Omnidirectional Displacements for Deformable Surfaces

Please always quote using this URN: urn:nbn:de:0296-matheon-10214
  • Deformable surface models are often represented as triangular meshes in image segmentation applications. For a fast and easily regularized deformation onto the target object boundary, the vertices of the mesh are commonly moved along line segments (typically surface normals). However, in case of high mesh curvature, these lines may intersect with the target boundary at “non-corresponding” positions, or may not intersect at all. Consequently, certain deformations cannot be achieved. We propose omnidirectional displacements for deformable surfaces (ODDS) to overcome this limitation. ODDS allow each vertex to move not only along a line segment but within a surrounding sphere, and achieve globally optimal deformations subject to local regularization con- straints. However, allowing a ball-shaped instead of a linear range of motion per vertex significantly increases runtime and memory. To alleviate this drawback, we propose a hybrid approach, fastODDS, with improved runtime and reduced memory requirements. Furthermore, fastODDS can also cope with simultaneous segmentation of multiple objects. We show the theoretical benefits of ODDS with experiments on synthetic data, and evaluate ODDS and fastODDS quantitatively on clinical image data of the mandible and the hip bones. There, we assess both the global segmentation accuracy as well as local accuracy in high curvature regions, such as the tip-shaped mandibular coronoid processes and the ridge-shaped acetabular rims of the hip bones.

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  • Preprint submitted to Medical Image Analysis

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Author:Dagmar Kainmueller, Hans Lamecker, Markus Heller, Britta Weber, Hans-Christian Hege, Stefan Zachow
Referee:Peter Deuflhard
Date of first Publication:2012/01/25
Institute:Zuse Institute Berlin (ZIB)
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D18 Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) / 68Uxx Computing methodologies and applications / 68U10 Image processing
Preprint Number:871