We propose a method for estimating inherent surface color robustly against image noises from two registered images taken under different outdoor illuminations. We formulate the estimation based on maximum likelihood manner while considering both inter-pixel and intra-pixel relationships. We define inter-pixel relationship based on stochastic behavior of image noises and properties of outdoor illumination chromaticity. We rely on the spatial continuity of both surface color and illumination to define intra-pixel relationship. We also propose to maximize the estimation function in two step manner. Experimental results demonstrate the significant improvement of the proposed method in estimation accuracy compared to previous methods.