Shape Registration by Simultaneously Optimizing Representation and Transformation

This paper proposes a novel approach that achieves shape registration by optimizing shape representation and transformation simultaneously, which are modeled by a constrained Gaussian Mixture Model (GMM) and a regularized thin plate spline respectively. The problem is formulated within a Bayesian framework and solved by an expectation-maximum (EM) algorithm. Compared with the popular methods based on landmarks-sliding, its advantages include: (1) It can naturally deal with shapes of complex topologies and 3D dimension; (2) It is more robust against data noise; (3) The registration performance is better in terms of the generalization error of the resultant statistical shape model. These are demonstrated on both synthetic and biomedical shapes.