Image segmentation is an important and challenging task in medical image analysis. Especially from low-quality images, segmentation algorithms have to cope with misleading background clutter, insufficient object boundaries and noise in the image. Statistical shape models are a powerful tool to tackle these problems. However, their construction as well as their application for segmentation remain challenging. In this thesis, we focus on the wisdom-tooth shape and its segmentation from Cone Beam Computed Tomography images. The large shape variation leads to difficult registration problems and an often too restrictive shape model, while the challenging appearance of the wisdom tooth makes the model fitting difficult.
To tackle these problems, we follow on kernel-based approaches to registration and shape modeling. We introduce a kernel, which considers landmarks as an additional prior in image registration. This allows
to locally improve the registration accuracy. We present a Demons-like registration method with an inhomogeneous regularization which allows to apply such a landmark kernel.
For modeling the shape variation, we construct a kernel comprising a generic smoothness and an empirical sample covariance. With this combined kernel, we increase the flexibility of the statistical shape model. We make use of a reproducing kernel Hilbert space framework for registration, where we apply this combined kernel as reproducing kernel. To make the approach computationally feasible, we perform a low-rank
approximation of the specific kernel function.
Because of a heterogeneous appearance inside the wisdom tooth, fitting the statistical model to plain intensity images is difficult. We build a nonparametric appearance model, based on random forest regression, which abstracts the raw images to semantic probability maps. Hence, the misleading structures become semantic values, which greatly simplificates the shape model fitting
