,20) = 23.6, 12 <.001). Target present trials also account for the main effect for target location (RT:F(2,20) = 30.4, 12 < .001; and errors: E(2,20) = 22.3, 12 < .001). AdditionalSlant - from - texture25interactions comparing target presence and target absence are described in Appendix A.Display size effects. There was a substantial increase in the range of RTs across display sizes intarget present trials, when the short target was far and the long target was near (RT:display size, target size and target presence -- F(2,20) = 6.4, g < .01; and display size,target size and target location, E(4,40) = 6.942 < .001). Two additional interactionsshow that this trend was stronger in slant conditions (display size, background, X targetpresence, F(2,20) = 5.9, 12. < .05; and display size, background, target presence, targetsize X target location, E(4,40) = 7.7, 12 < .001).Central location effects. An additional trend that is readily apparent in Figure 5 is the better performancethat occurred when the target was located in the central region (All long target trials RTs:Fisher's LSD tests,12 < .05). This facilitation effect is likely the result of surroundingdistractors acting to ease the size-discrimination task. This interpretation is supported byitem density influences on general visual search performance (Banks, Larson, &Prinzmetal, 1979; Boynton, Hayhoe, & MacLeod, 1977), and Gathercole andBroadbent's (1987) finding that the effects of distractors depend on their distance fromthe target. Several additional studies show that search accuracy can improve with moredistractors (Green, 1992; Sagi, 1990, Sagi & Julesz, 1985, 1987). Sagi and Juleszinterpret the latter effect as support for preattentive search making local comparisons in afeature gradient. More simply we can regard the effect as a consequence of facilitationfrom proximity -- as the items get closer together, comparisons become easier.Location and testing order.Surprisingly, location influences similar to those found in the slant conditionoccurred in the control conditions. Performance was easier when the short target was atthe bottom of the display and the long target was at the top. One potential cause forSlant - from - texture26these top-to-bottom effects may involve depth information from the slant conditionscarrying over into the control conditions. Even though slant and control trials werepresented in separate blocks, and the order of presentation was counterbalanced acrosssubjects, it is possible that a strong initial order effect could influence the data. Depthinformation carry over could only occur in one direction -- from slant to control, sincedepth information is present only in slant conditions. To test this hypothesis subjectswere separated across first condition received: long or short target, and slant or control.No relevant interactions, nor main effects involving order was significant. The onlysignificant interactions included presentation order X location for RT, F(6,14) = 3.4, 2 <.05, reflecting better performance in the top locations for those subjects who received thecontrol conditions first. Order of presentation therefore cannot account for the top-bottom trends that occurred in the control condition.DiscussionPerformance in the slant condition was consistent with the texture gradient elicitingan apparent depth effect -- search was more difficult when the short target was far and thelong target was near. However, smaller but similar effects occurred in the control condition-- search was more difficult when the short target was at the top of the display and the longtarget was at the bottom. Faster search for both conditions in the central region is easilyexplained by surrounding distractors providing comparison stimuli to ease discrimination.What accounts for the unexpected performance in the control condition? Since testing orderwas ruled out, we are left with some top-to-bottom influence, perhaps differentialsensitivity to information in the top versus the bottom of our visual field, depending uponthe size of target.Another possible account is that these locations are interpreted by subjects asproviding height-in-the-plane information, where items in the top region appear to be fartheraway than items in the bottom region. This interpretation is consistent with Sedgwick'sSlant - from - texture27(1986) demonstration that a picture reveals an object's size relative to the height of the planeeven without explicit horizon information being present. Moreover, Bruno and Cutting(1988) have shown such height-in-the-plane effects on performance in a magnitudeestimation and depth rating task. In a further attempt to isolate apparent distance effectsarising solely from the texture gradient, the visual search task in Experiment 2 separatedtop-to-bottom information from apparent-distance information in the texture gradient.Experiment 2:Separating top-to-bottom from apparent-distance effectsIn Experiment 1, performance was the poorest when the short target was locatedat the top of the display, and the long target was located in the bottom. This was true forboth slant and no slant conditions. This size-location influence on visual search in thecontrol condition may have been caused by either of two factors: (1) differentdiscrimination capabilities across the visual field, or (2) inferred depth from height-in-the-plane. Since performance strongly resembled predicted projective trends in thecontrol condition, a likely explanation is that subjects infer height-in-the-plane depthinformation from top-to-bottom cues.One way to separate top-to-bottom from apparent distance influences is to changethe orientation of the background surface texture. By doing so, display directions (i.e.,top, bottom, left, right) and apparent depth (i.e., near, far) are no longer confounded. Inthis experiment, visual search is performed in displays where the textured surfaceappears to slant sideways. Now instead of the texture gradient appearing as a texturedfloor (as in Experiment 1), the texture gradient appears as a textured wall that is slantedto the left or to the right. Because top-to-bottom information is no longer confoundedwith near-to-far information, we can isolate apparent distance effects arising solely fromthe texture gradient.Slant - from - texture28MethodSuWecta. Eleven University students participated in two one - hour, sessions tocomplete 3 sets of 60 trials for each of eight conditions. Eight subjects wereinexperienced in visual search tasks. Subject age ranged from 17 to 27 years; six werefemale and five were male. All subjects had normal or corrected to normal vision.Stimuli and Procedure. All stimuli and procedures were the same as those usedin Experiment 1. The only change involved rotating the display 90° to the left for halfof the trials, and 90° to the right for the other half of the trials. Left-right orientation wascounterbalanced across subjects to prevent lateral search biases that may arise in visualsearch performance.Displays were again subdivided into three regions to allow for an analysis of theeffects of target location on visual search performance. In the slant condition, the threeregions were designated as far, middle, and near. In the control condition, theseregions corresponded to left, middle, and right when the display was rotated to the left,and right, middle, and left when the display was rotated to the right.ResultsMean correct RT and percentage of errors for target present trials are shown inFigure 6; standard errors of the means are shown in Table 2. Since only target presenttrials were sensitive to differences in target location, the results focus on these trialswith a direct comparison of performance across the extreme locations of the slant andcontrol conditions. Performance here, as in Experiment 1, was affected by .targetlocation and size. However, in this experiment, size-location effects were different forthe slant and control conditions.^Insert Figure 6 & Table 2 ^In the slant condition, search was more difficult when the short target was in thefax location relative to the middle (RT and errors: Fisher's LSD tests, R < .01) and theSlant - from - texture29near locations (RT and errors: Fisher's LSD tests, 12 < .01). RTs were 262 msec slowerand errors 20% greater when the short target was far (mean RT = 1165 msec; meanerror = 26%) than when it was near (mean RT = 903 msec; mean error = 6% ). Thiscontrasts with the control condition where RT and errors were not significantly differenton either side (far control: mean RT = 897 msec, and mean error = 8%; near control:mean RT = 895 msec, and mean error = 7%).The expected inverse relation between performance and location emerged whensubjects searched for the ^target against short distractors on the slanted background.Search was more difficult when the long target was in the near location relative to themiddle (RT and errors: Fisher's LSD tests, 12 < .01) and far locations (RT and errors:Fisher's LSD tests, 12 < .01). Here RT was 379 msec slower and errors were 30%greater when the long target was near (mean RT = 1253 msec; mean error = 35%) thanwhen it was far (mean RT = 874 msec; mean error = 6%). This contrasts withperformance in the control condition where RT and errors were not significantlydifferent on either side (near control: mean RT = 1108 msec, and mean error = 16%; farcontrol: mean RT = 1014 msec, mean error = 11%).The inverse trend between the short and long target in the slant condition wasconfirmed by a significant 2-way interaction between target location and target size forRT, F(2,36) = 30.6, g < .001 and errors, F(2,34) = 46.3, 12 < .001, as well as thesignificant interaction between background and target size (RT: F(1,18) = 11.02 < .01).Separate main effects occurred for target location (RT :E(2,36) = 82.9,12 < .001, anderrors: F(2,34) = 35.9, g < .001), target size (errors : E(1,17) = 7.4, 12 < .05),background (RT: E(1,18) = 5.9, 12 < .05; and errors: F(1,17) = 13.5, p, < .001); andtarget presence (RT: E(1,18) = 49.5,12 < .001; and errors, F(1,17) = 26.7, 12 < .001).Additional interactions comparing target presence and target absence trials are noted inAppendix A along with an analysis of location using target absent trials as a control.— 1400Q.)rn 1200E1000HC4 8006101062Slanted Background^Control BackgroundTarget TargetShort^Long^Short^Longar Mid Near^ar Mid Near^Left Mid Right Left Mid RightTarget LocationFigure 6. Mean correct reaction time and percentage of errors for target present trials of Experiment 2. Two search items(short and long) were examined against two backgrounds (slant and control), and three display sizes (two, six and ten).Critical comparisons are between locations in the slant background (far, middle and near), and in the control condition(top, middle and bottom ). SEMs are reported in Table 2.Slant - from - texture31Table 2Standard Error of the Mean (SEM) in Experiment ZRT (msec)^Errors (%)Display Apparent Slant^Control^Slant^ControlSize^LocationSEM SEM^SEM SEMShort Target2 Far 63 38 5.9 2.1Mid 48 20 2.2 2.2Near 31 41 1.2 1.76 Far 70 35 5.2 1.2Mid 56 26 2.7 3.2Near 31 26 2.2 2.210 Far 71 51 4.9 4.0Mid 57 59 0.3 0.4Near 45 44 3.0 3.8Lon_gTarget2 Far 33 24 1.8 1.7Mid 34 28 2.8 3.2Near 59 40 5.8 2.96 Far 29 41 2.0 1.7Mid 35 28 2.8 2.2Near 63 53 4.5 0.010 Far 42 41 3.6 1.8Mid 44 35 0.0 3.9Near 61 56 5.6 4.9Slant - from - texture32Discrepancies in degrees of freedom for RT and Error data are due to software errors inidentifying subjects' data.Location effects in the control condition. Performance was easiest when the target was in the middle region. This trendwas supported by a significant main location effect on simple effects test of the controlcondition for the long (RT: F(2,42) = 20.1,12 < .001; and errors: F(2, 36) = 9.812 <.001), and short target trials (RT: E(2,42) = 17.4, 12 < .001). Fisher LSD testsconfirmed that performance improved when the long target was located in the centralregion (All RTs and errors, p < .05). For the short target, performance did notsignificantly differ across locations in the control condition (All Fisher's LSD tests, 12 >.05). Only when separated across display size did pairwise comparisons reachsignificance (i.e., ten item condition; see display size effects).Unlike the top-to-bottom effects in Experiment 1, performance did not differbetween the left and right locations of the control condition (All Fisher's LSD tests, 12 >.05). An analysis of left versus right orientation as a between factor revealed nodifference between these orientations for RT ((1,17) = .26), and errors (E(1,16) =.45), indicating that rotating the display was successful in controlling influences fromtop-to-bottom search biases.Display size effects.RTs showed the expected increase in display size -across all conditions, F(2,36)= 114.4, p_< .001. The widest range of RTs across display sizes occurred in the farlocation of the short target trials, and surprisingly in the extreme locations of the longtarget control condition. These trends were supported by the three-way RT interactionbetween display size, background and target size, (E(2,36) = 6.6, 12 < .01), the fiveway interaction between target presence, display size, background, target size, andlocation for RT, W(4,72) = 5.0, P < .001), and the additional interactions involvingSlant - from - texture33display size noted in Appendix A. RT slope analysis is described further in Figure 7and Chapter 3.Testing order.It is clear from the performance trends in the control conditions that testing orderwas not responsible for location effects. Nevertheless, the absence of an order effectwas confirmed by a between-subjects ANOVA that separated subjects into four groupsdiffering on the first condition received: long or short target, and the presence or absenceof slant. Presentation order was not significant for both RT, E(3,6) = .13; and errors,E(3,6) = .16. The only significant interaction involved presentation order x slant for RT(E(3,6) = 5.3, 12 < .05) showing a trend in the control condition inconsistent with thosein the slant condition.DiscussionExperiment 2 established that the speeded performance task is reliable inassessing our ability to access depth information from a texture gradient. Evidence fordepth processing was revealed in the slant condition -- search performance was poorestwhen the short target was far, and the long target was near (mean RT = 1215; meanerrors = 28%), and search performance was best when the long target was far and theshort target was near (mean RT = 889 msec; mean errors = 5%). These effectsdisappeared when information about distance was removed in the control condition(mean RT = 979 msec; mean errors 8%). The only remaining effects included theexpected central region improvement from the presence of surrounding distractors.Evidence for depth processing in the speeded visual search task suggests thatneither subjective judgments of depth, nor acts of volition drive the effect. Presumablycontemplative judgments are at a minimum in a task that avails the subject only aboutone second of viewing (See RTs in figure 6). Nonetheless, apparent depth andassumptions of projective size are evident in such rapid perceptual judgments. TheSlant - from - texture34remaining experiments use this visual search method to further clarify how early visionis sensitive to apparent depth in the texture gradient, and which texture dimensions arethe most informative in rapid perception.Slant - from - texture35Chapter 3: How early are the slant - from -texture influences?A two stage model of vision Contemporary psychophysical accounts of visual processing argue that visionconsists of two systems that may be defined in terms of (1) overall response time, or (2)visual search strategies. These two operational definitions allow us to make a furthertheoretical distinction between the processing complexity of early and late vision.The first and simplest definition of the visual subsystems is based on absoluteexposure time, where early vision occurs within 100 msec of the display onset and latevision requires at least 100 msec (Treisman, Cavanagh, Fischer, Ramachandran, andvon der Heydt, 1990). This rough delineation between early and late vision is typicallydetermined by restricted exposure experiments where subjects accurately detect an itemor group of items within the 100 msec of allotted time. The two systems, althoughsometimes described as dichotomous, are best regarded as continuous, given that testshave shown gradually changing accuracy with exposure (Callaghan, 1989; Duncan &Humphreys, 1989; Northdurft, 1985; Treisman & Souther, 1985).The second, definition is based on visual search and focuses on the ability toperform simultaneous processing of items. Here, parallel processing is spatial, ratherthan temporal. According to Treisman's Feature Integration Theory (1986) the firstpreattentive system detects features in parallel across the visual field, and the secondattentive system sequentially processes the relations between these features. In otherwords, the preattentive system initially encodes the features, and the attentive systemcombines the features to form object representations (Beck, 1982; Julesz, 1984;Treisman, 1986). Researchers typically operationalize preattentive and attentive systemsin terms of search rate as a function of the number of items in the display (i.e., RTslope). Slopes falling below 10 ms/item are usually classified as a parallel search andthose above are considered serial. Although recent evidence suggests that theSlant - from - texture36preattentive and attentive system lie on a continuum of processing strategies (Duncan &Humphreys, 1989; Treisman & Souther, 1985), for the purpose of exposition,reference will be made to two systems with the implication that these are gradedcategories of visual processing.An important theoretical distinction between early and late vision is derived fromthe previous operational definitions. This distinction focuses on the complexity ofinformation that each system can code. Data show that the earlier preattentive systemcodes simple geometric features, such as color, orientation, length, and curvature, andthe later attentive system operates on the conjunction of features (Beck, 1982; Julesz,1984; 1CrOse, 1987; Treisman & Sato, 1990). However, recent evidence suggests thatearly vision also may be capable of registering somewhat more complex information(Treisman & Gormican, 1988; Duncan & Humphreys, 1989; Enns & Rensink, 1990,1991; Humphreys, Quinlan, & Riddoch, 1989; Ramachandran, 1988). These findingshave prompted reevaluation of the function of each stage, and our conception ofprimitive features. One proposal is to expand early vision's sensitivity to includevarious combinations of features that correspond to properties of the scene (Enns,1992). For example, rapid search for conjunctions of features such as binoculardisparity and motion (Nakayama & Silverman, 1986), or motion and shape (McLeod,Driver, & Crisp, 1988), may reflect early sensitivity to apparent depth. Similarly rapidsearch for spatial relations among lines and shaded polygons suggests early sensitivityto 3-D orientation and the direction of lighting (Enns & Rensink, 1990a; 1990b; 1991).The scene-based properties of the texture gradient can be described in a variety of waysincluding the rules of projective geometry noted earlier that relate surface slant to thetexture variations in the image. An analysis of this scene-based information, itscorresponding image information, and their relation to early vision is presented in thefinal discussion.Slant - from - texture37Encoding slant-from-texture: Early or late? As noted in Chapter 3, the few published experiments that test early processingof projective information have restricted stimulus exposure to 150 msec or less (Epstein& Babler, 1990; Smets & Stappers, 1990), or have tested preattention by divertingattention to a secondary task (Epstein & Broota, 1986; Epstein & Babler, 1989). Thesestudies, along with a recent visual search experiment comparing search for a projectiveversus objective shape (Epstein, Babler, & Bounds, 1992), show that early vision issensitive to projective information. Certain qualifications are required in interpretingthese findings. First, in all of these studies, projective information was confoundedwith additional cues to depth. In Epstein et al's studies, projective information wasconfounded with binocular disparity and shading information, and in Smets andStappers' (1990) study texture gradient information was confounded with simpleorientation information. Second, only Smets and Stappers and Stevens actually usedtexture information. Epstein et al's experiments presented projective information onlythrough outlining contours. Perceptual sensitivity to projective information may differfor surrounding contour and surface-texture information. Given the research findings todate, it remains unclear how early slant-from-texture is registered in visual processing.One way to test early vision's sensitivity to slant-from-texture is to utilize aconventional test that distinguishes early and late vision. In visual search tasks, earlyand late vision are distinguished by how RTs are affected by the number of items in thedisplay. The system's sensitivity to information is determined by the further interactionwith the kind of search items. Early sensitivity is shown if visual search is eased to apoint where a slow-serial search is speeded up to a fast-parallel strategy when either theshort target is near or the long target is far.Slant - from - texture38RT Slope performance Figure 7 summarizes RT slope performance from Experiment 2 across near andfar locations of target present trials. The mean RT slope across locations is 30 ms/itemindicating that performance in all conditions requires the use of attention. Figure 7 alsoshows a trend towards faster search when the short item was near (Fisher LSD's, 12 <.05). Although, this trend is supported by the 4-way interaction between background,target size, target location, and target presence (E(2,36) = 6.7, lz < .05), there is nosimilar difference across locations for the long target.^Insert Figure 7^Additional RT slope effects presented below clarify the above noted trend. RTslopes were slightly smaller in slant relative to the control conditions ((1,18) = 7.7, 12< .05). This difference is a consequence of target location interacting with target size inslant conditions (E(2, 36) = 4.6,12 < .05). The only effect from location in the controlcondition was an improvement when the target was in the middle region. This trendwas supported by a significant main location effect ((2,36) = 9.5, 12 < .001), as wellas simple effects tests that showed the bulk of the effect on long target - control trials((2,57) = 9.9, 12 < .001). Search for the short target was not significantly differentacross locations in the control condition (All Fisher's LSD tests).Projective size or apparent proximity?RT slopes do not appear to be sensitive to slant-from-texture in long target trials.Yet, RT slopes for short-target trials do appear sensitive to apparent depth information.Perhaps in addition to a projective size effect arising from the textured gradient, theremay be an influence from the apparent proximity of the search items. The target thatappears closer, regardless of its size, may simply be easier to detect than a furthertarget. Fast target present RT slopes in the near location (23 msec/item) relative to far(39 msec/item) suggest this may be so.Far^Near^Left^RightSlant - from - texture39Slant^Target Control604020Ea) as0-4 .4;24(7) 8E 604020ShortLongFar^Near^Left^RightTarget LocationFigure 7. Mean correct reaction time slopes (ms/item) in Experiment 2. Twosearch items (short and long) were examined against two backgrounds (slant andcontrol) and two locations (far and near in the slant condition, and left and right inthe control condition).Slant - from - texture40Such a proximity effect was reported by Nakayama (1988) using binoculardisparity and occlusion in a timed recognition task. Although his effect occurred forraw response time, it is possible that RT slopes may be influenced in a similar way.An influence from proximity could explain the closer match between projective sizepredictions and findings when the target is short. Searching for the short target in thenear location may be easy because it is closer od unexpectedly small in size. Butwhen the long target is near, performance should be more difficult according to laws ofprojective geometry, yet easier according to proximity theory. These opposing effectscould cancel out and account for why RT slopes do not differ when searching for along target in near and far locations.To test for an influence from apparent proximity, subjects could search for atarget that is neutral to size information. One example might be to search for a gray itemagainst black items in a texture gradient display. If both target and distractor items varyrandomly in size, projective size influences would be controlled since item size is nowirrelevant to the task.Note that any influence from apparent proximity does not invalidate the findingsof this thesis. Evidence of either apparent proximity or projective influences on searchperformance confirms that subjects perceive apparent depth from the texture gradient.Therefore, it is not critical that the depth effect be mediated by apparent proximity orassumptions of projective size. The only potential problem is that if both are operating,we can expect to see the influence only on short target trials. Since promising trendswere revealed in absolute RT performance for both target size conditions, I willpostpone a test for apparent proximity for follow-up research and pursue the test forassumptions of projective geometry using an alternative strategy.Slant - from - texture41SummaryApparent depth influences on visual search were seen more reliably in absoluteRTs than in RT slopes. Apparent depth acted only to slow performance in searchconditions predicted to be more difficult (i.e., short target in the far location and longtarget in the near location) but did not speed up performance in the conditions predictedto be easier (i.e., short target in the near location and long target in the far location).Since performance remained within the attentive range for all locations (i.e., RT slopes> 10 msec/item) we know only that attention-based search (later vision) was influencedby apparent depth. These results suggest that the visual search test used in Experiment2 may be inadequate for assessing the sensitivity of early vision to slant-from-texture.Modification of the test to permit such an assessment is described in Experiment 3.Experiment 3:Slant-from-texture influences in early visionAlthough subjects used attention to search in all locations in the first twoexperiments, it does not preclude the possibility that preattentive processing can alsoextract depth information from texture gradients. The goal of Experiment 3 is todetermine whether early vision is also influenced by slant-from-texture. Since searchperformance in the previous experiments was only impaired by the presence of slant, analternative way to assess whether location effects persist in preattentive vision is to startout with a very easy task where search is performed in parallel. Such performance canbe obtained by taking advantage of the findings that visual search performance can beadjusted along the preattentive-attentive dimension simply by changing thediscriminability of the search items (Duncan & Humphreys, 1989; Treisman &Gormican, 1988). In the present study, sizes of the search items were adjusted for eachsubject. The aim was to have subjects performing parallel search on control trials. Anysubsequent decrement in performance from searching for a short target in the farSlant - from - texture42location, or the long target in the near location would show that preattentive visioncannot ignore the apparent distance information implicit in the texture gradient.MethodSubjects. Forty undergraduate students participated in two one-hour sessions,each consisting of six sets of 54 trials. Subject age ranged from 17 to 27 years; twenty-four subjects were female and sixteen were male. All subjects had no previousexperience with visual search tasks, and had normal or corrected to normal vision.Stimuli and Procedure. Visual search displays contained cylinder items on atextured background similar to the ones used in Experiment 2. Displays were modifiedin several ways to eliminate potentially confounding variables noted below. First, tocontrol for luminance differences caused by the gradient of texture, the density of darkpixels making up the texture were systematically varied. When this procedure wascompleted, every 2.25 X 2.25 region contained 20% black pixels as is shown in Figure8. Second, displays were presented in a square region, subtending 14° X 14°, tocontrol for influences from different aspect ratios.^Insert Figure 8 ^Each subjects' threshold for detecting the presence of a unique cylinderpreattentively was assessed using a staircase method. The long target ranged in sizefrom 1.40° x 1.10° to 1.72° x 1.42° across conditions in .04° (.35mm) increments;short distractors were held constant at 1.29° x .92° as is shown in Figure 9. Betweenfour and six threshold tests were administered depending upon performance onpreceding trials. Each threshold test contained 4 blocks of 20 trials. Displaypresentation and data collection were controlled by the VSearch program (Enns, Ochs,& Rensink, 1990).^Insert Figure 9Slant - from - texture43Figure 8. Illustration of combined texture gradient background used in Experiment 3.Displays equate for luminance and overall aspect ratio.Slant - from - texture44Short Item^Long Items 1.2901.42Figure 9. Full set of search items used in staircase procedure to assess subject thresholdfor early vision. The long target ranged in size from 1.40° x 1.10° to 1.72° x 1.42° acrossconditions in .04° (.35mm) increments; short distractors were held constant at 1.29° x .92°.Slant - from - texture45Changes to the stimuli and procedure for the primary visual search task were asfollows: (1) The size of the long items, determined by the staircase tests, fell within therange of 1.49° x 1.17° to 1.65° x 1.33°. The size of the short items was held constantat 1.25° x .92°. (2) The horizontal orientation of the background texture wascounterbalanced across subjects. Half of the subjects viewed slanted surfaces orientedso that the near region appeared on the left of the computer display, and the other halfof the subjects viewed slanted surfaces with near on the right. (3) Search itemorientation was also counterbalanced across subjects. Half of the subjects searched foritems oriented horizontally on the screen. Items were oriented either left-to-right orright-to-left depending upon the direction of the surface in the slant conditions (i.e.,when the surface was oriented with near on the left, and far on the right, cylinders wereoriented with their bottom edge to the left, and their top edge to the right). Thesecylinders appeared perpendicular to the textured surface and to recede into the distanceon top of the slanted surface. The remaining subjects searched for items orientedupright in the image. In the slant condition, these items appeared to rest on an imageplane separate from the underlying slanted surface. (4) Display presentation and datacollection for the search task were controlled by a Macintosh computer using theVScope Program (Enns & Rensink, 1992). (5) Feedback was presented at centralfixation following subjects' response after each trial. Correct responses were indicatedwith a "+" and incorrect responses were indicated with a "-". (6) Performanceasymmetries typically found in tests of visual search for item size (Treisman &Gormican, 1988) were also tested by exchanging the long and short target anddistractor items.Slant - from - texture46ResultsThreshold for preattentive vision.All subjects met the criterion for preattentive search within six sets of 60 trialsusing the staircase procedure. The target and distractor size difference necessary forsubjects to achieve preattentive performance, ranged from .25° to .40° of visual angle.Final RT slope values consistently fell within 4 and 10 msec/item on target presenttrials. Target absent trials were on average twice this magnitude.Visual search on textured surfaces.Mean correct search times across target present locations are reported in Table 3,along with the percentage of errors. The statistical analyses are based only on targetpresent trials since absent trials are not differentiated by target location. Analysescomparing target presence and target absence trials are presented in Appendix A.Apparent depth effects are reported after a brief description of central region effects.Similar to Experiment 2, performance was always relatively better when the target waslocated in the middle location. This advantage in searching for the target in the centralregion is supported by significant comparisons of performance in middle and extremelocations (all s, p < .05). Pairwise comparisons were based on Bonferroni I's thatutilized MSe from the overall ANOVA. Further support for central region facilitationwas found in the significant main effect for location that compared performance acrossthe three locations (RT: (F(2,70) = 116.8, 12 < .001; errors: F(2,80) = 30.2, 12 < .001).^Insert Table 3 ^To assess for influences from apparent depth, data from the near and far locationswere compared directly as shown in Figure 10. In the slant condition, search was onaverage 67 msec slower when the short target was far (left or right), and 27 msec slowerwhen the long target was near (all t's, p < .05). Only when the short target was in theslanted condition was there a significant difference in percent errors across near and farSlant - from - texture47Table 3Mean correct Reaction Time and Percentage of Errors in Experiment 3Combined Gradient RT (msec) Errors (%)SlantDisplay Apparent^Slant ^Control ControlSize^LocationM (SEM) M (SEM) M (SEM) M CSEM)Short Target2 Far 754 (19.8) 627 (13.3) 17.3 (2.2) 6.2 (1.2)Mid 614 (12.7) 604 (12.5) 3.0 (0.9) 3.0 (0.9)Near 658 (12.5) 643 (13.5) 5.9 (1.3) 4.8 (1.1)6 Far 758 (20.7) 674 (14.3) 6.7 (1.4) 4.6 (1.2)Mid 626 (12.4) 595 (10.9) 3.5 (1.0) 4.6 (I .2)Near 684 (14.7) 698 (19.8) 3.8 (0.9) 5.9 (1.1)10 Far 814 (20.4) 732 (15.6) 9.2 (1.6) 6.2 (1.2)Mid 673 (13.3) 686 (15.0) 1.9 (0.7) 3.8 (1.0)Near 781 (16.9) 738 (18.7) 9.4 (1.5) 10.0 (1.7)Long Target2 Far 589 (14.5) 580 (10.8) 6.5 (1.3) 7.5 (1.5)Mid 556 (12.2) 526 (8.4) 3.8 (1.0) 2.2 (0.8)Near 613 (13.2) 558 (8.9) 5.9 (.8) 3.0 (0.9)6 Far 597 (11.5) 574 (10.0) 5.1 (1.3) 3.2 (1.0)Mid 544 (9.7) 531 (12.9) 2.4 (0.8) 2.2 (1.0)Near 622 (13.6) 578 (12.1) 4.8 (1.1) 3.7 (1.2)10 Far 624 (12.2) 610 (11.8) 6.7 (1.4) 6.2 (1.2)Mid 591 (11.1) 554 (10.8) 5.9 (1.3) 4.0 (1.0)Near 654 (14.6) 582 (9.9) 7.3 (1.4) 5.9 (1.2)Slant - from - texture48locations (035), g < .05). In the control condition, RT and percentage of errors were thesame across left and right locations with the exception of the 10 item - short targetcondition; in this condition performance was opposite to the predicted apparent depthpattern (x(35), R < .05).^Insert Figure 10 ^These trends are supported by a significant 3-way interaction between the factors ofbackground, target size, and apparent depth location (i.e., Far and Near) on target presenttrials (RT: F(1,35) = 59.8, g < .001; errors: F(1,40) = 8.1, R < .01). Difficulty indetecting the short target in the far location is further suggested by a significant target sizeby location interaction for RT (E(1,35) = 14.2; p < .001). These interactions also supportthe inverse relationship between short and long target in near and far slant conditions.Further support for apparent depth having its influence in the slant condition wasevident from the significant interaction between background and apparent depth (RT:F(1,35) = 9.4; < .01; errors: F(2,80) = 5.0; g < .05). This interaction reflects the highRTs and percentage of errors in the far region of the slanted background (mean RT: 689msec; mean percent errors: 8.6 %) as contrasted with performance in the near region(mean RT: 668 msec; mean percent errors: 6.2%), or performance in either of the no slantlocations (mean RT: 632 msec; mean percent errors: 5.6%). Finally, there was not amain effect for apparent location on RT performance (E(1,35) = 2.4), even though therewere slightly more errors in the far region ( F(1,40) = 5.1; g < .05).Display size and apparent depth.Evidence for an influence from projective assumptions was also expected in anapparent depth by display size interaction for the slanted conditions. In difficult searchconditions (i.e., when the short target was in the far location), the influence of apparentdepth was expected to increase with display size so that RT functions would appear to "fanout" across display sizes. Although this pattern was observed in Experiment 2, it didZs 800r4 700204.1 10Short TargetSlant^ControlLong TargetSlant^ControlFar Near^Left Right^Far^Near^Left RightTarget LocationFigure 10. Mean correct reaction time and percentage of errors for target present trials of Experiment 3. Two search items(short and long) were examined against three display sizes (two, six and ten) and two backgrounds (slant and control).Critical comparisons are between locations (far and near for the slant condition, and left and right for the controlcondition). Error bars are SEMs.Slant - from - texture50not occur here. The 4-way interaction between background, target size, apparent location,and display size was not significant (E(2, 70) = 1.7) nor do the means in Figure 10indicate such an interaction.Furthermore, if the 4-way interaction were significant, it would be quite a differentpattern from the predicted one. Notice in Figure 10 that the RTs of the two and six item -far conditions appear much more inflated (relative to the their near counterparts), than theten item condition in short target trials. In support of this trend, pairwise 1-tests revealedno difference between the two and six item displays across the two locations of theslanted background. If there was a significant 4-way interaction involving display size, itwould indicate that apparent depth effects were strongest in short target conditions withthe fewest number of search items.For the long target conditions, display size interactions were completely absent.This is seen in the three parallel RT display size functions in all locations, as well as thenonsignificant pairwise comparisons across display sizes and apparent locations (all t's, g> .10). The only significant display size effect was for the ten item trials where search wasslower than two and six item trials for both the far and near locations (1(70), < .01).Subjects made the most errors when the short target was located in the far region ofthe two item display. A significant 3-way interaction between target size, background,and display size (F(2,80) = 4.5, g < .01), as well as a significant 2-way interactionbetween display size and apparent location for percent errors W(4, 160) = 10.0, g <.001), support the stronger apparent depth influence in small display size conditions.The absence of the predicted 4-way interaction involving display size isevidenced further by separate simple effects on target size and background factorcombinations. Only in an analysis of the short target - slanted background conditionswas there a significant interaction between apparent location and display size (E(2,74) =9.1, g < .01). The corresponding trend showed apparent depth had its greatestSlant - from - texture51influence in the displays with the fewest items. The absence of the predicted apparentdepth effects in the greater display size conditions is important since it shows that it isinappropriate to use RT slopes as a measure of the apparent depth influence.Nevertheless, since RT slopes on target present trials did fall within the range of 4 and11 ms/item (across locations) this ensures that early vision was used in all conditions.Additional influencesThe following analyses are included to assess secondary influences that couldaccount for some of the noted apparent depth effects. These include influences frompractice, top-to-bottom and left -to -right search biases, and potential biases introducedby item orientation.Practice.Main effects of trial block were not observed (RT: E(2,70) = 2.2; Error: F(2,80) =1.7). However, response time did improve over trials when there were many items in thedisplay (block x display size -- RT: F(4,140) = 4.3, 12 < .001; errors: F(4, 160) = 0.5).In addition, percent errors decreased with practice in the slant condition ( F(2,80) = 4.0,R < .05), but there was no change in response time W(2,70) = 0.8).Top - bottom search biases.Search performance across top, middle (horizontal meridian), and bottom locationsare shown in Table 4. Overall, subjects were 37 msec faster with 2 % fewer errorswhen the target was located in the top region relative to the bottom region (RT: F(2,80) =181.9, 12 < .001; errors: F(2,80) = 23.8, il < .001; 1(80), 12 < .01). Subjects were 32msec faster and made 2% fewer errors when the target was located in the central region(1(80), a < .01).^Insert Table 4 ^After removing the middle location from the analysis, subjects were stillsignificantly faster detecting the target when it was located in the top region (RT: F(1,40)Slant - from - texture52Table 4Mean correct Reaction Time and Percentage of Errors in Experiment 31011:...131211QMAnalxsisRT (msec)^ Errors (%)Slant ^Control^Slant ^ControlDisplaySizeLocation M (SEM) M MTarget(SEM) M tamShort2 Top 663 (15.0) 638 (13.2) 8.1 (1.5) 3.8 (1.0)Middle 646 (15.5) 591 (12.0) 5.7 (1.2) 3.0 (0.9)Bottom 694 (13.2) 647 (11.9) 2.4 (1.6) 7.3 (1.5)6 Top 684 (15.9) 662 (13.7) 6.0 (1.4) 6.5 (1.4)Middle 655 (15.7) 647 (14.9) 4.1 (1.2) 3.8 (1.1)Bottom 704 (14.4) 665 (13.8) 4.1 (1.1) 4.9 (1.2)10 Top 720 (14.4) 722 (16.0) 6.5 (1.2) 7.0 (1.2)Middle 708 (16.2) 676 (14.8) 5.1 (1.1) 3.8 (1.0)Bottom 804 (18.6) 756 (14.6) 8.9 (1.4) 9.2 (1.5)Long Target2 Top 582 (10.9) 541 (7.3)^3.5 (0.9) 2.4 (0.9)Middle 563 (13.0) 526 (7.5) 4.1 (1.0) 3.0 (0.9)Bottom 654 (16.6) 588 (9.1) 8.7 (1.5) 7.3 (1.0)6 Top 615 (12.1) 572 (12.1) 6.2 (1.2) 4.4 (1.1)Middle 559 (10.0) 529 (7.5) 2.2 (0.7) 0.6 (0.4)Bottom 623 (12.8) 597 (12.3) 4.1 (1.1) 4.3 (1.0)10 Top 626 (10.9) 584 (9.9) 6.0 (1.3) 4.3 (1.1)Middle 587 (11.3) 535 (9.1) 2.7 (0.9) 2.7 (0.8)Bottom 683 (14.4) 629 (13.8) 11.4 (1.8) 9.2 (1.5)Slant - from - texture53= 122.9,12 < .001; errors: F(1,40) = 9.5; all^< .01). Most of this difference isaccounted for by the slant and long target conditions. Subjects were 45 msec faster todetect the target at the top of the slanted condition, as compared to 26 msec in the controlcondition (i(40), < .001). Subjects were also 79 msec faster to detect the long target inthe top region, as compared to 30 msec faster for the short target (040), < .001).Supporting statistics include a significant background by location interaction (RT:E(1,40) = 8.1, < .01; errors: F(1, 40) = .01), and a target size by location interaction(RT: F(1, 40) = 4.2, 1? < .05; errors: F(1, 40) = 2.0). The possibility that thesedifference across target size and location conditions may be related to a height-in-planedepth interpretation is considered in the discussion.Location also interacted with display size (RT: F(2,80) = 14.6, 1? < .001; errors:F(2, 80) = 9.9) and together these interacted with target size (RT: E(2,80) = 3.7, 1? <.05; Error: F(2, 80) = 0.3). With the exception of the 6 item - short target condition,there was a significant difference in performance between top and bottom locationswhen collapsed across background displays (all i's, lz < .05). The greatest differenceof 60 msec occurred in the two item - long target trials and also in the ten item - shorttarget trials.Left - right search bias.Subjects were 19 msec faster in detecting the target when it was located on theleft side of the control display. This left side advantage, although small, was supportedby a significant interaction between background and location for RT (E(1,39) = 11.0, 12> .01), but not errors (.(1,40) = .8). This trend occurred only in conditions with six(1(40), < .01) or ten items (i(40), lz =.09) in the display. When only two items werepresent, subjects were better at detecting the target on the right side of the display.These distinct trends across display size and location are supported by a significantinteraction between location and display size for both RTs (E(2, 78) = 10.2, 12 > .001);Slant - from - texture54and errors ((2,80) = 3.8, 12 < .05). Perhaps these trends reflect the necessity ofmultiple items for a lateral search bias to emerge. One final interaction between targetsize and location reached significance, ((1,40)=7.1, < .01), indicating that subjectsmade fewer errors when the short target was located on the left side of the displayscreen. Note that these search biases cannot account for apparent depth effects.Item Orientation.Figure 11 presents performance across vertical and horizontal search itemconditions for three factors -- target size, background, and apparent location. Searchon the slanted surface was slower for horizontal items than vertical items with greaterdifferences across apparent location occurring on long target trials (I (34),12 < .01), andhorizontal orientations (1 (34), 12 < .05). For the short target slant conditions there weresignificant differences between apparent location for both the vertical and horizontalconditions (34), p < .01). The effect of item orientation on the long target trials, butnot short trials, were supported by an interaction between item orientation,background, and apparent location for RT performance (E(1,34) = 4 . 6 12 < .05).^Insert Figure 11 ^Item orientation also shows consistent influences across the different displaysizes as reflected in the absence of a further interaction with display size (RT: F(2,68) =.18; Error: F(2,78) = .46). However, display size did interact with item orientation onits own, (RT: E(2,68) = 7.6, 12 < .001; Error: F(2,78) = 4.8, p. < .01), and these twofactors interacted with target size for RT, W(2, 68) = 3.2, 12 < .05). These interactionsreflect an undifferentiated increase in RT with increases in display size for thehorizontal conditions, one that was strongest on short target trials. Such a trend isindicative of a manipulation that makes search more difficult.The mixed-design ANOVA revealed a marginally significant interaction betweenitem orientation and the remaining factors on percent errors (E(1, 39) = 3.3, 12 =.07),E 20EWe 10Far Near Left Right 1 fFar Near Left RightShort TargetSlant^ControlLong TargetSlant^ControlFigure 11. Mean correct reaction time and percentage of errors for target present trials of Experiment 3 separated acrossitem orientation. Filled circles and bars represent data from horizontal item trials; open circles and bars represent verticalitem trials. Error bars are SEMs.Slant - from - texture56but not RT W(1, 34) = 0.4). This interaction shows that error performance onhorizontal conditions were most consistent with the predicted apparent depth influencein that they were greatest when the short target was far. Pairwise comparisons supportthis trend with the only significant difference between the far and near locationsoccurring on the short target slant conditions that contain horizontal items (I (34), p_<.01).Size - depth consistency.To further investigate the influence of item orientation on apparent depth, targetsize and apparent depth were combined to form a factor representing size - depthconsistency. The consistent condition represents search for the short target in the farlocation, or the long target in the near location, and the inconsistent conditionrepresents search for the short target when it was near, or the long target when it wasfar. Notice that this factor collapses means across difficult search conditions so thatapparent depth influences now share the same prediction -- search should be moredifficult in the consistent conditions and easier in the inconsistent conditions. Insteadof having to rely on the interaction between target size and apparent location in the slantcondition to demonstrate apparent depth influences, only a main effect for size-depthconsistency is required.Interactions involving item orientation are reported since this is the variable ofinterest. Consistent trials were substantially slower than inconsistent trials when theitems were oriented horizontally and subjects were searching for the long target (itemorientation, target size, background by size-depth (RT: F(1,34) = 4.6,g < .05; errors:F(1,39) = 2.4). When subjects searched for the short target, this difference emergedonly in error performance (34), 12 < .05). Although the corresponding 4-wayinteraction noted above was not significant for error performance, there was amarginally significant interaction between item orientation, background and size-depthSlant - from - texture57consistency (F(1,34) = 3.3, 12 < .07) reflecting that horizontally oriented itemsproduced the greatest difference across consistent and inconsistent slant conditions.Discussion The visual search study presented here shows that early vision is influenced byslant-from-texture. The main evidence was a shift in performance from a fast to slowsearch in conditions where projected size rendered the size discrimination task moredifficult (i.e., when the short target was far or the long target was near). Furtherevidence that these are early vision effects is reflected in the consistently shallow RTslopes across all conditions. The implication is that subjective depth perception doesrelate to the underlying processes governing search, and that attention is not necessaryfor depth processing.The larger apparent depth effect in horizontal trials (seen in RT data for longtargets and percent error data for short targets), further supports the thesis that earlyvision is sensitive to apparent depth. Search items in this condition appeared to beattached to the underlying slanted surface. Recall the description of the appearance ofthe items in the method -- these cylinders appeared perpendicular to the textured surfaceand thus receded into the distance with the slanted surface.Item grouping?RT functions were expected to "fan out" across display sizes as usually occursin a difficult search task. Instead, apparent depth effects either did not differ acrossdisplay sizes, as in the long target trials, or were strongest in short target conditionswith the fewest number of search items. The small display size effect in the long targetcondition can be explained by an overall reduction in reaction times, but the reverseddisplay size effect in the short target condition must be explained by an alternativeinfluence -- perhaps item grouping. Manipulating the appearance of the underlyingsurface slant can provide the conditions for item grouping. Items that appear in aSlant - from - texture58separate plane from the apparent depth are easier to ignore. As the number of itemsincrease in the display, the apparent plane formed by the items is strengthened. Thispossibility of an item grouping influence is further supported by orientation influences,where weaker apparent depth influences were found in conditions with verticallyoriented items. The inconsistency between the flat plane of the items and the slant ofthe background on these trials may have reduced the effect of the texture on searchperformance.Search biases.Results showed that subjects were faster to detect the target when it was at thetop than when it was at the bottom of the display. A simple advantage in detecting thetarget in the top region could be explained by a systematic search bias, perhaps adoptedfrom reading experience. However, this top advantage was much more pronouncedfor long target trials than short target trials. Such performance differences across targetsize may reflect height-in-plane influences noted in the previous experiment, wherebythe top region may be interpreted, to some degree, as further away. A height-in-planeinterpretation should manifest itself in harder search in the top region for the shorttarget, and easier search in the top region for the long target. Height-in-plane effects inthe short target trials may have been reduced somewhat by competing top-to-bottominfluences where search in general is easier at the top of the display. Alternatively,height-in-plane interpretations may be more pronounced in later stages of visualprocessing. This interaction between item orientation and background is discussedfurther in the presentation of visual search performance in the isolated gradientconditions of Chapter 4.Implications.Evidence for sensitivity to apparent depth in early vision has interestingimplications for the representations that are formed there. One in particular concernsSlant - from - texture59whether these representations correspond to the retinal image, or whether they havebeen transformed through through a mechanism that adjusts for projected size to reflectproperties of external objects. By and large, researchers who work with the visualsearch paradigm adhere to an analytic view of perception, arguing that preattentiverepresentations resemble the retinal image. Their premise is that the experience ofcomplex wholes is built from elementary properties, and that perceptual processing firstinvolves some decomposition of the visual input into separate dimensions orcomponents. Considerable psychophysical ( Beck, 1966, 1967; Julesz & Bergen,1983; Treisman & Gelade, 1980) and physiological support exists for this view (i.e.,Hubei & Wiesel, 1977; Barlow & Levick, 1965; Blakemore, 1975; Campbell &Robson, 1968; Cowey, 1979; Zeki, 1978; 1981). Its proponents typically regardmore primitive features (i.e., size, orientation, and color) as the basic elements ofvision and cite evidence showing that such features are independently coded and stableacross different contexts.The opposing view that global attributes (i.e., surface properties such as overallshape or orientation) are detected before features (i.e., size) is supported bydemonstrations of global precedence (Navon, 1977); object identification precedingbrightness perception (Coren, & Komoda, 1973); and improved object-partidentification in the context of three-dimensional objects (Enns & Gilani, 1988; Lanze,Maguire, & Weisstein, 1985; Lanze, Weisstein, & Harris, 1982; Weisstein & Harris,1974). Texture segmentation and visual search evidence in favor of this view includeinfluences of global grouping on visual search (Banks & Prinzmetal, 1976); irrelevantvariation of features slowing texture segmentation (Callaghan, 1989), and redundantvariation among features speeding up segmentation (Callaghan, 1989; Callaghan,Lasaga, & Garner, 1986). There is also evidence showing context effects in visualsearch, as well as automatic depth detection (Aks & Enns, 1992; Enns & Rensink ,Slant - from - texture601990a; 1990b; Kleffner & Ramachandran, 1992; Nakayama & Silverman, 1986; andRamachandran & Plummer, 1989). These studies, together with the present findings,show that an apparent depth context can influence the earliest stages of perception inpredictable ways.Slant - from - texture61Chapter 4: An examination of the texture gradient dimensionsThe switch from fast to slow search in conditions where the short target is far andthe long target is near shows that early vision is sensitive to the apparent depth in thetexture gradient. One way to reconcile these data with current theory on early vision isto redefine visual information in terms of environmental coordinates rather than the 2-Dretinal coordinates. Experiment 4 investigated the question of which informationcontained within the texture gradient contributes most to the 3-D interpretation of earlyvision.Monocular Depth CuesLet us take a brief digression to further describe available depth information thatis related to the texture gradient. After all, it is a logical precursor to understandingwhat 3-D information is used by the human visual system. Only monocular depth cuesare described since texture gradients fall within this category of depth cues.Occlusion provides explicit information about front-to-back object relations inour frontal plane. Stimulus components that conceal other components are perceived aslying in front.Shadows provide information about convexity and concavity as well asinformation about object position (Cavanagh & Leclerc, 1989). This shape and depthinformation can be used if one assumes that light comes from above.Familiarity enables us to maintain size-constancy by comparing stimuli in ourvisual field with stimuli in our memory. Consequently, we can perceive changes indistances when the proximal representation of an object changes its size.Gradients of motion, shading, blur, and texture, all can be viewed asinformation that systematically grades, or changes within the visual field as a directfunction of changes in distance and shape. For instance, motion parallax, informs usabout distance because close objects are seen as moving faster than further objects.Slant - from - texture62Shading gradients provide depth information by signifying smooth depth changes ofconvexity or concavity (Mingolla & Todd, 1986; Ramachandran, 1988; Todd &Mingolla, 1983). Gradients of blurring can originate from either our own physicallimitations or from environmental interference. The former can refer to retinal blurringwhen we are unable to resolve fine details of receding and hence, shrinking images.The latter can refer to interference from haze or dust. Because both forms of blurringsystematically grade with receding objects, it is reasonable to classify these as gradient-like cues. Finally, texture gradients, being dominated by changing retinal sizeinformation, incorporate a number of the properties noted above.Additional important characteristics of all these monocular depth cues is that theyinteract with one another (i.e., familiarity can override size information), contribute toone another (i.e., element density gradients frequently are accompanied by shadinggradients) and contain information that can be treated as separate depth cues (i.e.,perspective and compression). These same properties apply to all of the dimensions thatmake up the texture gradient cue. For now, we will consider this particular gradient cueas an independent source of depth information that can contain within itself an entiresubset of depth cues.Decomposing the texture gradient.Since gradients can be regarded as sources of information that grade with thevisual angle, this implies that the dimensions can be logically separated. Using Cuttingand Millard's (1984) terminology, gradient information available in the environmentincludes perspective, compression,  and density. Figure 12 shows perspective andcompression in their separated and combined forms.^Insert Figure 12 ^The perspective gradient refers to one type of convergence information that is definedas the change in width of the textural element. It is also referred to here as the elementcf)Figure 12a. Reduced illustrations of visual-search displays from Experiment 4 containing vertical items. Two searchitems (long and short) were examined against six search backgrounds -- combined, perspective compression andcorresponding controls.Figure 12b. Reduced illustrations of visual-search displays from Experiment 4 containing horizontal items. Two searchitems (long and short) were examined against six search backgrounds -- combined, perspective compression andcorresponding controls.Slant - from - texture65width / element height, with height held constant across the gradient pattern.Compression gradient is synonymous with the artistic convention of foreshortening,and is represented by the change in element height / element width. Here, width is heldconstant across all the texture elements. (Notice that the gradients in this figure arerotated sideways. Although width still refers to the horizontal dimension of the elementsmaking up the gradient, it corresponds to the vertical dimension on the page. Theopposite is true of height.) Density gradients refer to the increasing number of textureelements per unit of visual angle. The density gradient can be defined in terms of aperspective or a compression gradient. A density gradient in the width of the textureelements can be classified as a perspective gradient, and a density gradient in the heightcan be classified as a compression gradient. For purposes of clarity and consistency,the terms perspective, compression, and density will be used throughout the remainderof this thesis, even when describing research that uses interchangeable terms such asaspect ratio, form ratio, area, scale, height, and size.Relative contribution of the texture dimensions to subjective perception.The most common methods used to test the relative importance of each cue to theperception of depth include isolating individual depth cues, pitting one against the other,and recording judgments about slant or depth (Braunstein, 1976). Typical proceduresinvolve asking subjects about the existence, the direction (towards or away), and theextent of the phenomenal depth impression that is evoked by the different informationcontained within texture gradients. A series of studies using these techniques found thatgradients of perspective and compression have a greater impact than do gradients ofdensity on judgments of slant (Braunstein, 1976; Braunstein and Payne, 1969). Noticethat in the present experiment, with the textured surface consisting of lines, density isinseparable from perspective or compression.Slant - from - texture66Flat slanted surfaces can be regarded as only a small subset of surface propertiesfound in the natural environment; accordingly, the study of the perception of curvedsurfaces has also been investigated. In keeping with this shift towards greaterecological relevance, Cutting and Millard (1984), employed a preference anddissimilarity paradigm to determine the relative importance of different depth cues in 3-Djudgments of flatness and curvature. In the preference procedure, subjects selected thetexture gradient pattern which appeared flat and the pattern which appeared curved. Inthe dissimilarity measure subjects rated, on a scale from 1 to 5, the extent to whichvarious texture gradients appeared either flat or curved. Cutting and Millard confirmedthat different texture information is used in the perception of flat versus curved surfaces.In the perception of flat surfaces, the variance explained by each dimension of thetexture gradient was: 65% by the perspective gradient, 28% by the density gradient, andonly 6% by the compression gradient. This contrasted with perceived curvature, with96% of the variance accounted for by the compression gradient, and less than 2% by theother two gradients.Similar findings were reported in subsequent research that tested the perceptionof textured images depicting spherical objects (Todd & Akerstrom; 1987). Texturegradient dimensions were isolated by randomizing variations in size, shape, andorientation, as well as manipulating the horizontal viewing angle which is known toinfluence the perspective gradient (i.e., width variation). The results showed thatsystematic variations in compression, together with the appropriate orientation positionsfor individual elements, contribute most to accurate curvature judgments. The latterorientation effects extend the findings of Cutting and Millard (1984), in showing theinsufficiency of local texture information and the importance of a global gradient ineliciting accurate impressions of curvature (but see, Stevens; 1981).Slant - from - texture67The literature on texture gradient perception shows that different information isused in perceiving flat and curved surfaces and that this information providesdifferently weighted contributions to our final impression of depth. Perspectiveinformation is used mostly for the perception of flat slanted surfaces, followed bydensity and then compression. For the perception of curvature, compressioninformation is the most informative with slight contributions from perspective anddensity.Experiment 4: Influences from dimensionsof the texture gradient on visual searchHaving established a tool for reliably measuring the slant-from-texture influenceon visual processing, we now can assess the relative influences of the texture gradientdimension. Given the evidence for separate contributions from the dimensions insubjective perception we might also expect separate contributions in visual search.However, this prediction must be made cautiously, given the dissociation betweensubjective perception and early perception discussed in Chapter 1.In Experiment 4, the perspective and compression dimensions of the texturegradient were separated across visual search conditions, as shown in Figure 12.Because these cues provide different spatial information (i.e. Cutting & Millard, 1984;Stevens, 1981; 1984), we may consequently have developed corresponding functionsin our visual systems. Stevens (1981) has demonstrated that these dimensions specifydistinct properties of the environment -- perspective informs us about distance, andcompression informs us about orientation (Cutting, 1984; Stevens, 1981; 1984;Witkin, 1981). Perspective (i.e., the characteristic dimension) is the only dimensionaffected solely by distance. All other dimensions of the projected texture are affectedby distance, orientation, and object height. Perspective is scaled only in width whilecompression is scaled in height =I width. Given that perspective is the only pureSlant - from - texture68measure of texture distance, and that compression is the dimension most foreshortenedby changes in slant, these two dimensions together are likely to be among the mostreliable means for extracting information about distance and slant.Stevens (1984) further speculates that perspective and compression may maponto depth and orientation representations similar to those proposed by Marr (1982)and Ullman (1984). According to this view, the distance information obtained fromperspective can be coded independently of the orientation information derived fromcompression. The advantage of independent coding is evident in the many situationswhere only one form of this information is available or recoverable.Support for such a distinction is available in the psychophysical literature.Cutting and Millard (1984), for example, found a performance asymmetry for thesetwo dimensions in judgments of flat (i.e., maximal distant information) and curved(i.e., maximal orientation information) representations -- the perspective gradient wasused most in judging the slant of flat surfaces and the compression gradient was usedmost in interpreting surface curvature.Before assessing the separability of these texture gradient dimensions in visualperformance, Experiment 4 first examines their relative impact on early visualprocessing. Experiment 5 takes the further step in assessing the independence of thesetexture gradient dimensions in early visual processing.MethodSubjects, stimuli, and procedures were the same as those used in Experiment 3,except for the addition of displays that isolate the dimensions of the texture gradient.The six conditions compared in this experiment included (1) combined gradients, (2)vertical and horizontal line grid (control for the combined gradients), (3) perspectivegradient, (4) vertical line grid (control for the perspective gradient), (5) compressionSlant - from - texture69gradient, and (6) horizontal line grid (control for the compression gradient). These areshown in reduced form in Figure 12. The perspective and compression gradients areused to test the apparent depth influence of the separate dimensions on the search taskrelative to the combined dimension condition. The corresponding control grids test forvertical or horizontal background influences on search and also provide baselines withwhich to compare apparent depth influences.As in Experiment 3, subjects viewed search items that were either vertical orhorizontal in their orientation. Testing these two orientations is especially important inthis experiment because it is possible that search items of different orientations mayinteract differently with the dimensions of the texture gradient.Results: Perspective & Compression CombinedTarget present data from the combined perspective and compression gradientcondition in Experiment 3 were collapsed across background conditions to further isolateinfluences from early assumptions of projective size. The difference for search in theslant and control backgrounds was used as a measure of the apparent depth influence.These are shown in Figure 13 along with the analyses of the individual dimensionsdescribed below. Apparent location and target size were combined into a single factor ofsize-depth consistency for the ANOVA, as in Experiment 3.^Insert Figure 13 ^Consistent with the previously noted trends, there was a greater difference acrossbackgrounds in the size-depth consistent condition relative to the inconsistent condition(RT: F(1,34) = 44.3 a < .001; errors F(1,39) = 8.8, p < .001). Short target trials showeda larger difference than long target trials (RT: F(1,39) = 4.2, p< .05; errors: F(1,39) =6.6, a < .01), and of the display size conditions, the two item trials showed the greatestdifference (RT: F(2, 68) = 3.3 a < .001; errors F(2, 78) = .40). ErrorsSlant - from - textureShort TargetCombined^Perspective Compression70so400804000a 80Er) 400aslyConsistent InconsistentSize - Depth ConsistencyFigure 13a. Mean reaction time difference and percentage error difference across slant andcontrol background for the perspective, compression and combined gradients inExperiment 4. Short targets are presented against three display sizes (two, six and ten) andtwo backgrounds (slant and control). Critical comparisons are between size - depthconsistent (short - far) and inconsistent conditions (short - near). Error bars are SEMs.26•102 6 1026102610Slant - from - textureLong TargetCombined^Perspective Compression 7180400080(7)400820Consistent InconsistentSize - Depth ConsistencyFigure 13b. Mean reaction time difference and percentage error difference across slantand control background for the perspective, compression and combined gradients inExperiment 4. Long targets are presented against three display sizes (two, six and ten)and two backgrounds (slant and control). Critical comparisons are between size - depthconsistent (long - near) and inconsistent conditions (long- far). Error bars are SEMs.Slant - from - texture72occurred most frequently in the two item - short target conditions (target size by displaysize, F(2, 78) = 3.5, D < .001).Item orientation.Figure 14 shows performance separated across the vertical and horizontal itemtrials and collapsed across display size. Only long target trials showed a significanteffect from item orientation -- the horizontal items produced reliable apparent deptheffects, unlike vertical item conditions (target size, size-depth consistency by itemorientation -- RT: F(1,34) = 4.6, D. < .05; errors F(1,39) = 1.6. The difference acrossconsistent and inconsistent trials was highly significant for all target size and itemorientation trials (1(34), p < .05) except the long target - vertical conditions. Pairwisecomparisons (based on Bonferonni t's) of consistent versus inconsistent trials acrossdisplay sizes were significant in all but three vertical item conditions: short target - tenitem trials, and long target - two and six item trials ((34), p < .05). Only marginalsignificance was obtained for the error data with a similar trend of horizontal itemsproducing greater differences across consistent and inconsistent trials (size-depthconsistency by item orientation -- F(1,39) = 3.2, p = .08).^Insert Figure 14^Results: Perspective Visual search data for the target present trials of the perspective gradientcondition are shown in Table 5. Search for the long target was 17 msec faster when itwas far (1(70), D < .01), and RTs and errors did not significantly differ acrosslocations on short target and control trials. Search was also 53 msec faster when thetarget was located in the middle region (E(2,70) = 78.9, D < .001; F(2,76) = 31.2, D. <.001). An additional ANOVA that omitted central region data was performed toremove influences from the overall faster performance in that region. The RTSlant - from - texture73Combined800 407544a4 N0Short TargetPerspective CompressionE.U a+a'cciv)804.2 IConsistent InconsistentSize-Depth ConsistencyFigure 14a. Short target trial mean reaction time difference and percent error differenceacross slant and control backgrounds in Experiment 4 separated by item orientation for eachof three background combinations (perspective, compression, combined conditions andcorresponding controls). Filled circles and bars represent data from horizontal item trials;open circles and bars represent vertical item trials. Error bars are SEMs.80400MbI.,Slant - from - texture74Long TargetCombined^Perspective Compression50-5Consistent InconsistentSize-Depth ConsistencyFigure 14b. Long target trial mean reaction time difference and percent error differenceacross slant and control backgrounds in Experiment 4 separated by item orientation for eachof three background combinations (perspective, compression, combined conditions andcorresponding controls). Filled circles and bars represent data from horizontal item trials;open circles and bars represent vertical item trials. Error bars are SEMs.Slant - from - texture75difference across far and near locations in the long target condition was confirmed by asignificant interaction between the factors of background, target size, and apparent location(RT: F(1,37) = 4.4, p < .05; errors: F(1,38) = 0.2). Further support for apparent deptheffects in the long target trials was found in an analysis based on background differencingdescribed below.Display size and apparent depth.Although apparent depth appears in Table 5 to have a greater impact on conditionswith fewer display items in the short target condition, this trend was not supported by thepredicted four-way interaction between background, apparent location, target size, anddisplay size (RT: F(2,74) = .37; errors: F(2,76) = 1.0); nor were the correspondingpairwise comparisons significant. Two interactions involving display size were significantbut are of secondary importance. One showed a strong positive linear relation between RTand display size for short target trials (display size X target size -- RT: F(2,74) = 7.5, p <.001; errors: F(2,76) = 12.3, p < .01). The second showed that the difficulty of the tenitem conditions was most pronounced in the short target - slant condition, and the longtarget - control condition (display size X target size X background -- RTs W(2, 74) = 3.2,p < .05; errors: W(2,76) = 1.7).^Insert Table 5^Performance difference across backgrounds.Differences in performance across the slant and no slant backgrounds wereexamined in the same manner as in the combined gradient condition. This includedcombining target size and apparent location as a size-depth factor. The differences acrossthe perspective background and the horizontal control grid are shown in Figure 13.In accordance with apparent depth predictions, the difference across backgroundsin the consistent conditions (19 msec) was highly significantly relative to the nullSlant - from - texture76Table 5Mean correct Reaction Time and Percentage of Errors in experiment 4perspective GradientRT (rnsec)^ Errors ()Display Apparent^Slant ^Control ^Slant ControlSize^LocationM Mal M (IEM) M (SEM) M (SEMIShort Target2 Far 659 (16.8) 617 (14.7) 6.5 (1.3) 5.7 (1.4)Mid 594 (12.9) 566 (9.9) 2.3 (0.8) 2.0 (0.7)Near 646 (15.3) 619 (10.6) 5.4 (1.4) 3.9 (1.0)6 Far 662 (14.8) 642 (13.1) 7.3 (1.3) 7.1 (1.4)Mid 590 (11.9) 596 (12.2) 2.6 (1.0) 1.7 (0.7)Near 657 (18.2) 665 (14.5) 5.6 (1.2) 4.0 (1.1)10 Far 707 (17.2) 689 (13.9) 10.5 (1.7) 11.9 (1.8)Mid 657 (12.7) 630 (11.0) 6.8 (1.3) 5.1 (1.1)Near 731 (19.8) 701 (16.3) 11.6 (1.6) 11.3 (1.6)Long Target2 Far 563 (10.8) 567 (9.5) 5.4 (1.1) 6.2 (1.3)Mid 524 (7.7) 520 (8.6) 1.1 (0.6) 2.0 (0.7)Near 577 (11.6) 574 (12.9) 5.4 (1.2) 3.9 (1.0)6 Far 573 (12.2) 575 (10.6) 5.1 (1.2) 5.1 (1.2)Mid 539 (9.7) 530 (10.8) 3.4 (0.9) 2.8 (0.9)Near 595 (12.9) 567 (9.2) 3.7 (1.1) 4.2 (1.0)10 Far 611 (14.4) 608 (14.1) 7.4 (1.4) 5.7 (1.2)Mid 577 (12.0) 567 (11.4) 4.2 (1.1) 3.7 (1.1)Near 625 (15.0) 593 (10.6) 4.8 (1.1) 4.0 (1.1)Slant - from - texture77difference in the inconsistent conditions. This trend is supported by a main effect forsize-depth consistency (RT: F(1, 35) = 8.2, p < .01; errors (E(1, 38) = 0.2). Whenseparated across target size and display size conditions, only the short target - two itemand the long target - ten item displays showed a significant RT difference for theconsistent condition over the inconsistent condition (1(38), p < .05). When collapsedacross display size only the long target showed a significant difference across consistentand inconsistent trials (1(38), p < .05). There was also a significant interaction betweentarget size and display size (RT: F(2, 70) = 3.7, p < .05; errors (E(2,76) = 0.2),reflecting the high RT difference in the two- and ten-item short target conditions.These results show that perspective does produce a significant difference acrosssize-depth consistent and inconsistent conditions thus indicating an apparent depthinfluence in early visual processing. These effects are reliable across long target trials butare limited to small display sizes in the short target trials. The following sections reportanalyses of influences from item and background orientation. These tests are ofsecondary interest but are included to check for potentially confounding influences onapparent depth performance.Item orientation.The middle panel of Figure 14 shows performance in the perspective conditionsseparated across the vertical and horizontal item trials. From these trends it is clear thatitem orientation accounts for some of the performance trends noted above. The strongestapparent depth influence occurred in short target - vertical item trials, and in long target -horizontal trials (1(35), p < .05). A mixed-design ANOVA, with item orientation as abetween factor, supported this asymmetry with a significant interaction between size-depth consistency, target size, and item orientation (RT: F(1, 35) = 6.4, p < .05; errors:Slant - from - texture78F(1, 37) = .5). In addition, there were fewer errors in horizontal item conditions (E(1,37) = 4.1, g < .05).Additional location influences.Overall, subjects were 23 msec faster when the target was in the top third ascompared to the bottom third of the display (RT: F(1,40) = 44.0, g < .001; errors:F(1,40) = 7.1, g < .05). This difference is accounted for primarily by the long targetconditions as supported by a significant target size X location interaction (RT: F(1, 40)= 31.5, g < .001; errors: F(1, 38) = 3.0).. There were also no significant differencesacross left and right locations in the control condition. However, subjects weremarginally faster (15 msec) detecting the target on the left in the slant condition(background by location -- RT (E(1,39) = 3.8, g =.06), errors (f(1,38) = 1.2).Summary of perspective effectsApparent depth effects were found in trials where the perspective gradient waspresent in the background. This effect was fairly robust across target size and displaysize conditions especially for long target trials and short target trials containing thefewest number of search items. Secondary influences from top-bottom or left-rightsearch biases could not account for these trends. Stronger apparent depth effectsoccurred when items were horizontal on long target trials, and vertical on short targettrials. This asymmetry across target size may be due to the local contrast of the items'orientation relative to the background (e.g., Gillam, 1973).Results: Compression Visual search data for target present trials of the compression gradient conditionand its control are shown in Table 6. The analysis of the far, middle, and near locationshowed only a significant location effect for the mid-region which was on average 52msec faster than either of the extreme locations (RT: F(2,78) = 103.7, g < .001;Slant - from - texture79F(2,78) = 16.7, p < .001). Differences in performance across near and far locationsonly emerged in particular display size conditions as described below.^Insert Table 6 ^When central region data were removed from the analysis, the 4-way interactionbetween background, target size, apparent depth, and display size was significant (RT:F(2, 72) = 3.5, p < .05; errors: F(2,78) = .08). Search was slower when the shorttarget was far in the two item displays, but faster in the ten item conditions (1(72), p <.05). The only other significant interaction was between apparent location and displaysize for errors (F(2, 78) = 3.5, p < .05), reflecting the poorest performance in the farlocation of the two item trials. In long target conditions there were no significantdifferences for far and near locations. However, significant effects do emerge inanalyses described below that isolate background differences and size-depthconsistency.Performance difference across backgrounds.A direct comparison of the difference in performance across backgrounds isshown in the right panel of Figure 13. In the analysis of size-depth consistency, the maineffect for size-depth consistency did not reach significance (RT: F(1, 39) = 1.2; errors((1, 38) = 1.2) indicating that the consistent condition did not significantly differ fromthe inconsistent condition across all target size and display size conditions. However, asimple effects test isolating the long target condition did show a significant main effect forsize-depth consistency (RT: F(1, 39) = 4.8, p < .05). Here subjects were slower in theconsistent condition relative to the inconsistent condition (1(39), p < .05).In the ANOVA based on short and long target sizes, size-depth consistencyinteracted with display size (RT: F(2, 76) = 3.2, p < .05; errors (F(2,78) = .12), andtogether these interacted with target size (RT: F(2, 76) = 3.3, p < .05; errors T(2,78) =Slant - from - texture80Table 6Mean correct Reaction Time and Percentage of Errors in Experiment 4Compression GradientRT (msec) ^Errors (%) Display Apparent^Slant ^Control ^Slant ^ControlSize^LocationM (SEM) M (SEM) M LEK M (SEM)Short Target2 Far 685 (18.5) 640 (18.4) 6.6 (1.3) 5.5 (1.2)Mid 582 (12.5) 585 (13.7) 1.7 (0.7) 3.9 (1.0)Near 635  (13.4) 652 (14.5) 3.3 (0.9) 4.4 (1.0)6 Far 663 (14.2) 662 (17.4) 5.0 (1.2) 6.1 (1.4)Mid 600 (10.8) 593 (11.8) 3.0 (0.9) 2.5 (0.9)Near 661 (15.7) 643 (14.9) 3.3 (0.9) 4.1 (1.0)10 Far 710 (16.2) 708 (15.9) 11.6 (1.7) 8.6 (1.5)Mid 649 (13.7) 648 (12.7) 4.1 (1.0) 4.4 (1.0)Near 746 (20.7) 702 (17.0) 10.5 (1.6) 7.5 (1.4)Jong Target2 Far 583 (9.6) 574 (10.5) 5.2 (1.1) 3.9 (1.1)Mid 550 (11.8) 534 (10.7) 4.1 (1.1) 3.6 (1.0)Near 594 (11.5) 563 (11.5) 6.6 (1.3) 4.1 (1.1)6 Far 596 (14.2) 574 (9.8) 3.3 (0.9) 3.6 (1.1)Mid 544 (9.2) 543 (11.1) 3.3 (0.9) .1 .7 (0.7)Near 601 (16.3) 559 (8.6) 5.2 (1.2) 4.1 (1.1)10 Far 611 (12.1) 608 (11.3) 5.8 (1.2) 6.1 (1.3)Mid 580 (12.9) 568 (10.5) 3.0 (0.9) 4.4 (1.2)Near 634 (15.5) 599 (11.6) 6.9 (1.4) 4.4 (1.1)Slant - from - texture81.40). Consistent trials were slower than inconsistent trials for two item displayscollapsed across target size (1(78), g < .05) in short target trials (1(78), < .05) andmarginally in long target trials (1(78), RT: p = .10; error: g = .07). When ten items werepresent on short target trials, the trend was reversed -- subjects took longer to detect thetarget on inconsistent trials (t(78), g < .05). This pattern of performance may be aconsequence of the grouping effect described in the Discussion, as well as the orientationinfluence described below. The following tests for potentially confounding influencesare of secondary importance.Item orientation.The right panel of Figure 14 shows RT differences separated across vertical andhorizontal item orientations in the compression conditions. Horizontal items producedslightly slower search as reflected in the marginally significant main effect for itemorientation F(1,35) = 3.2, g =.08). The poorer performance was most pronounced insize-depth consistent conditions for errors (E(1, 38) = 8.0, g < .001). Pairwisecomparisons of consistent versus inconsistent conditions were significant only in longtarget - horizontal trials (t(38), g < .05).Additional influences.Subjects were 31 msec faster when the target was in the top third relative to thebottom third of the display (RT: F(1,39) = 53.1, g < .001; errors: F(1,38) = 21.7, <.001; l's, < .001). Subjects were also faster with the target located on the left undertwo conditions -- when ten items were present in the display (location X display size --RT: F(2,78) = 13.5,1? < .001; errors: F(2,78) = 16.7, g < .001 ) and when the targetwas short (location X target size -- F(1,37) = 15.2, g < .001).Slant - from - texture82Summary of compression effects.Apparent depth effects were found when compression was present on its own inthe background of the display. This effect was most most reliable in the long targettrials. For short target trials, the effect was present only when two items were in thedisplay. Stronger apparent depth effects also occurred when items were horizontal.Secondary influences from top - bottom or left - right search biases could not accountfor these trends.Discussion.The results of Experiment 4 show that perspective and compression gradients,both together and in isolation, elicit apparent depth effects early in visual processing.Depth effects found in the isolated conditions were smaller than in the combinedgradient conditions, and at times emerged only in short target trials and displays with thefewest items. The impact on RT slopes is shown in Figure 15.^ Insert Figure 15^The diminished apparent depth effect in the long target trials is easily accountedfor by the reduced overall RTs. The reduced effect in the ten item trials is likely due tothe item grouping on vertical trials, as discussed in Experiment 3. In this view,grouping may result from multiple items forming a plane separate from the background.While the items appear to float in their own vertical plane, it may be easy to ignore thebackground slanting away from the the search items and the viewer.One additional influence from apparent depth emerged -- the type of backgroundinteracted with item orientation so that horizontal items most consistently producedthe strongest apparent depth effects. The one exception was for short target -vertical item trials; when perspective was present on its own the apparent depth10510510 105 5Il Combinedel Perspectiven CompressionFar Near Left RightLong TargetSlant - from - texture83Slant^ControlShort TargetLocationFigure 15. Mean correct reaction time slopes (ms/item) in Experiment 4. Twosearch items (short and long) were examined against two locations (far and near inthe slant condition, and left and right in the control condition) for each of sixbackgrounds (Perspective, Compression , Combined conditions and correspondingcontrols). Error bars are SEMs.Slant - from - texture84effects were reduced. This exception resembles Gillam's (1973) finding that size-scaling is largest when the orientation of the judged item is perpendicular to the gradient.The implication is that a large local contrast between the orientation of the item andsurrounding gradient produces large apparent depth effects. Note that on the visualsearch conditions where this asymmetry in size-scaling emerged, the distractors werelong, perhaps sufficiently so, to produce such a trend.Regardless of the weakened effect in long target and multiple item conditions,and the additional interactions from item orientation, there remains plenty of evidence ofapparent depth influences in the isolated gradient conditions. To assess the relativecontribution of the dimensions I will separately consider (1) the magnitude of the effect,and (2) the consistency of the effects across different display sizes. The magnitude ofthe effect was greater for compression than perspective in the two item - short targetcondition. Compression showed a 50 msec mean difference across near and farlocations for the two-item display while perspective showed only a 13 msec difference.However, the six-item trials in the compression conditions showed no location effect,and in the ten item trials there was a pronounced reversal in these trends, thus callinginto question the reliability of the size-consistency effects in the compressionconditions. If item grouping cannot account for the null or reversed location effects inthe compression conditions, then the predicted direction of the effect would have to beargued to be most consistent on perspective trials (even with its smaller magnitude). Aconsistent apparent depth effect is also observed in long target trials with perspective,again demonstrating a slight advantage over compression in the supporting statistics.Greater reliability in apparent depth trends on perspective trials may relate to itsgreater effectiveness in isolating distance information. Compression may be lessreliable because of its tendency to confound orientation and distance informationSlant - from - texture85(Stevens, 1981), and to be confused with items that may differ in their size rather thantheir distance (Stevens, 1983b). To summarize, the evidence presented here showsthat perspective may be more reliable across different conditions, but that the strengthof the effect may be greater for compression. If grouping can account for thediminished effect in the compression conditions, then it is feasible that compression hasboth the more pronounced and the more reliable apparent depth effect.Perhaps a better test of the relative influence of each dimension on searchperformance can be determined by comparing their influence when presentedsimultaneously. In this case, we are interested in how performance in the individualconditions predicts performance in the combined gradient conditions. Presumably, thedominant cue would be the better predictor of performance in the combined conditions.Such a test is presented at the end of Chapter 6.Interestingly, Cutting and Millard (1984) and Vickers (1971) raise a point whichmay override any absolute hierarchical ordering of depth cue salience. The importanceof the depth cues may be relative to the availability of alternative depth cues. Our visualsystem may simply use whichever information is available, and the contribution of eachof the texture gradient dimensions to depth processing will change depending upon theinformation that is present at that time. This possibility is also considered in the nextsection and the final discussion where we consider how perspective and compressioncombine when both kinds of information are available.Slant - from - texture86Chapter 5How does our visual system combine the dimensions?The experiments presented up to this point have shown the influence of slant-from-texture on visual search performance. It has been proposed that mechanisms sensitive toprojective geometry mediate this effect both early and late in visual processing. Inaddition, the individual texture gradient dimensions showed evidence for apparent deptheffects on visual search performance. The present analysis extends this research byshowing how these dimensions are combined by the early visual system. There are anumber of approaches to understanding how perceivers combine multiple sources ofinformation (e.g., Anderson, 1974; Ashby & Townsend; 1986; Garner, 1973; Sternberg,1969a, 1969b). The framework used here combines a standard analysis of main effectsand interactions derived from ANOVA (Anderson, 1974) with Sternberg's (1969a;1969b) Additive Factor Method. Together, these allow us to assess whether early visionadds or multiplies perspective and compression and to infer whether there is a commoncode for the separate dimensions of the texture gradient.Early vision can combine information from multiple sources in at least twogeneral ways. One may involve specialized mechanisms early in the visual stream for thedetection of particular surface properties. These detectors could be sensitive toinformation as simple as line orientation (Treisman, 1982; 1986) to as complex asshading gradients (Aks & Enns, 1992, Ramachandran, 1988), and may have evolvedbecause of the ecological and functional reliability of these cues to scene properties(Gibson, 1966; Ramachandran, 1985). The idea of specialized detectors andcorresponding trigger features can be traced to Barlow (1953) and can be seen in recenttheories of object perception which postulate specialized mechanisms for volumetricsolids (Biederman, 1987; Buffart, Leeuwenberg, & Restle, 1981; Leeuwenberg, 1988;Slant - from - texture87Pentland, 1986). The present results can be accommodated in a similar view byproposing that a projective mechanism is activated by the conjunction of appropriatetexture gradient dimensionsAn alternative explanation is that early vision independently combinesinformation from a number of sources. Cutting and Millard's (1984) finding of differentfactors responsible for the perception of flat and curved surfaces suggests that theperspective and compression gradients not only are independent sources of information,but they may be used for different purposes. Perspective may be used to detect theorientation of flat surfaces and compression may be used to detect the curvature insurfaces. The mechanisms that may detect this information could be similar to Stevens'(1981, 1983) depth and orientation map (see also Marr, 1982). Although Stevens (1981)differs from Cutting (1984) in his view of which computation is used to arrive at theestimates of depth and orientation (See Chapter 1 and Cutting, 1984), both agree thatperspective provides the best information about distance and compression provides thebest information about orientation or curvature.One potential means for implementing multiple independent interpretations ofunique image information could involve a large number of rapid and spatially-parallelprocesses that make "best guesses" about the scene based on information in the image(Enns & Rensink; 1990, 1991). These processes may be able to signal important sceneproperties collectively and stochastically. For example, one process might examine theperspective gradients in the image — a converging gradient would be interpreted as asurface receding away from the observer, whereas a diverging gradient would beinterpreted as a surface slanting toward the observer. A second process might be involvedin the analysis of compression gradients — a contracting gradient would be interpreted as asurface receding or curving away from the observer, whereas an expanding gradient wouldSlant - from - texture88be interpreted as a surface approaching the observer. Moreover, a first order change incompression may signal the presence of a flat slanted surface, while a second order changemay signal the presence of a curved surface. Taken together, these processes would beable to signal the presence of important scene properties such as surface orientation (i.e.,curvature) and distance (i.e., slant).A test of additivityIn the test of additivity, the presence and absence of the texture gradient dimensionsis varied orthogonally and subjected to an analysis of variance. This analysis can signalone of two broad strategies for combining information. First, an additive model wouldcombine information by adding, subtracting, or averaging various sources. Second, amutiplicative model would combine information by multiplying or dividing. Additivity isoperationalized in the ANOVA by the presence of main effects and the absence ofinteractions (Anderson, 1974). Interactions are most consistently associated withmultiplicative models, although exceptions are possible (McClelland, 1979).The present study also uses Sternberg's (1969a, 1969b) additive factors method(AFM) as a framework to further distinguish between an explanation of a specializedmechanism versus separate processes. A brief review of relevant assumptions of AFM arepresented along with a description of the analysis and predictions (see also Taylor, 1976).First, AFM assumes that successive and independent stages (or mechanisms) ofprocessing intervene between the presentation of a search display and the subject'sresponse. The relations between proposed stages of processing are established byselectively varying their temporal durations. In the present study, the duration of thepotential apparent depth stage was manipulated by varying the type of texture gradient, thesize of the target, and the apparent location of the target. The duration of an apparent depthstage is varied by the consistency of the target location and size on the apparently slantedSlant - from - texture89surfaces. Slowing of this stage is expected in the consistent conditions and speeding ofthis stage is expected in the inconsistent conditions. In addition, the usual visual-searchvariables of display size and target presence versus absence were varied to influence thenumber of items that needed to be inspected.Second, if orthogonal variation in the difficulty of two factors such as perspectiveand compression leads to an additive pattern of performance, then the existence of twosuccessive and independent stages of processing is implied. An additive RT pattern wouldbe consistent with the operation of several processes where each make decisions on thebasis of information available in the image. A detection decision in the visual search taskwould simply involve pooling the information from these independent processes. To theextent that decisions can be made quickly for each putative process, there should be acorresponding increase in search speed.If, on the other hand, variation in the texture dimension results in an interactivepattern, then a common stage is implied. This would be most consistent with a specializedprocessor for slanted-texture surfaces. Combinations of texture gradient dimensions usedby a specialized mechanism would influence search rate in a manner consistent with aninterpretation of apparent depth (e.g., a perspective gradient in combination with acompression gradient would excite a slant-from-texture detector), whereas texture gradientcombinations that were inconsistent would result in no apparent-depth influences on search(e.g., a vertical or horizontal line grid would not activate a slant-from-texture detector).Finally, it is noted that AFM is not without its critics (e.g. Eriksen & Schultz,1979; McClelland, 1979; Turvey, 1973), and that our experiment is not designed tocompare AFM directly with alternative models. Nevertheless, these models all agree onthe interpretation of an additive performance pattern: they all use this as diagnostic ofseparate stages. Where the models differ is in their interpretation of interactions. ForSlant - from - texture90example, some models predict interactions from separate processing stages that overlapin time (McClelland, 1979). The path analysis presented in the final section helpsdistinguish between these potential interactive models.MethodThe first test of dimension additivity is based on a repeated measures ANOVA thatincludes perspective and compression as separate factors. The presence of each dimensionwas based on the data from the perspective, compression and combined conditions used inExperiment 4. The absence of perspective and compression were represented by thecorresponding controls: horizontal and vertical grid conditions, and the absence of thecombined gradients was represented by the average of the vertical and horizontal controlconditions.To aid in the presentation of these data, the main and interactive effects wereexpressed as contrast scores. The main effects from perspective (P), and compression(C), and the interaction from perspective and compression (PC) were represented bycontrasts which combined the means of relevant dimension conditions. The means of thedifference across dimension present and absent conditions were used to representperspective: [(P1C1 - POC1) + (PiCO - PoCo)V2, and compression ([(P1C1 - PICO) +(POC1 - POCO)]/2). The interaction between the dimensions was represented by the fourcontrasts that comprise the perspective and compression effects [(P1C1 + POCO) - (PICO+ POC1)]/2.An interaction contrast with a significant nonzero value indicates a reliableinteraction between the texture dimensions. A positive interaction indicates that thecombined dimension effects were larger than predicted by an additive model. A negativeinteraction indicates that the combined dimension effects were smaller than predicted by anadditive model. Either type of nonadditivity would suggest that the dimensions influenceSlant - from - texture91a common mechanism of processing (Sternberg, 1969).ResultsFigure 16 shows mean RTs and percent errors across the factors of perspective,compression, target size, apparent depth, and display size for target present trials.Statistical analysis of these data included target size and apparent depth as a single factor --size -depth consistency. Data were collapsed across trial blocks and missing values wereignored.^Insert Figure 16^The presence of either or both texture dimensions made search more difficult whenthe target was present in the size-depth consistent condition (i.e., the short targetwas far or the long target was near). For each dimension of the texture gradient,performance was slower on consistent trials (size-depth consistency X perspectiveRT: F(1,38) = 17.0, g <.001, errors: F(1, 38) = .10; and size-depth consistencyX compression -- RT: F(1,38) = 24.4,1? <.001, errors: F(1,38) = 6.3, 2 < .05).These simple interactions along with the absence of their three-way interaction isthe first suggestion of additive processing of the dimensions (RT: F(1,38) = 2.4,errors: F(1, 38) = .6). Pairwise comparisons between the texture dimensions'present and absent consistent conditions were all significant (1(38), p_< .05), exceptfor the six and ten item short target trials; here performance was approximately thesame for perspective present and absent trials. Additive trends were furthersupported by a significant main effect for perspective (RT: F(1,38) = 8.9, g <.01,errors: F(1,38) = 8.4,1? <.01) and compression (RT: F(1,38) = 10.9,1? <.001,errors: F(1,38) = .8), showing search was slower in the presence of either of thetexture gradient conditions. Notice that the effect is proportionally the same forshort and long target trials. The appearance of a smaller difference on long targetDS10Slant - from - texture92Size Depth ConsistencyConsistentDS6Short- Far800700600DS2 Compression - Absent 0Present ■Long-Near700CdI-- 6001005 1 1Absent Present Absent Present Absent PresenPerspectiveFigure 16a. Mean reaction time and percent errors across the factors of perspective(present, absent), compression (present, absent), and display size (2, 6,10) for consistentsize-depth conditions (short target - far, long target - near). Error bars are SEMs.Size Depth Consistency^93InconsistentDS2^DS6^DS10ri 1 CompressionAbsent ^Present ■i^: t ..t1 i ri 1 1 iriISlant - from - textureShort- NearI 800E 700i-c460010t. 5Long- Far...-,.1 700txI— 6002 100tE4^5seAbsent Present Absent Present Absent PresentPerspective Figure 16b. Mean reaction time and percent errors across the factors of perspective(present, absent), compression (present, absent), and display size (2, 6,10) for inconsistentsize-depth conditions (short target - near, long target - far). Error bars are SEMs.Slant - from - texture94trials is a consequence of the overall lower RTs for these trials and the enlargement of thegraph's scale to match the scale of the short target trials.When the dimensions were presented together, subjects were much slower (i.e.,overadditive on short target trials) in conditions with consistent size - depth information.These trends were supported by the interaction between perspective, compression, targetsize, and size-depth consistency (RT: F(1, 38) = 7.8, P <.01; errors (F(1, 38) = 4.6, P <.05). Inclusion of both texture dimensions in this interaction along with the notedidiosyncrasy of the six- and ten-item short target trials suggests that the visual system doesnot always engage in a purely additive strategy of processing texture gradient information.Instead, these trends indicate some dependence between processing the dimensions of thegradient in addition to independent processing occurring on long target trials. Perhapsthese two strategies operate at different points in visual processing. This possibility isexplored in further analyses of influences from target size, display size, item orientation,and processing time.Contrast test of Additivity.To further combine the effects of all conditions containing common texturedimensions, a contrast analysis was performed. The results are presented in Figure 17where the approximately equal main effects of perspective and compression on searchperformance are immediately clear.^Insert Figure 17^Consistent with the earlier analysis, two combination rules emerged -- short targettrials showed some interactive trends, and long target trials showed only additive trends.An analysis across the different display sizes confirmed that target size was not the solepredictor of additivity.Display Sizeo 2N 6■ 1060408 201—Cd 0Slant - from - texture95Target SizeShort^LongC PC^P C PCBackgroundP = PerspectiveC = CompressionPC = PC interactionFigure 17. Mean difference in response time and percent error across all texture(perspective and compression) present and absent trials as a function of target size (short,long) and display size (two - white bars; six - gray bars; ten - black bars) for consistentsize-depth conditions in Experiment 4.Slant - from - texture96Processing speed and additivity.Assessing the relation between RT and additivity showed that processing speedmay be a more reliable predictor of dimension additivity than either target size or displaysize. Recall that long target trials were substantially faster than short target trials as weretrials with small display sizes relative to large display size trials (see Figure 16 & 17 andTables 3, 5, & 6 ). Thus faster trials which included long target and small display sizeconditions show additive trends, whereas slower trials which included short target andlarge display size conditions show interactive trends. This relationship between processingspeed and additivity was supported by a highly significant correlation, r(5) = .84, p <.001,between the PC interaction contrast and the average RTs that comprise the dimensions ofall the contrasts. This correlation was based on mean values separated across target sizeand display size.Item orientation.Item orientation provided an additional influence on performance as shown inFigure 18 (perspective, compression, target size, display size X item orientation (RT: F(2,74) = 3.9, p < .05). Search was slower on trials with horizontal items (RT: F(1,37) =4.1, p < .05, errors: F(1, 37) = 9.3, p <.01), especially in the consistent size-depth (itemorientation X size-depth consistency -- RT: F(1,37) = 10.3, p <.01, errors: F(1, 37) =9.4, p <.01), and large display size conditions (item orientation X display size -- RT: F(2,74) = 7.3, p <.01; errors: F(2, 74) = 2.5). Long target trials were most influenced by theorientation of the search items, with horizontal ones showing the greatest performancedifference across consistent and inconsistent conditions (target size, size-depth consistencyX item orientation -- RT: F(1,37) = 4.5, p < .05, errors: F(1, 37) = .05).^Insert Figure 18^DS2Size Depth ConsistencyConsistentDS6^DS10Vertical Items Short- Far800 -E 700 -1-sc460097Compression Absent o-^Present ■Long-Near700Cd1— 600Slant - from - textureAbsent Present Absent Present Absent PresentPerspectiveFigure 18a. Mean reaction time and percent errors across the factors of perspective(present, absent), compression (present, absent), size-depth consistency(consistent, inconsistent) and display size (2, 6,10) for vertical item conditions.Error bars are SEMs.Horizontal Items Short- Far, 8008N 700§-Cd600^20Xr 00"L..^c)DS2ConsistentDS6II i1 1I ICompressionAbsent 0Present ■I iSlant - from - texture98Size Depth ConsistencyLong-NearI 700Ea1-- 600Absent Present Absent Present Absent PresetPerspectiveFigure 18b. Mean reaction time and percent errors across the factors of perspective(present, absent), compression (present, absent), size-depth consistency(consistent, inconsistent) and display size (2, 6,10) for horizontal item conditions.Error bars are SEMs.Slant - from - texture99The contrast analysis confirmed these effects from item orientation. In addition, thecontrast analysis shown, in Figure 19, suggests approximately equal contributions from thetexture dimensions in both vertical and horizontal trials. There are only two exceptions.First, the contribution from perspective is slightly weaker when items are oriented vertically.This however could be the result of a floor effect in long target trials, with the effect ofreducing apparent depth influences. Second, compression contributes more than perspectivein short target - horizontal trials when two items were in the display.^Insert Figure 19^More pertinent to the question of additivity, the evidence is overwhelming for theabsence of interactions in long target trials and the presence of interactions on large displaysize - short target trials, regardless of item orientation. Even though size-depth consistenteffects were larger on horizontal trials, the pattern of additivity was unaffected.Speed of Processing, additivity, and item orientation.The relationship between processing speed and additivity was again supported bystrong positive correlations between the compression by perspective interaction contrastand mean RTs of the conditions making up the contrasts (vertical trials: r(5) = .90,<.001; horizontal trials: r(5) = .64). Low statistical power is likely causing the absence ofsignificance in the horizontal condition correlation.Discussion The tests of additivity, together with correlations between average RT andcombined dimension RT, provided evidence for independent coding of two dominantdimensions of a texture gradient in fast visual search conditions and shared coding inslow search conditions. These findings support the view that separate visual pathwaysoperate on the two dimensions at the earliest stages of visual processing and that theiroutput may feed into a single pathway later in visual processing.4-)0 60Qs.!:44 4000 20g 0Display Sizeo 2B1 6■ 10Short TargetVertical Items^Horizontal ItemsSlant - from - texture1 00P C PC^P C PCBackgroundP = PerspectiveC = CompressionP X C = PC interactionFigure 19a. Mean difference in response time and percent error for short target conditionsacross all texture (perspective and compression) present and absent trials as a function ofdisplay size (two - white bars; six - gray bars; ten - black bars) and item orientation (verticaland horizontal).4a0 60as40a8 20HC4 0Vertical Items Horizontal ItemsDisplay SizeO 2■ 6■ 10Slant - from - texture101Long TargetC PC^P C PCBackgroundP = PerspectiveC = CompressionP X C = PC interactionFigure 19b. Mean difference in response time and percent error for long target conditionsacross all texture (perspective and compression) present and absent trials as a function ofdisplay size (two - white bars; six - gray bars; ten - black bars) and item orientation (verticaland horizontal).Slant - from - texture102Evidence for additive processing is consistent with a number of findings andtheories in the texture gradient literature. First, the present findings compliment those ofCutting and Millard's (1984) who suggest that different performance for flat and curvedsurfaces implies that the perspective and compression gradient are independent sourcesof information and are coded independently in vision. Vickers (1971) also has shownthat slant and depth impressions become additively stronger with increases in the amountof available perspective and compression information. Possible computationalinstantiations of such independent coding include Marr's (1982) and Stevens' (1981;1983) depth and orientation maps, to which we will return to later in this discussion.Interactions between the dimensions found in later visual processing require analternative mechanism that integrates the information from these earlier distinctive codes.One candidate, suggested earlier, may be mechanisms receptive to fairly complexinformation used for the detection of particular surface or object properties. Sensitivityto a shading gradient, for example, would involve detecting the direction of a luminancegradient, perhaps reflecting early sensitivity to 3-D curvature and the direction of light inthe scene (Ramachandran, 1988). However, further research including the presentresults show some limits to the specificity and complexity of the initial coding of shading(Aks & Enns, 1992) and texture gradient information. At the earliest stages, theindividual dimensions, on their own, may activate a mechanism sensitive to depthinformation and at least for the texture gradient, that scales for size. Sensitivity to thecombination of the dimensions occurs slightly later in visual processing with the texturegradients triggering an even stronger signal in the size -scaling mechanism.There are at least two interpretations for the additive effects of perspective andcompression at the earliest stages of visual processing and the interactive effectsoccurring later in visual processing. One possibility is that the dimensions are registeredSlant - from - texture103in parallel at two separate sites, each with its own function -- one for orientation and onefor distance (i.e., Marr, 1982; Stevens, 1983). Although the output of one does notdepend on the other there may be some overlap in the information that each map codes --such redundancy is advantageous in an environment where information is known tovary. After the separate computations are completed they may combine later in amechanism that provides a full representation of surface shape. For this interpretation tobe valid, we would expect that perspective and compression should independentlypredict performance in the combined conditions and that their temporal coding order isnot contingent upon each other. This possibility is explored in a final analysis of theprocessing sequence.An alternative explanation of the additive findings is that only one dimension maybe processed at a time, since the output of one mechanism might improve the output ofthe other. Here we might expect a dependency in the processing of dimensions whichmay in turn be reflected in sequential processing of perspective and compression. Such aview allows for prioritizing the use of these mechanisms for particular (but redundantlycoded) tasks. For example, since perspective codes only distance information andcompression combines orientation and distance in its code, it would make sense for thevisual system to first use perspective to establish the distance to a surface rather than relyon potentially erroneous data from the confounded compression information.Compression may be used later to add information about surface orientation and shape.Both parallel processing or perspective-first models are consistent with thetheories of Stevens (1981; 1983) and Marr (1982), and provide concrete predictionsabout processing sequence. The discernible nature of perspective and the ease ofextracting distance information from it (see discussion on the characteristic dimension),makes it a likely candidate for being processed prior to compression. Accordingly,Slant - from - texture104perspective should better predict performance in the combined condition regardless ofwhether compression is available. The plausibility of these alternatives are tested in anassessment of the temporal sequence of dimension processing.Processing sequence.To assess the temporal order of dimension processing a path analysis derived fromcorrelations between the texture conditions was performed. The technique is based onWright (1921), Simon (1953), and Blalock (1962; 1985); a brief summary and applicationto illusion magnitude is presented in Coren and Ward (1979). This path analysis allows usto distinguish between an interpretation of parallel and sequential processing of the texturegradient dimensions and to assess the independence of processing the separate texturedimensions. Earlier results from the combined conditions show that spatial processingoccurred in parallel -- RT slopes were relatively shallow in both size-depth consistent (7.1msec/item) and inconsistent trials (8.7 msec/item). However, spatial processing of searchitems need not relate to either the spatial or temporal processing of the underlying texture.Locating an item among related items may be a distinct process from one that registersbackground depth information. Similarly, additivity found in Experiment 4 does notinform us as to whether the underlying processes operate temporally in serial or parallel.Hence the path analysis.MethodA path analysis based on correlations between RTs from the separate dimension[i.e., perspective (P) and compression (C)], and combined conditions [i.e., perspectiveand compression (PC)] was performed to determine the order of dimension processing.According to this analysis, a nonsignificant correlation between P and C (rpc), andsignificant correlations between the individual and combined dimensions [rp(pc); rc(pc)]Slant - from - texture105indicate a parallel model. A finding of all significant correlations [rp,c; rp(pc); rc(pc)]indicate a sequential model.Partial correlations were used to further determine the order of dimensionprocessing and to indicate the interdependence of the individual dimensions in predictingthe combined performance. A nonsignificant partial correlation: rp(pc•c, wherecompression is controlled, with a significant correlation: rc(pc •p, where perspective iscontrolled, indicates a dependence of perspective on compression and imply a processingorder of P -> C -> PC. In other words, removing the influence from compressioneliminates the effectiveness of perspective predicting search performance in the combinedgradient condition. A nonsignificant partial correlation: rc(pc •p with a significant,rp(pcyc indicate a dependence of compression on perspective and implies a processingorder of C -> P -> PC. Notice that an asymmetry in the significance of the partialcorrelations indicates the path's direction.ResultsCorrelations between RTs from the separate and combined dimension conditionsare presented in Table 7. In the long target trials, perspective was the only significantpredictor of combined gradient performance (rp(pc) ..43, g <.01). The non-significantcorrelation between perspective and compression (rp c =.22, p =.17) indicates that theindividual dimensions, if indeed both are coded, are coded in parallel. However, theabsence of a significant correlation between compression and the combined gradients,(rc(puc) = .08) indicates that the parallel model reduces to one where perspective alonepredicts performance in the combined trials, as shown in Figure 20.^Insert Table 7 and Figure 20 ^In the short target trials, correlations between perspective and compression weresignificant (rpc = .40, p < .01), as were each of their correlations with the combinedSlant - from - texture106Table 7.^If^.111^I.^1 ^ 0^III^III^IIPerspective (P). Compression (C). and Perspective & Compression (PC)TargetCorrelations PCShutPC^PLosC^PC^P^CP .37* .43 **C .45** .40** ---^.08 .22^---PartialCorrelations PCP .22 --- .42**C .35 * .29 * ---^-.02 .21*p<.05**p<.01Slant - from - texture107Performance Speed Fast^ Slow .42 .29^.3513 —*PC --> C --> PCFigure 20. Results of path analysis of texture gradient dimensions separated byperformance speed. Fast performance in the combined gradient conditions is predicted bestby perspective alone. Slower performance is represented best by a sequential process withperspective coded prior to compression. Partial correlations between the texture gradientconditions are reported.Slant - from - texture108gradient trials (Lp(pc) ..37, p < .05; rc (pc) = .45, p <.01). The three significantcorrelations indicate that a sequential model is likely to be operating. An assessment of thepartial correlations, rp(puc)'c •22, n.s., and Lc(puc•p = .35, p < .05, indicates thatperspective reliably predicts combined performance only when compression information isalso present. Given the asymmetries in the partial correlations together with the significantcorrelations between the isolated dimensions and combined conditions for the short targettrials, the implied order of processing requires perspective to precede compression asshown in Figure 20.In an analysis of the relation between RTs and processing sequence, short targettrials -- also the slower conditions (RT > 650 msec) -- showed evidence for sequentialprocessing. One might expect this trend to be reflected in processing of the separatedimensions (i.e., one dimension should be processed prior to another even when presentedseparately). However separate dimension conditions did not show this. Instead, thetexture gradient dimensions were processed in an equal amount of time in trials where theywere presented on their own. Mean RT for perspective was not significantly faster thancompression on short target (perspective = 679 msec, compression = 682 msec) and longtarget trials (perspective = 600 msec, compression = 606 msec), reflecting no difference inRTs for the interactive - sequential strategy, as well as the additive-parallel processingstrategy. Keep in mind that these RTs were extracted from the separate texture conditionsand that processing strategies can (and appear) to change when new information is present.Also note that asymmetrical correlations do not necessarily reflect a temporal sequence butinstead may indicate intervening mechanisms (Blalock, 1985). In this case the dependencyof perspective on compression can be interpreted as compression simply intervening in theprocessing sequence, perhaps providing additional information about surface orientation orshape.Slant - from - texture109DiscussionIn the present study, only perspective information was needed in fast searchconditions to predict performance in combined texture conditions. In slow search trials,both texture dimensions were needed, with the restriction that perspective was coded first.To account for these performance trends let us return to the two models described earlier --the parallel processing and the perspective coded first model. Parallel processing issupported by uncorrelated influences between the two texture dimensions on searchperformance, and implies independent coding at two separate sites, each with its ownfunction -- one for orientation and one for distance. According to this view, the output ofone does not depend on the other but there still may be some overlap in the information thateach map codes (i.e., perspective and compression code distance information). The outputof the separate computations may combine later in a mechanism that provides a morecomplete description of surface shape.Although perspective was largely unaffected by the presence of compression in thefast search conditions, the overall pattern of results from the path analyses did not supportthe parallel processing view. Instead, trends were most consistent with the alternative --perspective first model. According to this view and the results of the path analysis, onlyone dimension is processed at a time, and the output of the perspective mechanismcontributes interactively to the output of the compression mechanism. The fast trials reflectinfluences only from the perspective segment of the processing sequence. The slowertrials, which are also driven by early vision, last long enough to capture the entire sequenceof perspective then compression processing.A number of interesting questions arise regarding the characteristics of processingin fast and slow conditions and what function they might serve; two are considered here.Slam - from - texture110Why does early vision need both components on slow trials while one is sufficient on fasttrials? and Does sequential processing imply a priority of processing?One of the more plausible answers to the first question is that slow trials mayrequire additional information because of the difficulty involved in detecting the shorttarget, especially in the presence of many distractors. The difficulty of short target trialsrelative to long target trials is likely due to the search asymmetry that occurs reliably in anytask involving size-discrimination -- finding a small object among large ones (of the sametype) is almost always more difficult than finding a large object among small ones. Here itis argued that detection of a small object (or an object located among many items) may beimproved by adding information about its orientation. Results of the path analysis,together with those of Experiments 3 and 4, showed that the texture gradient elicited astronger apparent depth effect when compression was used with perspective. Withperspective yielding information about distance, the extra orientation information fromcompression is likely to improve estimations of object distance and size in the 3-Denvironment.An answer to the second question about the sequence and priority of processingfollows from an explanation of why more information may be used in slow searchconditions. Granted, the act of combining the texture dimensions may constrain ourvisual system to register information sequentially. But the question of priority remains.Logically, the donor process must come first -- that is the process whose outputsupplements a subsequent process. Perspective would be expected to have processingpriority for a number of reasons -- its greater ecological validity (Coren, personalcommunication), its greater reliability in signaling distance information (Stevens, 1984),or it may simply be easier to extract from the image (Stevens, 1981). Thus it seemsplausible that early vision extracts distance first from perspective, and afterwards, thisSlant - from - texture111information is used to isolate orientation from the compression gradient. Certainly,knowing the correct distance and orientation of an object helps us decipher ambiguousinformation and make better judgments about other object properties (e.g., size).General DiscussionThe existing literature on the perception of depth from texture is inconclusiveregarding how subjective depth impressions relate to rapid and spontaneous depthdetection. The present set of experiments shows that there are strong parallels betweenthe texture information used in phenomenal perception and speeded performance.Differences that do occur appear to be in the way in which the information is combined.The present studies show independent coding of the perspective and compressiondimensions at the earliest stages of visual processing and integrated coding later in visualprocessing. Presumably this pattern reflects a progression of visual processing frominitial coding in distinct neural subsystems to a synthesis in a common system that leadsto our final unitary percepts. A summary of the results leading up to this conclusion ispresented, followed by a discussion of the implications for theories of early vision andscene perception.The first two experiments confirmed that subjective perception of slant-from-texture predicts speeded performance in a visual search task and that the mediatingrepresentation relies on principles of projective geometry. The third experiment showedfurther that even early vision is sensitive to this apparent depth information in the texturegradient. However, one unexpected finding was that trials with many items showed theweakest apparent depth effects. This result was attributed to a novel groupingphenomenon induced by a large number of same-size items against the texture gradient,allowing subjects to ignore the apparent depth information in the background. Thefourth experiment showed that both dimensions of the texture gradient are detected bySlant - from - texture112early vision. Stronger apparent depth influences were found in trials where bothperspective and compression dimensions of the texture gradient were available, andwhen search items were oriented horizontally so that they appeared to be attached to theunderlying gradient. The fifth experiment assessed how early vision combines thedimensions of the texture gradient. The texture dimensions were shown to haveindependent influences early in visual processing. However, subjects showed greatersensitivity to the interaction of the dimensions during slower search conditions. Thesefindings support the view that perspective and compression are coded separately at theearliest stages of visual processing and are brought together only later.Implications for theories of early vision,Recall from the discussion in Experiment 3 that researchers who use the visualsearch test typically regard early vision as an analytical process where a limited set offeatures are coded in parallel (Beck, 1966, 1967; Julesz & Bergen, 1983; Treisman,&Gelade, 1980; see also theories of surface perception below). The data presented herequestion this strict view. Early vision's sensitivity to texture information, along with itscorresponding apparent depth interpretation, contradicts this view. Each dimension,even on its own, conveys visual information that when viewed from a conventionalperspective would be defined as a conjunction of simple geometric features -- the radialperspective pattern consists of multiple orientations, and the foreshortened compressionarrangement contains a range of different sizes. These experiments suggest that earlyvision may detect an alternative form of information such as the constant variations(derivatives) in size and orientation in the texture gradient. However, these have notbeen classified as primitive features (Northdurft, 1985; Treisman & Gelade, 1986), norare they easy to estimate (see Stevens, 1981, 1984).Slant - from - texture113Recent studies, however, show support for greater processing sophistication atthe earliest stages of visual processing. These include studies that show sensitivity tobinocular disparity and motion (McLeod, Driver, & Crisp, 1988; Nakayama &Silverman, 1986), spatial line relations and shading, (Enns & Rensink, 1990a, 1990b),and direction of lighting source and luminance gradients ( Aks & Enns, 1992; Kleffner& Ramachandran, 1992; Ramachandran, 1988). In all of these studies early visionrecovers 3-D scene properties which, when described in terms of the image, arecomplex conjunctions. The present study also shows early encoding of a conjunction(or 3-D representation) and, in addition, size-scaling at the earliest stages of visualprocessing.It is important to note that different performance in the near and far locations ofthe present study may have been a consequence of the texture gradient or the localcontrast of the items' size relative to the size of the surrounding background. The latterinfluence would reflect a strategy where subjects compare the size of the target with itslocal background. Detecting a large item against small texture elements may be easierthan detecting a large item against large texture elements. One way to distinguishbetween a search strategy based on detection of the local contrast versus the gradientwould be to compare search trials with small texture elements in the background relativeto trials with large elements in the background Smaller performance differences acrossthese conditions relative to the differences across the locations of the gradient conditionswould suggest that the global gradient, and not just local contrast, is responsible forshifts in performance.Even if local contrast rather than global gradient information is responsible forperformance trends, additional apparent depth effects did emerge. These included top-bottom influences resembling a height-in-plane interpretation, large apparent depthSlant - from - texture114effects when items were oriented horizontally so that they were consistent with theslanted surface, and item grouping in the ten-item condition with its subsequent item-background segregation. In all of these cases, apparent depth appears to haveinfluenced search performance. The same may also be true of a search strategy basedon local contrast. Early assumptions of projected size -- small background textureelements signaling greater distance than large elements -- may be applied to thisinformation either when it is presented as part of a gradient or as a homogeneousbackground.Regardless of whether local contrast or gradient information governs these trends,early and late systems both appear to have been influenced by the same information. Thissensitivity to common information poses further problems for distinguishing stages oftexture processing. At least with respect to texture gradient information, the differencebetween the two stages may not be in what information is used, but in how it is combined.Perhaps a more discerning diagnostic for early and late visual processing of texturegradient information may be based on how the systems code multiple sources ofinformation. The trends presented here suggest separate encoding for early and integratedencoding for late processing.Implications for theories of surface perception.Similar to the analytic view of early visual processing, independent coding forvarious depth cues has also been proposed (Attneave, 1972; Marr & Nishihara, 1978),and supported by psychophysical demonstrations (Bruno & Cutting; 1988; Cutting &Millard, 1984; Stevens, Lees, & Brookes, 1991). When the texture dimensions areclassified as depth cues, rather than as a collection of simple-geometric features,evidence for independent processing of the texture dimensions agrees with the analyticviews of early vision researchers and findings in the field of depth perception. WhatSlant - from - texture115has been neglected in the field of depth perception is a description of how early theindependent processing occurs.How compatible are the present results with models of depth perception? Theappropriate models to assess are those that concentrate on surface perception. Most wellknown is Marr's (1978, 1982) three stage model, which includes an important distinctionbetween distance and surface orientation at the intermediate stage of the 2 1/2-D sketch.The 2 1/2-D sketch describes surfaces visible from a given viewpoint, with values ofdistance and surface orientation metaphorically represented by thousands of "needle-like"points. Orientation is coded by the direction of each surface normal (i.e., the needle) asprojected on this surface, and slant is indicated by the length of each needle (e.g., zerolength indicates no slant). Marr's model assumes a gradient space corresponding to eachpoint in the visual field, which can provide a full description of surface shape in a localregion.Stevens (1981; 1983) has elaborated Marr's model by describing the most efficientinformation and computations necessary to give rise to such a surface mapping. Brieflystated, distance information is most easily extracted from the perspective dimension (orequivalently the characteristic dimension) of the texture gradient. Perspective is simply thedirection of least texture variation, and distance is the reciprocal of this scale. To extractslant, there are a number of potential solutions including coding the gradient of the CDs,detecting various surface derivatives, or performing any one of a number of trigonometricanalyses. Although a number of these solutions are plausible, none has been shown to bethe one used in human vision. Also, many are prone to error as they tend to confoundinformation about distance and orientation. Note that for the size-discrimination task usedhere, only distance is needed. When perspective is available, distance can be directlyextracted from this information. When compression information is presented on its own, itSlant - from - texture116is easier to extract distance after calculating surface slant or orientation. In accounting forthe apparent depth effects of the present study, the most parsimonious account is likely toinvolve scaling for size to adjust for early assumptions of projected size and perceiveddepth. The present results, together with Mares and Steven's theoretical accounts, showthat particular dimensions may be more prone to size-scaling (i.e., perspective) but wheninformation is limited we use what is available (i.e., compression).Early vision and surface perception. A complete model of early vision must be able to explain how we perceive surfacesspecified by texture gradients. Such a model must unify data from two traditionallydistinct fields of perception -- early vision and surface perception. Each of these fieldsmust be able to account for various aspects of the present findings.First, theories of early vision (i.e., Treisman, 1986) and surface perception (Marc,1982) already both propose that vision must have early independent codes that can beactivated rapidly and in parallel. Second, at least some of these early codes must respondto combinations of features that signal important information about properties of surfacesin the environment. Only recently has this been argued to be an important aspect of earlyvision (Enns & Rensink, 1990a, 1990b; Ramachandran, 1988). The present studycontributes to this suggestion in showing that a radial and foreshortened pattern of linescan also signal apparent depth information early in vision. Third, these codes must besensitive to viewer-centered information and have intrinsic scaling properties. The firstpart of this criterion is consistent with Epstein's theory that preattentive vision is sensitiveto projective information (Epstein & Babler; 1989, 1990). However, the addition of size-scaling mechanisms, at this early stage, has yet to be incorporated into theories of earlyvision. Theorists must heed the clear evidence that even simple size judgments, driven byearly vision, compensate for surrounding depth information. Finally, these codes areSlant - from - texture117integrated over time (as exposure duration is lengthened) to enhance depth signals andassumptions of projective geometry.Existing models of early vision and scene perception (i.e., Enns & Rensink, 1990,1991; Epstein & Babler, 1989; Grossberg & Mingolla, 1985; Marr, 1982; Treisman,1986) need to include these essential components to provide a more complete account ofhuman vision. Perhaps most important is the need to incorporate early coding of separatetexture dimensions so that depth information is intrinsic to each code. In addition, sinceboth visual systems are sensitive to the same texture information, theorists should considerthat early and late coding of surface properties may be best distinguished on the basis ofhow fundamental dimensions are coded. When time is limited, early vision codes manysources of information independently, perhaps even selecting the most direct signals forsurface properties. 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NY: John Wiley.128Appendix AExperiment 1 Target presence versus target absence.Visual search on target present trials was substantially faster and less accurate thantarget absent trials (RT: F(1,10) = 36.6, 12 <.001; and errors: E(1,10) = 8.5, 12 <.05).RTs increased with display size (RT: F(2,20) = 69.7, 12 <.001; errors: F(2,20) = .4, nom)primarily for target present trials as confirmed by significant interaction of display size withtarget presence (RT: F(2,20) = 34.6, 12 < .001; errors: F(2,20) = 3.3, rid.).Experiment 2 Target presence versus target absence.Visual search on target present trials was substantially faster and less accuratethan target absent trials (RT: F(1,18) = 49.5,12<.001; and errors: F(1,17) = 26.7,2<.05). RTs increased with display size (RT: F(2,36) = 114.4, 12 <.001; errors: F(2,34)= .1.4, ni.) primarily for target present trials as confirmed by the significant interactionof display size with target presence (RT: F(2,20) = 34.6, 12 < .001; errors: F(2,20) =3.3, 12 <.01).To ensure apparent depth effects were due to the presence of a target in apparentlocations rather than to configural effects of the display, target absent trials were analyzedby location. This was possible since the arrangement of target absent trials was the sameas target present trials with the exception that the target was replaced by a distractor item onthe absent trials. These distractors, therefore, behaved as an additional control for targetpresent trials. Evidence for apparent location trends occurring only in target present trialswere supported by non-significant differences across all locations of the target absent trials(All Fisher's LSD tests, 12 > .05). Further support for slant-from-texture effects beingunique to target present trials include the significant interaction between slant, target size,target location and target presence (RT: F(2,36) = 28.2, 12 <.001; and errors: F(2,34) =12922.9, p <.001), and the three-way interaction between target location, target size, andtarget presence for RT, F(2,36) = 41.3, p <.001; and errors, F(2,34) = 29.7, p <.001.The restriction of slant effects to target present trials was confirmed by the interactionbetween target presence and slant for errors, F(1,17) = 25.4, p_<.001; and the interactionbetween target presence and location for RT, F(2,36) = 51.8, p <.001; and % errors,F(2,34) = 28.1, p <.001.Experiment 3 Target presence versus target absence.Visual search on target present trials was substantially faster and less accurate thantarget absent trials (RT: F(1,39) = 104.9, p <.001; errors: F(1,40) = 135, p <.001). RTsand errors increased with display size (RT: F(2,80) = 174.8, p < .001; errors: F(2,80) =12.0, p < .001), resulting in mean RT slopes of 7 msec/item for target present trials and 13msec/item for target absent trials. This RT Slope difference was supported by a significantinteraction between display size with target presence (RT: F(2,80) = 31.3, p < .001;errors: F(2,80) = 7.99, p < .001).PracticeA significant main effect of trial block was observed (RT: E(2,78) = 14.8, p <.001; Error: F (2, 80) = 2.7, ;La.) which interacted with target presence (RT: F(2,78) =3.4 p < .05; error: F (2, 80) = .29, nui.). This block X target presence interaction is aresult of RT performance showing the greatest improvement over blocks on targetabsent trials.Experiment 4Perspective.Similar to the combined gradient conditions, performance on target present trialswas substantially faster and less accurate than target absent trials (RT: F(1,40) = 106.9,p<.001; errors: F(1,38) = 135.3, g<.001). RTs (E(2,80) = 117.4, p<.001) and130percent errors (F(2, 76) = 12.8,12<.001) increased with display size resulting in RTslopes of 6.6 msec/item for target present trials and 8.3 msec/item for target absenttrials. This RT Slope difference was supported by a significant interaction betweentarget presence and display size for RTs, (F(2, 80) = 8.3, g<.001), and errors, (E(2,80) = 34.2, g<.001).Practice.A significant main effect of trial block was observed for RT (E(2, 80) = 7.4,12<.001), but not for errors (E(2, 76) = 0.5 , p<.001). Most of the improvement in RTsis accounted for by target absent trials F(2, 80) = 5.6, p<.01). Fewer errors were madeon intermediate display size trials in the first block's slant condition, and in the thirdblock's no slant condition. These trends were supported by a significant interactionbetween trial block, background, and display size (E(4, 152) = 2.8, g<.05).Compression.Performance on target present trials was substantially faster and less accuratethan target absent trials (RT: F(1,39) = 137.4, g<.001; errors: F(1,38) = 79.9,P<.001). RTs (F(2,78) = 121.6, p<.001) and percent errors (F(2, 78) = 121.5?,P<.001) increased with display size resulting in RT slopes of 6.4 msec/item for targetpresent trials and 11.7 msec/item for target absent trials. This RT Slope difference wassupported by a significant interaction between target presence and display size (RT:(F(2, 78) = 20.0, a<.001; errors: (E(2, 76) = 16.3, 12<.001).Practice.Subjects showed a general improvement in performance in the compressioncondition as reflected in the significant trial block effect for RT (E(2, 78) = 22.5,R<.001), but not for errors (F(2, 76) = 0.5 , n.s.). Most of the improvement occurredin trials where the target was on the left or right of the six or ten item displays (trialblock, location X display size (E(4, 152) = 2.5, <.05).


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