NDLI: A Generic and Provably Convergent Shape-from-Shading Method for Orthographic and Pinhole Cameras

Content Provider	Springer Nature Link
Author	Prados, Emmanuel Faugeras, Olivier
Copyright Year	2005
Abstract	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.
Starting Page	97
Ending Page	125
Page Count	29
File Format	PDF
ISSN	09205691
Journal	International Journal of Computer Vision
Volume Number	65
Issue Number	1-2
e-ISSN	15731405
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-10-14
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	shape from shading Lambertian reflectance pinhole camera orthographic and perspective projection black shadows discontinuous images viscosity solutions Pattern Recognition Artificial Intelligence (incl. Robotics) Computer Imaging, Graphics and Computer Vision Image Processing
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Vision and Pattern Recognition Software

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