  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.
