Folds and cuts: how shading flows into edges

We consider the interactions between edges and intensity distributions in semi-open image neighborhoods surrounding them. Locally this amounts to a kind of figure-ground problem, and we analyze the case of smooth surface occluding one another. Techniques from differential topology permits a classification of edges based on what we call folds and cuts. Intuititively, folds arise when a surface "folds" out of sight, which in turn may "cut" another surface from view. The classification depends on tangency between an edge tangent map and a shading flow field. Examples are included.

[1]  A S Thorndike,et al.  The structure and evolution of flow fields and other vector fields , 1978 .

[2]  J J Koenderink,et al.  What Does the Occluding Contour Tell Us about Solid Shape? , 1984, Perception.

[3]  Steven W. Zucker,et al.  How Folds Cut a Scene , 2001, IWVF.

[4]  William T. Freeman,et al.  The generic viewpoint assumption in a framework for visual perception , 1994, Nature.

[5]  P U Tse,et al.  Amodal Completion in the Absence of Image Tangent Discontinuities , 1998, Perception.

[6]  D. Knill,et al.  Geometry of shadows. , 1997, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  Katsushi Ikeuchi,et al.  Numerical Shape from Shading and Occluding Boundaries , 1981, Artif. Intell..

[8]  Steven W. Zucker,et al.  Shadows and shading flow fields , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[9]  M. Golubitsky,et al.  Stable mappings and their singularities , 1973 .

[10]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[11]  J. P. Dufour,et al.  Families de courbes planes differentiables , 1983 .

[12]  S. M..  Shape-from-shading on a cloudy day , 1992 .

[13]  Jan J. Koenderink,et al.  Solid shape , 1990 .

[14]  B. Dundas,et al.  DIFFERENTIAL TOPOLOGY , 2002 .

[15]  Joachim H. Rieger,et al.  The Geometry of View Space of Opaque Objects Bounded by Smooth Surfaces , 1990, Artif. Intell..