TY - THES A1 - Lamecker, Hans T1 - Variational and statistical shape modeling for 3D geometry reconstruction N2 - The reconstruction of geometric shapes plays an important role in many biomedical applications. One example is the patient-specific, computer-aided planning of complex interventions, which requires the generation of explicitly represented geometric models of anatomical structures from medical image data. Only solutions that require minimal interaction by medical personnel are likely to enter clinical routine. Another example is the planning of surgical corrections of deformities where the target shape is unknown. Surgeons are often forced to resort to subjective criteria. These applications still pose highly challenging reconstruction problems, which are addressed in this thesis. The fundamental hypothesis, pursued in this thesis, is that the problems can be solved by incorporating a-priori knowledge about shape and other application-specific characteristics. Here, we focus mainly on the aspect of geometric shape analysis. The basic idea is to capture the most essential variations of a certain class of geometric objects via statistical shape models, which model typical features contained in a given population, and restrict the outcome of a reconstruction algorithm (more or less) to the space spanned by such models. A fundamental prerequisite for performing statistical shape analysis on a set of different objects is the identification of corresponding points on their associated surfaces. This problem is particularly difficult to solve if the shapes stem from different individuals. The reason lies in the basic difficulty of defining suitable measures of similarity. In this thesis, we divide the correspondence problem into feature and non-feature matching. The feature part depends on the application, while the non-feature part can be characterized by a purely geometric description. We propose two different approaches. The first approach has proved useful in many applications. Yet, it suffers from some practical limitations and does not yield a measure of similarity. Our second, variational, approach is designed to overcome these limitations. In it, we propose to minimize an invariant stretching measure, constrained by previously computed features. An important property, which sets our method apart from previous work, is that it does not require the computation of a global surface parameterization. KW - correspondence problem KW - surface matching KW - image segmentation KW - model-based shape reconstruction KW - 2d-3d shape reconstruction Y1 - 2008 UR - http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000005805 ER - TY - GEN A1 - Lamecker, Hans A1 - Lange, Thomas A1 - Seebass, Martin T1 - Segmentation of the Liver using a 3D Statistical Shape Model N2 - This paper presents an automatic approach for segmentation of the liver from computer tomography (CT) images based on a 3D statistical shape model. Segmentation of the liver is an important prerequisite in liver surgery planning. One of the major challenges in building a 3D shape model from a training set of segmented instances of an object is the determination of the correspondence between different surfaces. We propose to use a geometric approach that is based on minimizing the distortion of the correspondence mapping between two different surfaces. For the adaption of the shape model to the image data a profile model based on the grey value appearance of the liver and its surrounding tissues in contrast enhanced CT data was developed. The robustness of this method results from a previous nonlinear diffusion filtering of the image data. Special focus is turned to the quantitative evaluation of the segmentation process. Several different error measures are discussed and implemented in a study involving more than 30 livers. T3 - ZIB-Report - 04-09 KW - Statistical Shape Model KW - 3D Correspondence Problem KW - Model-Based Segmentation KW - Diffusion Filtering KW - Geometric Distortion KW - Surface Distance Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7847 ER - TY - GEN A1 - Sander, Oliver A1 - Runge, Daniel T1 - Fast Surface Reconstruction Using a Probe Sphere N2 - We introduce a new method for reconstructing a triangular surface from an unorganized set of points in space. It is based on placing a probe sphere on the point set and rolling it around, connecting all triples of points with a triangle that the sphere comes to rest on. Therefore, the algorithm interpolates, rather than approximates, the input points. The method needs considerably less running time than previous algorithms and yields good results on point sets that are reasonably well-behaved. T3 - ZIB-Report - 00-50 KW - Surface Reconstruction KW - Computational Geometry Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6181 ER -