| Planar shape plays an important role in human vision. However, the way in which the human visual system groups stimuli into shape percepts, and how these percepts are represented, is not fully understood. This thesis aims to advance our understanding of both these issues.;This non-local shape information could therefore condition early visual grouping processes by means of a generative shape model. However, a review of existing shape frameworks finds that no existing representation is suitable for generative modelling. The primary contribution of this thesis is thus a computational investigation into a new representation of natural planar shape based on the composition of primitive wavelet-like shape transformations called formlets. Each formlet subjects the space in which a shape is embedded to a localized isotropic radial deformation tuned in location and scale. By constraining these transformations to be diffeomorphisms of the plane, the topology of shape is preserved over composition. We present a formlet pursuit algorithm for constructing sparse multi-scale approximations of arbitrary shape by composing formlets over a shape prototype, e.g. an ellipse. Evaluation of the formlet representation against competing methods on a shape completion task suggests that formlets are well-suited for the generative modeling of natural planar shape.;Although the role of local geometric information in perceptual grouping is fairly well understood, debate exists concerning the effects of non-local shape geometry. This thesis presents a psychophysical investigation into the role of non-local geometric shape cues, reporting evidence that geometric information, beyond local pair-wise statistics, facilitates the perceptual organization of natural planar shape. |
