Shape from shading
Existence and uniqueness in photometric stereo
Applied Mathematics and Computation
Robot Vision
Nonlinearities and Noise Reduction in 3-Source Photometric Stereo
Journal of Mathematical Imaging and 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
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In this paper a 2D Leap Frog Algorithm is applied to solve the so-called noisy Photometric Stereo problem. In 3-source Photometric Stereo (noiseless or noisy) an ideal unknown Lambertian surface is illuminated from distant light-source directions (their directions are assumed to be linearly independent). The subsequent goal, given three images is to reconstruct the illuminated object's shape. Ultimately, in the presence of noise, this problem leads to a highly non-linear optimization task with the corresponding cost function having a large number of independent variables. One method to solve it is 2D Leap Frog Algorithm. During reconstruction, problem that commonly arises, renders the outliers generated in the retrieved shape. In this paper we implement 2D Leap Frog. In particular we focus on choosing snapshot size and on invoking two algorithms that can remove outliers from reconstructed shape. Performance of extended 2D Leap Frog is illustrated by examples chosen especially to demonstrate how this solution is applicable in computer vision. Remarkably, this optimization scheme can also be used for an arbitrary optimization problem depending on large number of variables.