Gaussian Process Morphable Models for Spatially-Varying Multi-Scale Registration

Registration is crucial for the automated analysis of shapes and images. Its purpose is to establish point-to-point correspondence between a population of shapes or images of the same kind. Obtaining correspondence is a difficult problem and depends profoundly on different factors that change from dataset to dataset. A successful outcome of a registration does depend on how much knowledge about the specific dataset can be incorporated. There is a growing body of literature in the field of medical image analysis and computer vision about image considering registration, of which most lack a clear concept on how to integrate prior knowledge.
In this thesis, expert knowledge is integrated by modeling it as a Gaussian process model. We build upon the Gaussian Process Morphable Model (GPMM) framework, whose concept it is to cleanly separate the incorporation of prior knowledge from the general registration algorithm. In this thesis, we keep the general idea of the GPMM and extend its modeling capabilities as a first main contribution. We describe how important registration concepts, such as multiple levels of details and spatially varying deformations can be unified using kernel modeling and how they can be applied to practical examples, such as the registration of faces.
The high flexibility of modeling with kernels also impacts the second main contribution in this thesis: the low-rank approximation, where the GPMM is parameterized with a set of basis functions. In contrast to the initially proposed solution, our method has a known approximation accuracy and does not rely on the customization of additional parameters. Moreover, we present an alternative basis function for the Gaussian process morphable models, which enable a recursive refinement of the model approximation.
The applicability of all the proposed methods is demonstrated with three applications: the registration of human faces and facial expressions, the image volume registration of the human Ulna and the modeling of pathological shapes. In theory, as well as in practice, the contributions take the registration and fitting with Gaussian process morphable models a big step forward.