A Method for Enforcing Integrability in Shape from Shading Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct Analytical Methods for Solving Poisson Equations in Computer Vision Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape from shading
Height and gradient from shading
International Journal of Computer Vision
Integrability disambiguates surface recovery in two-image photometric stereo
International Journal of Computer Vision
Existence and uniqueness in photometric stereo
Applied Mathematics and Computation
Robot Vision
Computer Vision: Three-Dimensional Data from Images
Computer Vision: Three-Dimensional Data from Images
The 2-D leap-frog: integrability, noise, and digitization
Digital and image geometry
Noise Reduction in Surface Reconstruction from a Given Gradient Field
International Journal of Computer Vision
Denoising images: non-linear leap-frog for shape and light-source recovery
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Outlier removal in 2d leap frog algorithm
CISIM'12 Proceedings of the 11th IFIP TC 8 international conference on Computer Information Systems and Industrial Management
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1-D Leap-Frog (L. Noakes, J. Math. Australian Soc. A, Vol. 64, pp. 37–50, 1999) is an iterative scheme for solving a class of nonquadratic optimization problems. In this paper a 2-D version of Leap-Frog is applied to a non optimization problem in computer vision, namely the recovery (so far as possible) of an unknown surface from 3 noisy camera images. This contrasts with previous work on photometric stereo, in which noise is added to the gradient of the height function rather than camera images. Given a suitable initial guess, 2-D Leap-Frog is proved to converge to the maximum-likelihood estimate for the vision problem. Performance is illustrated by examples.