Computer Vision, Graphics, and Image Processing
Local and semi-local shape from shading for a single perspective image of a smooth object
Computer Vision, Graphics, and Image Processing
A Shape From Shading Analysis for a Single Perspective Image of a Polyhedron
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape from shading
Shape from shading as a partially well-constrained problem
CVGIP: Image Understanding
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape from shading with perspective projection
CVGIP: Image Understanding
Tracking level sets by level sets: a method for solving the shape from shading problem
Computer Vision and Image Understanding
Computer Vision and Image Understanding
On convergence in the methods of Strat and of Smith for shape from shading
International Journal of Computer Vision
Computer Vision and Image Understanding
Uniqueness in Shape from Shading Revisited
Journal of Mathematical Imaging and Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ambiguous Shape from Shading with Critical Points
Journal of Mathematical Imaging and Vision
Extending viscosity solutions to Eikonal equations with discontinuous spatial dependence
Nonlinear Analysis: Theory, Methods & Applications
Numerical Shape-From-Shading for Discontinuous Photographic Images
International Journal of Computer Vision
Optimal Algorithm for Shape from Shading and Path Planning
Journal of Mathematical Imaging and Vision
Shape from Shading and Viscosity Solutions
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
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
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Coupled Lighting Direction and Shape Estimation from Single Images
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
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 Under Perspective Projection
International Journal of Computer Vision
Numerical methods for viscosity solutions and applications
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Shape-from-shading with discontinuous image brightness
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
A Unifying and Rigorous Shape from Shading Method Adapted to Realistic Data and Applications
Journal of Mathematical Imaging and Vision
Numerical methods for shape-from-shading: A new survey with benchmarks
Computer Vision and Image Understanding
Recovering Shape by Shading and Stereo Under Lambertian Shading Model
International Journal of Computer Vision
Estimating Facial Reflectance Properties Using Shape-from-Shading
International Journal of Computer Vision
Variable-Source Shading Analysis
International Journal of Computer Vision
A new shape from shading approach for specular surfaces
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part III
Driving 3D morphable models using shading cues
Pattern Recognition
Fast marching method for generic shape from shading
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations
SIAM Journal on Imaging Sciences
Reconstructing shape from dictionaries of shading primitives
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
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We describe a mathematical and algorithmic study of the Lambertian "Shape-From-Shading" problem for orthographic and pinhole cameras. Our approach is based upon the notion of viscosity solutions of Hamilton-Jacobi equations. This approach provides a mathematical framework in which we can show that the problem is well-posed (we prove the existence of a solution and we characterize all the solutions). Our contribution is threefold. First, we model the camera both as orthographic and as perspective (pinhole), whereas most authors assume an orthographic projection (see Horn and Brooks (1989) for a survey of the SFS problem up to 1989 and Zhang et al. (1999), Kozera (1998), Durou et al. (2004) for more recent ones); thus we extend the applicability of shape from shading methods to more realistic acquisition models. In particular it extends the work of Prados et al. (2002a) and Rouy and Tourin (1992). We provide some novel mathematical formulations of this problem yielding new partial differential equations. Results about the existence and uniqueness of their solutions are also obtained. Second, by introducing a "generic" Hamiltonian, we define a general framework allowing to deal with both models (orthographic and perspective), thereby simplifying the formalization of the problem. Thanks to this unification, each algorithm we propose can compute numerical solutions corresponding to all the modeling. Third, our work allows us to come up with two new generic algorithms for computing numerical approximations of the "continuous solution of the "Shape-From-Shading" problem as well as a proof of their convergence toward that solution. Moreover, our two generic algorithms are able to deal with discontinuous images as well as images containing black shadows.