A Convex Optimization Approach for Depth Estimation Under Illumination Variation

Abstract—Illumination changes cause serious problems in many computer vision applications. We present a new method for ad-dressing robust depth estimation from a stereo pair under varying illumination conditions. First, a spatially varying multiplicative model is developed to account for brightness changes induced between left and right views. The depth estimation problem, based on this model, is then formulated as a constrained optimization problem in which an appropriate convex objective function is minimized under various convex constraints modelling prior knowledge and observed information. The resulting multicon-strained optimization problem is finally solved via a parallel block iterative algorithm which offers great flexibility in the incorpora-tion of several constraints. Experimental results on both synthetic and real stereo pairs demonstrate the good performance of our method to efficiently recover depth and illumination variation fields, simultaneously. Index Terms—Convex constraints, convex optimization, depth estimation, illumination variation, regularization, set theoretic es-timation, stereo vision, total variation, variational methods. I