From Boundaries to Bumps: when closed (extremal) contours are critical

TL;DR

This paper introduces closed extremal curves as a new shape invariant that surrounds bumps, unifying various shape inference cues and predicting phenomena in bump perception, thus advancing understanding of shape perception.

Contribution

It defines closed extremal curves as a novel topological shape invariant that formalizes bump perception and unifies multiple shape inference methods.

Findings

Extremal curves surround bumps and are topologically invariant.

They unify shape inferences from shading, texture, and specular reflections.

Predict new phenomena in bump perception.

Abstract

Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in terms of isophotes, and surface meaning, in terms of surface normal. We relax the notion of occluding contour to define closed extremal curves, a new shape invariant that exists at the topological level. They surround bumps, a common but ill-specified interior shape component, and formalize the qualitative nature of bump perception. Extremal curves are biologically computable, unify shape inferences from shading, texture, and specular materials, and predict new phenomena in bump perception.