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The reconstruction of an object's shape or surface from a set of 3D points is a common topic in materials and life sciences, computationally handled in computer graphics. Such points usually stem from optical or tactile 3D coordinate measuring equipment. Surface reconstruction also appears in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or the alignment of intra-operative navigation and preoperative planning data. In contrast to mere 3D point clouds, medical imaging yields contextual information on the 3D point data that can be used to adopt prior information on the shape that is to be reconstructed from the measurements. In this work we propose to use a statistical shape model (SSM) as a prior for surface reconstruction. The prior knowledge is represented by a point distribution model (PDM) that is associated with a surface mesh. Using the shape distribution that is modelled by the PDM, we reformulate the problem of surface reconstruction from a probabilistic perspective based on a Gaussian Mixture Model (GMM). In order to do so, the given measurements are interpreted as samples of the GMM. By using mixture components with anisotropic covariances that are oriented according to the surface normals at the PDM points, a surface-based tting is accomplished. By estimating the parameters of the GMM in a maximum a posteriori manner, the reconstruction of the surface from the given measurements is achieved. Extensive experiments suggest that our proposed approach leads to superior surface reconstructions compared to Iterative Closest Point (ICP) methods.
Deformable model-based approaches to 3D image segmentation have been shown to be highly successful. Such methodology requires an appearance model that drives the deformation of a geometric model to the image data. Appearance models are usually either created heuristically or through supervised learning. Heuristic methods have been shown to work effectively in many applications but are hard to transfer from one application (imaging modality/anatomical structure) to another. On the contrary, supervised learning approaches can learn patterns from a collection of annotated training data. In this work, we show that the supervised joint dictionary learning technique is capable of overcoming the traditional drawbacks of the heuristic approaches. Our evaluation based on two different applications (liver/CT and knee/MR) reveals that our approach generates appearance models, which can be used effectively and efficiently in a deformable model-based segmentation framework.
Statistical shape models (SSM) describe the shape variability contained in a given population. They are able to describe large populations of complex shapes with few degrees of freedom. This makes them a useful tool for a variety of tasks that arise in computer-aided madicine. In this chapter we are going to explain the basic methodology of SSMs and present a variety of examples, where SSMs have been successfully applied.