Results 1 
4 of
4
A Tangent Bundle Theory for Visual Curve Completion
, 2012
"... Visual curve completion is a fundamental perceptual mechanism that completes the missing parts (e.g., due to occlusion) between observed contour fragments. Previous research into the shape of completed curves has generally followed an “axiomatic” approach, where desired perceptual/geometrical prope ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Visual curve completion is a fundamental perceptual mechanism that completes the missing parts (e.g., due to occlusion) between observed contour fragments. Previous research into the shape of completed curves has generally followed an “axiomatic” approach, where desired perceptual/geometrical properties are first defined as axioms, followed by mathematical investigation into curves that satisfy them. However, determining psychophysically such desired properties is difficult and researchers still debate what they should be in the first place. Instead, here we exploit the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle R 2 S 1, which abstracts the primary visual cortex (V1) and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed. Exploring here the elementary principle of least action in V1, we show how the problem becomes one of finding minimumlength admissible curves in R² x S 1. We formalize the problem in variational terms, we analyze it theoretically, and we formulate practical algorithms for the reconstruction of these completed curves. We then explore their induced visual properties visàvis popular perceptual axioms and show how our theory predicts many perceptual properties reported in the corresponding perceptual literature. Finally, we demonstrate a variety of curve completions and report comparisons to psychophysical data and other completion models.
General Geometric Good Continuation: From Taylor to Laplace via Level Sets
, 2010
"... ... that parts often group in particular ways to form coherent wholes. Perceptual integration of edges, for example, involves orientation good continuation, a property which has been exploited computationally very extensively. But more general localglobal relationships, such as for shading or color ..."
Abstract
 Add to MetaCart
(Show Context)
... that parts often group in particular ways to form coherent wholes. Perceptual integration of edges, for example, involves orientation good continuation, a property which has been exploited computationally very extensively. But more general localglobal relationships, such as for shading or color, have been elusive. While Taylor’s Theorem suggests certain modeling and smoothness criteria, the consideration of level set geometry indicates a different approach. Using such first principles we derive, for the first time, a generalization of good continuation to all those visual structures that can be abstracted as scalar functions over the image plane. Based on second order differential constraints that reflect good continuation, our analysis leads to a unique class of harmonic models and a cooperative algorithm for structure inference. Among the different applications of good continuation, here we apply these results to the denoising of shading and intensity distributions and demonstrate how our approach eliminates spurious measurements while preserving both singularities and regular structure, a property that facilitates higher level processes which depend so critically on both of these classes of visual structures.