Critical Contours: An Invariant Linking Image Flow with Salient Surface Organization
This work addresses shape perception in computer vision by providing a method to derive stable, invariant contours from shading, which is incremental in combining existing psychophysical insights with geometric invariants.
The paper tackles the problem of inferring qualitative 3D shape from shading patterns by linking shape-from-shading with shape-from-contour inference, using the Morse-Smale complex as an invariant to identify critical contours that partition surfaces into bumps and valleys.
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.