Shape from shading
Height and gradient from shading
International Journal of Computer Vision
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
On convergence in the methods of Strat and of Smith for shape from shading
International Journal of Computer Vision
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
Shape from Shading and Viscosity Solutions
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Shape-from-Shading Under Perspective Projection
International Journal of Computer Vision
Reillumination-driven shape from shading
Computer Vision and Image Understanding
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
A fast marching formulation of perspective shape from shading under frontal illumination
Pattern Recognition Letters
High frequency and numerical Eulerian methods for aeroacoustic problems
Journal of Computational and Applied Mathematics
Shape-from-shading for oblique lighting with accuracy enhancement by light direction optimization
EURASIP Journal on Applied Signal Processing
Numerical methods for shape-from-shading: A new survey with benchmarks
Computer Vision and Image Understanding
Photometric and geometric restoration of document images using inpainting and shape-from-shading
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Reillumination-driven shape from shading
Computer Vision and Image Understanding
Shape-from-shading algorithm for oblique light source
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
Variable-Source Shading Analysis
International Journal of Computer Vision
Spherical surface parameterization for perspective shape from shading
Pattern Recognition Letters
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This article presents an approach to the shape from shading problem which is based upon the notion of viscosity solutions to the shading partial differential equation, in effect a Hamilton-Jacobi equation. The power of this approach is twofolds: 1) it allows nonsmooth, i.e. nondifferentiable, solutions which allows to recover objects with sharp troughs and creases and 2) it provides a framework for deriving a numerical scheme for computing approximations on a discrete grid of these solutions as well as for proving its correctness, i.e. the convergence of these approximations to the solution when the grid size vanishes.Our work extends previous work in the area in three aspects. First, it deals with the case of a general illumination in a simpler and a more general way (since they assume that the solutions are continuously differentiable) than in the work of Dupuis and Oliensis [9]. Second, it allows us to prove the existence and uniqueness of "continuous" solutions to the shading equation in a more general setting (general direction of illumination) than in the work of Rouy and Tourin [24], thereby extending the applicability of shape from shading methods to more realistic scenes. Third, it allows us to produce an approximation scheme for computing approximations of the "continuous" solution on a discrete grid as well as a proof of their convergence toward that solution.