| With the advent of active and passive 3D sensing techniques, 3D geometric data now plays vital roles in many applications. The geometric features of 3D object inherently scatters at varying scales. In order to accurately describe the geometry of 3D objects, a comprehensive method for extracting such scale-dependent 3D shape features becomes crucial for deriving a concise representation of the original shape. This dissertation exploits this hidden dimension of 3D geometry--the geometric scale variability, for a stable, scalable, compact shape representation which can effectively support matching and comparison of large-scale geometric data.;Based on the multiscale geometry representation, automatic non-rigid registration of 3D data is solved for the essential role it plays in a wide range of applications and its technical challenges. We model this problem from a novel perspective as diffeomorphic shape evolutions from one to the other, the merits of which include ensured smoothness, inherent topological preservation, invertibility, etc. As a plus, the shapes are studied in a more abstract space of diffeomorphisms. The optimal transition from one shape to another can be computed as a geodesic path that links the two shapes. A more general and in-depth understanding of surface shapes is provided in this dissertation, with an emphasis on shape matching.;The proposed framework has been successfully applied to multimodal neuro-imaging data analysis, which is demonstrated in the end. |
