3D nonrigid motion analysis under small deformations

We present a novel method for estimating motion parameters and point correspondences between 3D surfaces under small nonrigid motion. A vector point function is utilized as the motion parameter, called the displacement function. Differential-geometric changes of surfaces are then used in tracking small deformations. Discriminant (of first fundamental form), unit-normal and Gaussian curvature are the invariant differential-geometric parameters that have been utilized for nonrigid motion analysis. Tests were performed by generating nonrigid motion on a simulated data set to illustrate performance and accuracy of our algorithms. Experiments were then performed on a Cyberware range data sequence of facial motion. A total of 16 sets of facial motion images were used in our experiments, belonging to eight different persons, each having two facial expressions. We have demonstrated the correct point correspondence recovery by tracking features of the face during each facial expression and comparing against the manual tracking of feature points by different users. In addition, nonrigid motion segmentation and interpolation of intermediate frames of data were successfully performed on these images. We have also performed experiments on cardiac data in order to estimate the motion parameters related to the abnormality in cardiac motion. Two sets of volumetric CT data of the left ventricle of a dog’s heart in cardiac cycle were used in our experiments. All our experiments indicate that the system performs very well and proves to be extremely useful in other nonrigid motion analysis applications. q 2002 Elsevier Science B.V. All rights reserved.