Critical Contours: An Invariant Linking Image Flow with Salient Surface Organization
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We exploit a key result from visual psychophysics -- that individuals perceive shape qualitatively -- to develop 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 qualitative 3D shape from shading patterns that link the shape-from-shading inference with shape-from-contour. For a given shape, certain shading patches become "line drawings" in a well-defined limit. Under this limit, and invariantly, these shading patterns provide a topological description of the surface. We further show that, under this model, the contours partition the surface into meaningful parts using the Morse-Smale complex. 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.
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