From Deterministic to Stochastic Methods for Shape From Shading

Shape from shading designates the problem of shape rebuilding of a surface, starting from one image only of this surface. We compare different iterative methods of resolution of shape from shading. An analysis of the various discrete formulations of the problem is made, which allows the proposition of a certain number of error functions. Three deterministic methods to minimize these errors are tested, including the new method that we propose, and that we call “optimal gradient descent”, which is the only one which guarantees convergence. In addition, we show that it is necessary to use stochastic methods to improve the results given by the deterministic methods. Finally, we confirme that the direct resolution of the problem with height as the only unknown leads to failure.

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

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

[3]  Anna R. Bruss.  The Eikonal equation: some results applicable to computer vision , 1982 .

[4]  Demetri Terzopoulos,et al.  Image Analysis Using Multigrid Relaxation Methods , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Michael J. Brooks,et al.  The variational approach to shape from shading , 1986, Comput. Vis. Graph. Image Process..

[6]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[7]  Duk Lun Lee,et al.  A provably convergent algorithm for shape from shading , 1989 .

[8]  Richard Szeliski,et al.  Fast shape from shading , 1990, CVGIP Image Underst..

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

[10]  Maurizio Falcone,et al.  An Algorithm for the Global Solution of the Shape-from-Shading Model , 1997, ICIAP.

[11]  Jean-Denis Durou,et al.  Creation of real images which are valid for the assumptions made in shape from shading , 1999, Proceedings 10th International Conference on Image Analysis and Processing.