Abstract
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.
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Noakes, L., Kozera, R. Nonlinearities and Noise Reduction in 3-Source Photometric Stereo. Journal of Mathematical Imaging and Vision 18, 119–127 (2003). https://doi.org/10.1023/A:1022104332058
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DOI: https://doi.org/10.1023/A:1022104332058