Critical Contours: An Invariant Linking Image Flow with Salient Surface Organization

TL;DR

This paper introduces critical contours as invariant image features linked to surface shape, enabling qualitative 3D shape inference from shading and contours that are stable across rendering variations.

Contribution

It develops a geometrical/topological invariant based on the Morse–Smale complex to connect image structure with surface shape, facilitating shape inference from shading and contours.

Findings

Critical contours are stable and invariant across rendering models.

They partition surfaces into meaningful parts like bumps and valleys.

The method enables qualitative 3D shape reconstruction from shading patterns.

Abstract

We exploit a key result from visual psychophysics---that individuals perceive shape qualitatively---to develop the use of a geometrical/topological "invariant'' (the Morse--Smale complex) relating image structure with surface structure. Differences across individuals are minimal near certain configurations such as ridges and boundaries, and it is these configurations that are often represented in line drawings. In particular, we introduce a method for inferring a qualitative three-dimensional shape from shading patterns that link the shape-from-shading inference with shape-from-contour inference. For a given shape, certain shading patches approach "line drawings'' in a well-defined limit. Under this limit, and invariably with respect to rendering choices, these shading patterns provide a qualitative description of the surface. We further show that, under this model, the contours partition the surface into meaningful parts using the Morse--Smale complex. These critical contours are the (perceptually) stable parts of this complex and are invariant over a wide class of rendering models. Intuitively, our main result shows that critical contours partition smooth surfaces into bumps and valleys, in effect providing a scaffold on the image from which a full surface can be interpolated.