Correct extraction of fine structures in the field of medical image processing is a challenging task. It constitutes a crucial prerequisite for further automated analysis and quantification tasks, as well as for surgery planning/simulation and for determining the type of surgery, e.g. minimal invasive or open intervention.
Due to changing topologies and minuscule sizes, fine structures can be easily overlooked by current segmentation techniques or confounded with other entities or artifacts. Therefore, this thesis proposes methods for a reliable extraction of fine structures in medical images.

It will be differentiated between structures surrounding objects such as bones, heart, lungs, which possess Similar Basic Morphology (SBM) and, secondly, fine structures of Extreme Inter-Patient Variability (EIPV). The similar basic inter-patient morphology of SBM fine structures endorses usage of geometrical form models for their extraction. On the other hand, EIPV structures mostly arise/deviate from the healthy case following pathologies or injuries (e.g., the aortic dissection membrane, bone/cartilage lesions) or reveal a high inter-patient variability regarding topology and/or morphology by their inherent nature (e.g., the retinal vessel network).
Therefore, this thesis proposes spatial, as well as spectral local signal models for their extraction, since the high variability requires models operating on a more basic level, closely related to the image formation process. Exemplarily focusing on a vascular and an orthopedic application, namely Aortic Dissections in CTA and Femoroacetabular Impingement in MRI, the sought fine structures are the aortic boundaries (SBM) and the dissection membrane (EIPV), respectively the surfaces of femoral head and acetabulum (SBM).

In case of SBM structures this thesis further differentiates between 1-manifolds and 2-manifolds. Longish objects, which possess a centerline without ramifications, are defined as intrinsic almost 1-manifolds (briefly referred to as 1-manifolds). Delineating the boundaries of such tubular entities can be achieved by space transformation (e.g., 3D to 2D) and serialization. The simplification given by planes extracted orthogonally to the centerline endorses direct parameter estimation for segmentation of 1-manifolds.
Detection of the aorta lumen boundary via enforcing cross-sectional continuity by graph optimisation proves itself as a robust approach in this case. On the other hand, 2-manifolds with SBM possess a more complex morphology and are handled in 3D by two successive steps of iterative parameter adaption.
As an example, the surfaces of the femoral head and acetabulum are extracted utilizing a three-stage registration process followed by active models.

For delineating the aortic dissection membrane (2-manifolds with EIPV) this dissertation employs spectral, respectively spatial filterbank techniques in order to retrieve multiple orientations and scales of the fine structure. Spectral phase congruency as well as a spatial template filter serve to discern EIPV structures with discountinuous appearance embedded within a noisy environment. In order to demonstrate the feasibility of our proposed segmentation techniques also in case of 1-manifolds with EIPV, both types of local signal models (i.e., spectral and spatial) are being applied for segmenting the retinal vessel network in optical 2D image data. Extraction of such networked structures has been extensively covered by the medical image processing community, so that this chapter is solely treated as an excursion.

This thesis represents the first contribution to address segmentation of true lumen and thrombosed false lumen in case of aortic dissections. Such an endeavour poses a great challenge, since the coagulated blood forming the thrombus leads to a poor differentiation from surrounding tissue outside the aorta. A combination of batch, respectively sequential machine learning methods and local spectral signal models is proposed within an excursion in the field of Machine Learning by Support Vector Machines or k Nearest Neigbors classifiers.

Determining the inner and outer 3D surface lengths of the ascending aorta and the validation against ground truth of their quantification represents a step towards enabling minimally invasive techniques within the ascending aorta by manufacturing patient-specific stent-grafts.
Regarding the membrane extraction, this thesis proposes an algorithm for completing missing parts while removing false positive filter responses. The handling of heterogeneous datasets of different capture areas and anisotropic voxel sizes in case of the hip joint is tackled by a three-stage registration scheme in combination with adapted statistical models.