Global shape from shading

A new approach for the reconstruction of a smooth three dimensional object from its two dimensional gray level image is presented. An algorithm based on topological properties of simple smooth surfaces is provided to solve the problem of global reconstruction. Classifying singular points in the shading image as maxima minima and two kinds of saddle points, serves as the key to the solution of the problem. This classification is performed globally with no assumptions on the local behavior of characteristics near singular points. The global reconstruction procedure, being deterministic and using topological properties of the surface performs better than other approaches proposed so far, based on classification of singular points according to the local behavior of characteristics in their neighborhood. The proposed algorithm is simple, easy to implement and works remarkably fast on a parallel machine.

[1]  Berthold K. P. Horn.  Obtaining shape from shading information , 1989 .

[2]  Alfred M. Bruckstein,et al.  Subpixel distance maps and weighted distance transforms , 1993, Optics & Photonics.

[3]  P. Lions,et al.  Shape-from-shading, viscosity solutions and edges , 1993 .

[4]  Berthold K. P. Horn,et al.  Shape from shading , 1989 .

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

[6]  P. Giblin,et al.  Curves and singularities : a geometrical introduction to singularity theory , 1992 .

[7]  Alfred M. Bruckstein,et al.  Shape From Shading , 2006, Handbook of Mathematical Models in Computer Vision.

[8]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[9]  E. Rouy,et al.  A viscosity solutions approach to shape-from-shading , 1992 .

[10]  Alfred M. Bruckstein,et al.  Tracking Level Sets by Level Sets: A Method for Solving the Shape from Shading Problem , 1995, Comput. Vis. Image Underst..

[11]  John Oliensis,et al.  A global algorithm for shape from shading , 1993, 1993 (4th) International Conference on Computer Vision.

[12]  P. Dupuis,et al.  Direct method for reconstructing shape from shading , 1991, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  Paul Dupuis,et al.  Direct method for reconstructing shape from shading , 1991, Optics & Photonics.

[14]  P. Giblin,et al.  Curves and Singularities , 1984 .