Nonlinearities and noise reduction in 3-source photometric stereo

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.