Ordinal Measures for Visual Correspondence

We present ordinal measures of association for establishing visual correspondence in images. Linear correspondence measures like correlation and the sum of squared differences are known to be fragile. Ordinal measures, which are based on relative ordering of intensity values in windows, have demonstrable robustness to depth discontinuities, occlusion, and noise. The relative ordering of intensity values in each window is represented by a rank permutation which is obtained by sorting the corresponding intensity data. By using distance metrics between the rank permutations of windows, ordinal correlation coefficients can be arrived at. These coefficients are independent of absolute intensity scale, i.e they are normalized measures. Further, since rank permutations are invariant to monotone transformations of the intensity values, the coefficients are unaffected by nonlinear effects like gamma variation between images. We discuss two crucial properties of ordinal measures for stereo application, namely, robustness and discriminatory power. We have developed simple algorithms for efficient implementation of the ordinal correlation coefficients. Experiments on synthetic images suggest the superiority of ordinal measures over existing techniques under non-ideal conditions. We also present experiments on real images which indicate the applicability of ordinal measures for practical application. Though we present ordinal measures in the context of stereo, they serve as a general tool for image matching that is applicable to other vision problems such as motion estimation and texture-based image retrieval.