Spatio-temporal tracking of material shape change via multi-dimensional splines

A new method for modeling shape changes in multidimensional image sequences of deforming objects is presented. The method consists of defining an orthogonal coordinate system on the segmented object in the first image frame and then calculating the deformations of this coordinate system over time. The deformations are found by minimizing an energy functional that consists of a linear combination of a data fidelity term and a shape-change constraint term. The shape-change constraint is based on the differential geometric properties of the parametrized material coordinate system. The deforming material coordinate system models an object´s shape changes both locally and globally. The mathematics is first developed for an n-dimensional sequence of images. Examples are given for both 2D and 3D image sequences of both real and synthetic images