We present an evolutionary measure for image matching that is based on the Ulam's distance. Given two strings, the Ulam's distance is the smallest number of mutations, insertions and deletions that can, be made within the strings such that the resulting substrings are identical. We reinterpret the Ulam's distance with respect to permutations that represent window intensities expressed on an ordinal scale. The motivation for using this measure is twofold: it not only gives a robust measure of correlation between windows but also helps in, identifying pixels that contribute to the agreement (or disagreement) between the windows. We investigate computational issues for efficient implementation of the measure. Experiments suggest the utility of the Ulam's distance in applications like stereo.

We present ordinal measures of association for image correspondence in the context of stereo. Linear correspondence measures like correlation and the sum of squared difference between intensity distributions are known to be fragile. Ordinal measures which are based on relative ordering of intensity values in windows-rank permutations-have demonstrable robustness. By using distance metrics between two rank permutations, ordinal measures are defined. These measures are independent of absolute intensity scale and invariant to monotone transformations of intensity values like gamma variation between images. We have developed simple algorithms for their efficient implementation. Experiments suggest the superiority of ordinal measures over existing techniques under nonideal conditions. These measures serve as a general tool for image matching that are applicable to other vision problems such as motion estimation and texture-based image retrieval.

We present a method for motion estimation using ordinal measures. Ordinal measures are based on relative ordering of intensity values in an image region called rank permutation. While popular measures like the sum-of-squared-difference (SSD) and normalized correlation (NCC) rely on linearity between corresponding intensity values, ordinal measures only require them to be monotonically related so that rank permutations between corresponding regions are presented. This property turns out to be useful for motion estimation in tagged magnetic resonance images. We study the imaging equation involved in two methods of tagging and observe temporal monotonicity in intensity under certain conditions though the tags themselves fade. We compare our method to SSD and NCC in a rotating ring phantom image sequence. We present an experiment on a real heart image sequence which suggests the suitability of our method.

We present ordinal measures for establishing image correspondence. 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 a novel distance metric between the rank permutations, we arrive at ordinal correlation coefficients. 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 have developed a simple algorithm for their efficient implementation. Experiments suggest the superiority of ordinal measures over existing techniques under non-ideal conditions. 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 image registration.

This paper presents algorithmic methods to generate progressive, whip-type motions, characteristic of experienced humans in high speed athletic activities like throwing and striking. In deriving these methods, we deduce boundary conditions for dynamic quantities by analysing the motion of a two-link system. A control algorithm based on cascading gains is introduced and is shown to be efficient when compared to fixed-gain proportional control. Principles of energy redistribution within links are used to explain the mechanical advantage gained by a whip-type motion, and the efficiency of cascading gain control. The results can be applied in motion synthesis for animation which is demonstrated through simulation of a multi-link system. Our aim has been to obtain biomechanically plausible solutions which approximate natural motions.

The problem of accurate depth estimation using stereo in the presence of specular reflection is addressed. Specular reflection, a fundamental and ubiquitous reflection mechanism, is viewpoint dependent and can cause large intensity differences at corresponding points, resulting in significant depth errors. We analyze the physics of specular reflection and the geometry of stereopsis which led us to a relationship between stereo vergence, surface roughness, and the likelihood of a correct match. Given a lower bound on surface roughness, an optimal binocular stereo configuration can be determined which maximizes precision in depth estimation despite specular reflection. However, surface roughness is difficult to estimate in unstructured environments. Therefore, trinocular configurations, independent of surface roughness, are determined such that at each scene point visible to all sensors, at least one stereo pair can compute produce depth. We have developed a simple algorithm to reconstruct depth from the multiple stereo pairs.>