In this paper, we propose a novel and robust algorithm for the groupwise non-rigid registration of multiple unlabeled point-sets with no bias toward any of the given pointsets. To quantify the divergence between multiple probability distributions each estimated from the given point sets, we develop a novel measure based on their cumulative distribution functions that we dub the CDF-JS divergence. The measure parallels the well known Jensen-Shannon divergence (defined for probability density functions) but is more regular than the JS divergence since its definition is based on CDFs as opposed to density functions. As a consequence, CDF-JS is more immune to noise and statistically more robust than the JS. We derive the analytic gradient of the CDF-JS divergence with respect to the non-rigid registration parameters for use in the numerical optimization of the groupwise registration leading a computationally efficient and accurate algorithm. The CDF-JS is symmetric and has no bias toward ...
Fei Wang, Baba C. Vemuri, Anand Rangarajan