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The Representation of Discontinuities along Curves

Authors: [tex2html_wrap4098]L. Iverson, S. W. Zucker

Investigator username: zucker

Category: perception

Subcategory: computational neuroscience

The precise localization of discontinuities is key to both vision (e.g., detecting object occlusions) and visual computations (e.g., avoiding inappropriate smoothing). The standard approach is to assume that large values of a variational parameter (e.g., change in orientation) signal discontinuities, except this approach assumes (i) there is no difference between high curvatures and discontinuities; and (ii) orientation can be measured accurately enough to locate large values in its derivative. This second point indicates the chicken-and-egg nature of the problem: since it is necessary to know where the discontinuities are before orientation can be estimated accurately, how can estimates of orientation be used to locate discontinuities! We have been exploring a novel approach to discontinuities, in which they are represented by multiple values of orientation at a given point. Along a curve, for example, mathematically this amounts to taking the limit in both directions into the discontinuity. The implementation fits naturally into our biological model of curve detection, and sensitivity predictions have been shown to be quantitatively in agreement with human performance. Mathematically such techniques are related to the Zariski tangent space in algebraic geometry.