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UBC Theses and Dissertations

The use of the Gabor expansion in computer vision systems Braithwaite, Richard Neil


This thesis explores the use of the Gabor expansion in computer vision systems. The exploration is performed in two parts: the properties of the Gabor expansion are reviewed, and various image segmentation algorithms whose basis is the Gabor expansion are presented. The first part comprises a review of Gabor's original expansion of a one-dimensional signal [1] and Daugman's two-dimensional generalization [2] [3]. In both cases, important properties are discussed: the optimality of the "elementary function" with respect to minimal uncertainty, and the proper spacing of these functions to ensure a unique Gabor expansion. Methods for solving the Gabor expansion are investigated. Two non-iterative methods are discussed: the "inverse of the overlap matrix", and Bastiaans' "biorthonormal projection function" [4] [5]. One iterative method, Daugman's "steepest descent" [3], is reviewed. Two new iterative methods, the "warping method" and the "locally biorthonormal projection function," are presented. The complexity and convergence properties of these new methods are intermediate to Daugman's and Bastiaans' methods. In the second part of this thesis, Gabor expansion-based segmentation algorithms are presented. The properties of these algorithms—edge detection, texture segmentation, motion segmentation, and segmentation by depth—are investigated. It is shown that "local measures", which are by-products of the segmentation algorithms, can be used to both segment images and to provide three-dimensional descriptions of viewed objects. It is concluded that the Gabor expansion is a useful preprocessing step for computer vision systems.

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