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Finite element surface registration incorporating curvature, volume preservation, and statistical model information
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Albrecht, Thomas, Dedner, Andreas, Lüthi, Marcel and Vetter, Thomas (2013) Finite element surface registration incorporating curvature, volume preservation, and statistical model information. Computational and Mathematical Methods in Medicine, Volume 2013 (Article number 674273). pp. 1-14. doi:10.1155/2013/674273
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Official URL: http://dx.doi.org/10.1155/2013/674273
Abstract
We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Finite element method, Image registration, Mathematical statistics, Curvature | ||||
| Journal or Publication Title: | Computational and Mathematical Methods in Medicine | ||||
| Publisher: | Hindawi Publishing Corporation | ||||
| ISSN: | 1748-670X | ||||
| Official Date: | September 2013 | ||||
| Dates: |
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| Volume: | Volume 2013 | ||||
| Number: | Article number 674273 | ||||
| Page Range: | pp. 1-14 | ||||
| DOI: | 10.1155/2013/674273 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access | ||||
| Funder: | Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung [Swiss National Science Foundation] (SNSF), Hasler Stiftung, Landesstiftung Baden-Württemberg gGmbH |
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