In the research literature, maximum likelihood principles were applied to stereo matching by altering the stereo pair so that the difference would have a Gaussian distribution. In this paper we present a novel method of applying maximum likelihood to stereo matching. In our approach, we measure the real noise distribution from a training set, and then construct a new metric which we denote the maximum likelihood metric for comparing the stereo pair. The maximum likelihood metric is optimal in the sense that it maximizes the probability of similarity. In our experiments and discussion, we compared the maximum likelihood metric to other promising algorithms from the research literature using international stereo data sets. Furthermore, we showed that the algorithms from the research literature could be improved by using the maximum likelihood metric instead of the sum of squared differences.