Pre-organizing Shape Instances for Landmark-Based Shape Correspondence

The major challenge in constructing a statistical shape model for a structure is shape correspondence, which identifies a set of corresponded landmarks across a population of shape instances to accurately estimate the underlying shape variation. Both global or pairwise shape-correspondence methods have been developed to automatically identify the corresponded landmarks. For global methods, landmarks are found by optimizing a comprehensive objective function that considers the entire population of shape instances. While global methods can produce very accurate shape correspondence, they tend to be very inefficient when the population size is large. For pairwise methods, all shape instances are corresponded to a given template independently. Therefore, pairwise methods are usually very efficient. However, if the population exhibits a large amount of shape variation, pairwise methods may produce very poor shape correspondence. In this paper, we develop a new method that attempts to address the limitations of global and pairwise methods. In particular, we first construct a shape tree to globally organize the population of shape instances by identifying similar shape instance pairs. We then perform pairwise shape correspondence between such similar shape instances with high accuracy. Finally, we combine these pairwise correspondences to achieve a unified correspondence for the entire population of shape instances. We evaluate the proposed method by comparing its performance to five available shape correspondence methods, and show that the proposed method achieves the accuracy of a global method with the efficiency of a pairwise method.