Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Integrability disambiguates surface recovery in two-image photometric stereo
International Journal of Computer Vision
Existence and uniqueness in photometric stereo
Applied Mathematics and Computation
On Photometric Issues in 3D Visual Recognition from aSingle 2D Image
International Journal of Computer Vision
Computer Vision and Image Understanding
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
Reconstruction of Medical Images by Perspective Shape-from-Shading
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Shape-from-Shading Under Perspective Projection
International Journal of Computer Vision
Photometric Stereo under Perspective Projection
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Photometric Stereo with General, Unknown Lighting
International Journal of Computer Vision
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Generic Scene Recovery Using Multiple Images
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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
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Shape-from-Shading and photometric stereo are two fundamental problems in Computer Vision aimed at reconstructing surface depth given either a single image taken under a known light source or multiple images taken under different illuminations, respectively. Whereas the former utilizes partial differential equation (PDE) techniques to solve the image irradiance equation, the latter can be expressed as a linear system of equations in surface derivatives when 3 or more images are given. It therefore seems that current photometric stereo techniques do not extract all possible depth information from each image by itself. This paper utilizes PDE techniques for the solution of the combined Shape-from-Shading and photometric stereo problem when only 2 images are available. Extending our previous results on this problem, we consider the more realistic perspective projection of surfaces during the photographic process. Under these assumptions, there is a unique weak (Lipschitz continuous) solution to the problem at hand, solving the well known convex/concave ambiguity of the Shape-from-Shading problem. We propose two approximation schemes for the numerical solution of this problem, an up-wind finite difference scheme and a Semi-Lagrangian scheme, and analyze their properties. We show that both schemes converge linearly and accurately reconstruct the original surfaces. In comparison with a similar method for the orthographic 2-image photometric stereo, the proposed perspective one outperforms the orthographic one. We also demonstrate the method on real-life images. Our results thus show that using methodologies common in the field of Shape-from-Shading it is possible to recover more depth information for the photometric stereo problem under the more realistic perspective projection assumption.