Surface descriptions from stereo and shading
Image and Vision Computing
Shape from shading
Uniqueness in shape from shading
International Journal of Computer Vision
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Shape from shading: level set propagation and viscosity solutions
International Journal of Computer Vision
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ambiguous Shape from Shading with Critical Points
Journal of Mathematical Imaging and Vision
Robot Vision
Numerical Approximation of the Maximal Solutions for a Class of Degenerate Hamilton-Jacobi Equations
SIAM Journal on Numerical Analysis
An Algorithm for the Global Solution of the Shape-from-Shading Model
ICIAP '97 Proceedings of the 9th International Conference on Image Analysis and Processing-Volume I - Volume I
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
Towards Shape from Shading under Realistic Photographic Conditions
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 2 - Volume 02
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
The Implicit Upwind Method for 1-D Scalar Conservation Laws with Continuous Fluxes
SIAM Journal on Numerical Analysis
A Generic and Provably Convergent Shape-from-Shading Method for Orthographic and Pinhole Cameras
International Journal of Computer Vision
A Unifying and Rigorous Shape from Shading Method Adapted to Realistic Data and Applications
Journal of Mathematical Imaging and Vision
Shape from shading for the digitization of curved documents
Machine Vision and Applications
Numerical methods for shape-from-shading: A new survey with benchmarks
Computer Vision and Image Understanding
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
Some remarks on perspective shape-from-shading models
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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In this paper we study a perspective model for shape from shading and its numerical approximation. We show that an ambiguity still persists, although the model with light attenuation factor has previously been shown to be well-posed under appropriate assumptions. Analytical results revealing the ambiguity are complemented by various numerical tests. Moreover, we present convergence results for two iterative approximation schemes. The first is based on a finite difference discretization, whereas the second is based on a semi-Lagrangian discretization. The convergence results are obtained in the general framework of viscosity solutions of the underlying partial differential equation. In addition to these theoretical and numerical results, we propose an algorithm for reconstructing discontinuous surfaces, making it possible to obtain results of reasonable quality even for complex scenes. To this end, we solve the constituting equation on a previously segmented input image, using state constraint boundary conditions at the segment borders.