The reconstruction of an object's shape or surface from a set of 3D pointsplays an important role in medical image analysis, e.g. in anatomyreconstruction from tomographic measurements or in the process of aligningintra-operative navigation and preoperative planning data. In such scenarios,one usually has to deal with sparse data, which significantly aggravates theproblem of reconstruction. However, medical applications often providecontextual information about the 3D point data that allow to incorporate priorknowledge about the shape that is to be reconstructed. To this end, we proposethe use of a statistical shape model (SSM) as a prior for surfacereconstruction. The SSM is represented by a point distribution model (PDM),which is associated with a surface mesh. Using the shape distribution that ismodelled by the PDM, we formulate the problem of surface reconstruction from aprobabilistic perspective based on a Gaussian Mixture Model (GMM). In order todo so, the given points are interpreted as samples of the GMM. By using mixturecomponents with anisotropic covariances that are "oriented" according to thesurface normals at the PDM points, a surface-based fitting is accomplished.Estimating the parameters of the GMM in a maximum a posteriori manner yieldsthe reconstruction of the surface from the given data points. We compare ourmethod to the extensively used Iterative Closest Points method on severaldifferent anatomical datasets/SSMs (brain, femur, tibia, hip, liver) anddemonstrate superior accuracy and robustness on sparse data.
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