Abstract
The reconstruction of geometry or, in particular, the shape of objects is a common issue in image analysis. Starting from a variational formulation of such a problem on a shape manifold we introduce a regularization technique incorporating statistical shape knowledge. The key idea is to consider a Riemannian metric on the shape manifold which reflects the statistics of a given training set. We investigate the properties of the regularization functional and illustrate our technique by applying it to region-based and edge-based segmentation of image data. In contrast to previous works our framework can be considered on arbitrary (finite-dimensional) shape manifolds and allows the use of Riemannian metrics for regularization of a wide class of variational problems in image processing.
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Fuchs, M., Scherzer, O. Regularized Reconstruction of Shapes with Statistical a priori Knowledge. Int J Comput Vis 79, 119–135 (2008). https://doi.org/10.1007/s11263-007-0103-7
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DOI: https://doi.org/10.1007/s11263-007-0103-7