CURVATURE-BASED APPROACH TO POINT CORRESPONDENCE RECOVERY IN CONFORMAL NONRIGID MOTION

This paper describes a novel method for the estimation of point corres pondences on a surface undergoing conformal nonrigid motion based on c hanges in its Gaussian curvature. The use of Gaussian curvature in non rigid motion analysis is justified by its invariancy towards rigid mot ion and the type of surface parameterization. Input to the algorithm i s the set of 3D points before and after the motion. We deal with a res tricted class of nonrigid motion called conformal motion. In conformal motion, the stretching is equal in all directions, but different at d ifferent points. Small motion assumption is utilized to hypothesize al l possible point correspondences. Curvature changes are then computed for each hypothesis. Finally, the error between computed curvature cha nges and the one predicted by the conformal motion assumption is calcu lated. The hypothesis with the smallest error gives point corresponden ces between consecutive time frames. The algorithm requires calculatio n of the Gaussian curvature at points on surface before and after the motion. It also requires computation of the coefficients of the first fundamental form at points on surface before the motion. Estimation of point correspondences and stretching can also be refined so as to red uce the error introduced by sampling. Simulations are performed on an ellipsoidal data to illustrate performance and accuracy of derived alg orithms. Then, the proposed algorithm is applied to volumetric CT data of the left ventricle (LV) of a dog's heart. Stretching of the LV wal l during its expansion and contraction phases is depicted along with t he estimated point correspondences. Stretching comparisons are made be tween the normal and abnormal LV. (C) 1994 Academic Press, Inc.