Volumetric morphometrics

Geometric morphometrics (GMM) methods are very popular in physical anthropology. One disadvantage common to the existingGMM methods is that despite significant advancements in computed tomography (CT) and magnetic resonance imaging (MRI)technology, these methods still depend on landmarks or features that are either digitized directly from subject surface or extractedfrom surface models or outlines derived from a laser surface scan or from a CTor MRI scan. All the rest image contents contained ina CTor MRI scan are ignored by these methods. In this paper, we present a complementary solution called Volumetric Morphometrics(VMM). With VMM, we are aiming for a paradigm shift from landmarks and surfaces used in existing GMM approaches todisplacements and volumes in the new VMM approaches, taking the full advantage of modern CTand MRI technology. Preliminaryvalidation results on ancient human skulls are presented.

Expectation Conditional Maximization-Based Deformable Shape Registration

This paper addresses the issue of matching statistical and non-rigid shapes, and introduces an Expectation Conditional Maximization-based deformable shape registration (ECM-DSR) algorithm. Similar to previous works, we cast the statistical and non-rigid shape registration problem into a missing data framework and handle the unknown correspondences with Gaussian Mixture Models (GMM). The registration problem is then solved by fitting the GMM centroids to the data. But unlike previous works where equal isotropic covariances are used, our new algorithm uses heteroscedastic covariances whose values are iteratively estimated from the data. A previously introduced virtual observation concept is adopted here to simplify the estimation of the registration parameters. Based on this concept, we derive closed-form solutions to estimate parameters for statistical or non-rigid shape registrations in each iteration. Our experiments conducted on synthesized and real data demonstrate that the ECM-DSR algorithm has various advantages over existing algorithms.