As 3D digital photographic and scanning devices produce higher resolution images, acquired geometric data sets grow more complex in terms of the modeled objects’ size, geometry, texture, and topology. To use and analyze such data, developing new algorithms and techniques for shape registration and analysis has become a common and long-term mission in the computer vision and graphics field. In this dissertation, we propose a novel framework for shape matching, registration, and scientific analysis especially for 3D facial data and biomedical data. In particular, we address the challenges of 3D shape registration and analysis with noise, occlusion, resolution variation and non-rigid deformation.

Firstly, we analyze a family of quasi-conformal maps including harmonic maps, conformal maps, and least squares conformal maps with regards to 3D shape matching. As a result, we propose a novel and computationally efficient shape matching framework by using least squares conformal maps. The robustness of least squares conformal maps is evaluated and analyzed comprehensively in 3D shape matching with occlusion, noise, and resolution variation. In addition to the above conformal geometry approaches, we also propose a framework of shape registration and analysis using Ricci flow. Previous methods based on conformal geometries, such as harmonic maps and least squares conformal maps, which can only handle 3D shapes with simple topology are subsumed by our Ricci flow based method which can handle surfaces with complex topology. Furthermore, we introduce a method that constrains Ricci flow computation using feature points and feature curves. We also demonstrate the applicability of this intrinsic shape representation through standard shape analysis problems, such as 3D shape matching and registration.

As 3D scanning technologies continue to improve, dynamic densely-sampled 3D data is becoming more and more prevalent for analysis and synthesis. To study and analyze such huge data, an efficient non-rigid registration algorithm is necessary to establish one-to-one inter-frame correspondences automatically. Toward this goal, we present a new framework for automatic non-rigid registration of 3D dynamic facial data. Based on this registration framework, we also develop a new system of facial expression synthesis and transfer.

We have implemented our framework in a wide range of applications which represent the identified challenges in shape registration and analysis. This includes dynamic noise, occluded data, resolution variation, non-rigid deformation, etc. Furthermore, we describe these applications in detail and outline a few new applications which include surface matching, alignment and stitching, dynamic non-rigid deformable shape registration, facial expression synthesis and transfer.