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In this correspondence, we propose a wavelet-based hierarchical approach using mutual information (MI) to solve the correspondence problem in stereo vision. The correspondence problem involves identifying corresponding pixels between images of a given stereo pair. This results in a disparity map, which is required to extract depth information of the relevant scene. Until recently, mostly correlation-based methods have been used to solve the correspondence problem. However, the performance of correlation-based methods degrades significantly when there is a change in illumination between the two images of the stereo pair. Recent studies indicate MI to be a more robust stereo matching metric for images affected by such radiometric distortions. In this short correspondence paper, we compare the performances of MI and correlation-based metrics for different types of illumination changes between stereo images. MI, as a statistical metric, is computationally more expensive. We propose a wavelet-based hierarchical technique to counter the increase in computational cost and show its effectiveness in stereo matching.