This paper proposes a novel local color correction algorithm that uses three dimensional (3D) point set registration especially for underwater stereo images. Due to the limited visibility in an underwater environment, underwater stereo images are usually captured by a half-mirror-based stereo camera that helps to prevent the unwanted visual fatigues induced by excessive disparities. However, the interaction between the half mirror and the scattered light components in the water may produce strong local color discrepancies. Thus, the proposed algorithm extracts sufficient information on the entire image area between the left and right images using 3D point set registration to counteract these effects. Since the proposed algorithm simultaneously processes all three color channels in the local color space, it is robust to the strong local color discrepancies in underwater stereo images. The proposed algorithm is both subjectively and objectively evaluated by comparing the histograms, the color similarities, and the disparity images before and after color correction. After color correction, the proposed algorithm achieves a color similarity up to 96.67%, while other conventional algorithms show color similarities only up to 90.66%. Although the proposed algorithm is designed for underwater stereo images, it can be used for various stereo images and applications.