Regularized Reconstruction of Shapes with Statistical a priori Knowledge

Authors:
Matthias Fuchs;Otmar Scherzer
Affiliations:
Institute of Computer Science, University of Innsbruck, Innsbruck, Austria 6020;Institute of Computer Science, University of Innsbruck, Innsbruck, Austria 6020
Venue:
International Journal of Computer Vision
Year:
2008

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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.