A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape from Shading and Viscosity Solutions
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
A New Perspective [on] Shape-from-Shading
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
"Perspective Shape from Shading" and Viscosity Solutions
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Shape from Shading: A Well-Posed Problem?
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
A New Formulation for Shape from Shading for Non-Lambertian Surfaces
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
A fast marching formulation of perspective shape from shading under frontal illumination
Pattern Recognition Letters
A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations
Journal of Scientific Computing
Fast Shape from Shading for Phong-Type Surfaces
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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We propose a new mathematical formulation for perspective shape from shading (PSFS) problems. Our approach is based on representing the unknown surface as a spherical surface, expressed by Euclidean distance to the optical centre, as opposed to the traditional representation by distance from the image plane. We show that our parameterization is better suited for perspective camera models and results in simpler models and equations for classical PSFS problems with a light source in the optical centre. The unknown distance field satisfies a simple isotropic Eikonal equation on the unit sphere in the case of a Lambertian surface reflection model. This is in contrast to previous methods with depth field parameterization, which result in anisotropic equations. Adding light attenuation to the model, we show that the distance field satisfies an Eikonal type of equation with a zero order term. We show how both Eikonal equations can be approximated by very efficient Fast Marching methods. A number of numerical tests and examples are provided to demonstrate our approach, and to compare with previous work. Our results indicate competitive accuracy and computational time that are several orders of magnitude faster than state-of-the-art iterative algorithms. A preliminary investigation indicates that our method could be used in more general PSFS problems.