2017/05/20 by Benjamin Kunsberg, Kunsberg, Benjamin S., Steven W. Zucker +1
Computer Science · Neuroscience · #Advanced Vision and Imaging #Computer Graphics and Visualization Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Topological and Geometric Data Analysis #Visual perception and processing mechanisms
paper · pdf · doi:10.48550/arxiv.1705.07329
openalex publication_date 2017/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We exploit a key result from visual psychophysics---that individuals perceive\nshape qualitatively---to develop the use of a geometrical/topological\n"invariant'' (the Morse--Smale complex) relating image structure with surface\nstructure. Differences across individuals are minimal near certain\nconfigurations such as ridges and boundaries, and it is these configurations\nthat are often represented in line drawings. In particular, we introduce a\nmethod for inferring a qualitative three-dimensional shape from shading\npatterns that link the shape-from-shading inference with shape-from-contour\ninference. For a given shape, certain shading patches approach "line drawings''\nin a well-defined limit. Under this limit, and invariably with respect to\nrendering choices, these shading patterns provide a qualitative description of\nthe surface. We further show that, under this model, the contours partition the\nsurface into meaningful parts using the Morse--Smale complex. These critical\ncontours are the (perceptually) stable parts of this complex and are invariant\nover a wide class of rendering models. Intuitively, our main result shows that\ncritical contours partition smooth surfaces into bumps and valleys, in effect\nproviding a scaffold on the image from which a full surface can be\ninterpolated.\n