Paper Info
Title
Shape from Shading: A Well-Posed Problem?
Abstract
Shape From Shading is known to be an ill-posed problem. We show in this paper that if we model the problem in a different way than it is usually done, more precisely by taking into account the 1/r2 attenuation term of the illumination, Shape From Shading becomes completely well-posed. Thus the shading allows to recover (almost) any surface from only one image (of this surface) without any additional data (in particular, without the knowledge of the heights of the solution at the local intensity "minima", contrary to [6, 23, 8, 25, 12]) and without regularity assumptions (contrary to [17, 10], for example). More precisely, we formulate the problem as that of solving a new Partial Differential Equation (PDE), we develop a complete mathematical study of this equation and we design a new provably convergent numerical method. Finally, we present results of our new Shape From Shading method on various synthetic and real images.
Year
DOI
Venue
2005
10.1109/CVPR.2005.319
CVPR
Keywords
Field
DocType
computer vision,convergence of numerical methods,image reconstruction,partial differential equations,convergent numerical method,partial differential equation,real images,shape from shading
Iterative reconstruction,Computer vision,Well-posed problem,Maxima and minima,Artificial intelligence,Real image,Numerical analysis,Partial differential equation,Photometric stereo,Mathematics,Shading
Conference
Volume
ISSN
ISBN
2
1063-6919
0-7695-2372-2
Citations 
PageRank 
References 
98
3.20
28
Authors
2
Name
Order
Citations
PageRank
Emmanuel Prados145020.47
Olivier D. Faugeras293642568.69