  Shape registration is the process of aligning one 3D model to another. Most
previous methods to align shapes with no known correspondences attempt to solve
for both the transformation and correspondences iteratively. We present a shape
registration approach that solves for the transformation using fuzzy
correspondences to maximize the overlap between the given shape and the target
shape. A coarse to fine approach with Levenberg-Marquardt method is used for
optimization. Real and synthetic experiments show our approach is robust and
outperforms other state of the art methods when point clouds are noisy, sparse,
and have non-uniform density. Experiments show our method is more robust to
initialization and can handle larger scale changes and rotation than other
methods. We also show that the approach can be used for 2D-3D alignment via
ray-point alignment.
