A Branch and Bound Algorithm for Globally Optimal Photometric Stereo Using Color Image Inputs

초록

This paper proposes a branch-and-bound(BnB) global optimization algorithm to compute the shape and the albedo of the object surface when the measurements consist of color images. It is difficult to find the global solution for a photometric stereo problem because the error function of surface albedo and normal is highly non-linear and non-convex. The BnB algorithm is developed to enable the efficient global search over a non-convex space. We adopted the BnB algorithm to the photometric stereo problem with multi-channel input. The L2-norm errors are minimized for which three ingredients are devised: 1) an appropriate scheme of representation and sub-division of the search domain, 2) a feasibility problem given a sub-domain, and 3) a solution method to solve the problem. Experimental results of synthetic and real data are also presented to qualify our method. We evaluated the relative performance of the BnB algorithm compared to the Newton's method as local optimization.

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