Nonrigid shape correspondence for statistical shape analysis

Statistical Shape Analysis has become a very important tool in medical imaging and image processing due to its ability to extract the shape information and shape variation of an anatomic structure from a set of random shape instances. Prior research has revealed that the accuracy of Statistical Shape Analysis and the resultant statistical shape modeling is highly dependent upon the accuracy of shape correspondence. Shape correspondence is the process which aligns a given set of shape instances by finding a set of corresponded landmark points across them. This thesis presents a systematic investigation of shape correspondence in which several new methods of shape correspondence are developed using the thin-plate model to describe nonrigid shape variation across individual biologic and anatomic shape instances. First, a new general method to complete shape correspondence is developed. Different from prior shape-correspondence methods, this method explicitly considers several factors that are known to be important in Statistical Shape Analysis to measure the shape-correspondence error: landmark-correspondence error, topology preservation, shape-representation error, and landmark sampling rate. Based on these factors, a landmark-sliding algorithm is developed to achieve highly accurate corresponded landmarks. Second, this thesis presents a method to get an improved initial estimate of the corresponded landmarks to address the partial-shape correspondence problem. This problem arises when a one-to-one mapping of correspondence across all shape instances does not exist. To evaluate the performance of these developed methods, quantitative experiments are performed on several data sets of shape instances extracted from medical images as well as artificially constructed data sets with a known ground-truth result. An empirical study is conducted to compare the new methods to the current state-of-the-art Minimum Description Length method.