  Shape inference is classically ill-posed, because it involves a map from the
(2D) image domain to the (3D) world. Standard approaches regularize this
problem by either assuming a prior on lighting and rendering or restricting the
domain, and develop differential equations or optimization solutions. While
elegant, the solutions that emerge in these situations are remarkably fragile.
We exploit the observation that people infer shape qualitatively; that there
are quantitative differences between individuals. The consequence is a
topological approach based on critical contours and the Morse-Smale complex.
This paper provides a developmental review of that theory, emphasizing the
motivation at different stages of the research.
