Outlier Removal in 2D Leap Frog Algorithm

Overview & Synopsis

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.