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Computational methods for the shape from shading problem

University of British Columbia

The aim of this thesis is to explore computational methods for the shape from shading problem as formulated through the image irradiance equation. We seek to develop robust, efficient methods and test our algorithms on synthetic images ranging from simple smooth surfaces to complex digital terrain model data. We consider three different approaches. The first approach revisits the method of characteristic strips with a view to using more stable integration schemes than had been used in earlier works. Stable schemes, coupled with projections onto the image irradiance equation are used. Although the effects of noise are thereby reduced, the solution is still deemed unsatisfactory even for very simple surfaces. The second approach considers Horn's variational technique as a basis for producing a fast solver. We devise a discretization scheme coupled with a special continuation-multi grid method for this formulation. We also allow for multiple image data and explicit knowledge of the location of discontinuities in surface height and orientation. Given multiple image data, we obtain excellent results even in the presence of discontinuities. The third approach examines a class of solution techniques based on fluid flow which are new to the shape from shading literature. This formulation is ill-posed in general, so we propose a regularization of the problem. We observe that the algorithm is prone to producing spurious results. Analysis shows that these are due to the non-random accumulation of errors in the computed solution. Of the three approaches considered, the variational method yields the most promising results. Efficient, good quality reconstructions are obtained, especially when data from more than one image are available.

Thesis/Dissertation

application/pdf

2008-09-16

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http://hdl.handle.net/2429/2021

Mathematics

University of British Columbia

UBCV

DSpace