Regularized Reconstruction of Shapes with Statistical a priori Knowledge |
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Authors: | Matthias Fuchs Otmar Scherzer |
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Affiliation: | (1) Institute of Computer Science, University of Innsbruck, Technikerstr. 21a/2, Innsbruck, 6020, Austria |
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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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Keywords: | Statistical shape analysis Variational methods Regularization theory Image segmentation Shape recognition |
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