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Benjamin Kunsberg, Steven Zucker; Critical contours link surface inferences with image flows. Journal of Vision 2017;17(10):319. doi: 10.1167/17.10.319.
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Three-dimensional shape can be inferred from shading and/or contours, but both problems are ill posed. Computational efforts impose priors to force a unique solution. However, psychophysical results indicate that viewers infer qualitatively similiar but not quantitatively identical shapes from shading or contours or both. The challenge is to connect shading and contour inference and find the family of related solutions. We have discovered a solution to this challenge by reformulating the problem not as an inference from images directly to surfaces, but rather as one that passes through an abstraction. At the heart of this abstraction is another fundamental question rarely addressed: how can local image information, given e.g. by image derivatives, integrate to global constructs, e.g. surface ridges. Artists achieve it intuitively with strokes; suggestive contours attempt it by presuming the surface is given. Our theory uses a geometrical-topological construct (the Morse-Smale complex). We introduce a novel shading-to-critical-contour limiting process, which identifies image regions (e.g., consecutive narrow bands of bright, dark, and bright intensity) with a distinct gradient flow signature. Curves through the flow flanked by steep gradients are the critical contours. They capture generic aspects of artists' drawings and have a physiologically-identifiable signature. Importantly, this shading-limit holds for a variety of rendering functions, from Lambertian to specular to oriented textures, so it applies to many materials. Our main mathematical result proves that the image critical contours are one-to-one with corresponding structures on (the slant of) surfaces. This is the invariance that, in turn, anchors the equivalence class of surfaces. The theory is novel in that (i) it reveals an invariance at the core of surface inferences; (ii) connects the shading, contour, and texture problems; and (iii) transitions from local to global. Psychophysical predictions follow.
Meeting abstract presented at VSS 2017
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