Curvature-based algorithms for non-rigid motion and correspondence estimation

Two new algorithms for estimation of non-rigid motion in range data in the absence of correspondence information are presented. We derive a new relationship between Gaussian curvatures and other differential- geometric parameters before and after small deformation. This relationship depends linearly on derivatives of a motion model, which provides a closed-form, least squares solution for motion estimation. The first algorithm built solely on the new relationship demonstrates significant improvement of motion and correspondence estimation accuracy on certain artificial shapes; however, its poor numerical conditioning results in higher error in the presence of inaccurate values of differential-geometric parameters. The second algorithm combines the Gaussian curvature relationship with the previously known relationship between unit normals before and after deformation. The combined algorithm achieves higher accuracy of motion and correspondence estimation.