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In this paper, we propose a new algorithm that solves both the stereo matching and the image denoising problem simultaneously for a pair of noisy stereo images. Most stereo algorithms employ L1 or L2 intensity error-based data costs in the MAP-MRF framework by assuming the naive intensity-constancy. These data costs make typical stereo algorithms suffer from the effect of noise severely. In this study, a new robust stereo algorithm to noise is presented that performs the stereo matching and the image de-noising simultaneously. In our approach, we redefine the data cost by two terms. The first term is the restored intensity difference, instead of the observed intensity difference. The second term is the non-local pixel distribution dissimilarity around the matched pixels. We adopted the NL-means (non-local means) algorithm for restoring the intensity value as a function of disparity. And a pixel distribution dissimilarity is calculated by using PMHD (perceptually modified Hausdorff distance). The restored intensity values in each image are determined by inferring optimal disparity map at the same time. Experimental results show that the proposed algorithm is more robust and accurate than other conventional algorithms in both stereo matching and denoising.