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Area preserving parameterisation of shapes with spherical topology

: Kirschner, Matthias; Wesarg, Stefan

Fischer, S. ; Gesellschaft für Informatik -GI-, Bonn:
Informatik 2009. Im Focus das Leben : Beiträge der 39. Jahrestagung der Gesellschaft für Informatik e.V. (GI), 28.9. - 2.10.2009 in Lübeck
Bonn: GI, 2009 (GI-Edition - Lecture Notes in Informatics (LNI) - Proceedings 154)
ISBN: 978-3-88579-248-2
ISSN: 1617-5468
Gesellschaft für Informatik (Jahrestagung) <39, 2009, Lübeck>
Conference Paper
Fraunhofer IGD ()
surface parameterization; model-based segmentation; statistical shape model (SSM); point correspondence

Statistical shape models are powerful tools for model-based segmentation and have been successfully applied to the segmentation of various structures in medical images. Though the segmentation algorithms based on statistical shape models are simple, finding corresponding landmarks for the construction of the models is a challenging optimisation task. State-of-the-art algorithms that solve the correspondence problem require a representation of the training shapes in a suitable parameter space. The mapping of a shape to a parameter space can introduce large area distortions so that simple sampling techniques can not reconstruct the original shapes sufficiently well.
In this paper, we propose an algorithm to construct area preserving parameterisations of shapes with spherical topology. Using our approach, good reconstructions of the original shapes can be achieved by uniform sampling. In contrast to previously published methods that use a black box optimisation approach, we exploit knowledge about the shortcomings of initial parameterisations.