### Shape from contour and segmentation using symmetries

Shiu Yin Kelvin Yuen

Submitted for the degree of D.Phil. This thesis is an investigation of how shape should be represented in order to interpret two-dimensional shapes in three dimensions - the "shape from contour problem". Most past work has concentrated on finding a simple formula for maximizing the "goodness" of a shape so that we perceive 3D because the 3D shape is more "good" than the 2D shape. However, the problem of isolating the particular 2D shape to maximize - the "segmentation problem" - is neglected. This in unfortunate, as part of the utility of shape from contour is to enable segmentation. In this thesis, we treat both problems simultaneously by a shape representation based on symbols and their simplest combinations, formulated in terms of point sets. These symbols are based on two kinds of symmetries, namely, reflectional and rotational symmetries under parallel projection, which give rise to skewed and turned symmetries. On the philosophical plane, this extends Gibson's idea of direct perception to a symbolic paradigm based on invariant seeking. An interesting consequence of this viewpoint is the dissolution of the top down/bottom up distinction in vision.

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