Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes
This paper presents recent advances in the use of diffeomorphic active shapes which incorporate the conservation laws of large deformation diffeomorphic metric mapping. The equations of evolution satisfying the conservation law are geodesics under the diffeomorphism metric and therefore termed geode...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Biomedical Imaging |
| Online Access: | http://dx.doi.org/10.1155/2013/205494 |
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| author | Daniel J. Tward Jun Ma Michael I. Miller Laurent Younes |
| author_facet | Daniel J. Tward Jun Ma Michael I. Miller Laurent Younes |
| author_sort | Daniel J. Tward |
| collection | DOAJ |
| description | This paper presents recent advances in the use of diffeomorphic active shapes which incorporate the conservation laws of large deformation diffeomorphic metric mapping. The equations of evolution satisfying the conservation law are geodesics under the diffeomorphism metric and therefore termed geodesically controlled diffeomorphic active shapes (GDAS). Our principal application in this paper is on robust diffeomorphic mapping methods based on parameterized surface representations of subcortical template structures. Our parametrization of the GDAS evolution is via the initial momentum representation in the tangent space of the template surface. The dimension of this representation is constrained using principal component analysis generated from training samples. In this work, we seek to use template surfaces to generate segmentations of the hippocampus with three data attachment terms: surface matching, landmark matching, and inside-outside modeling from grayscale T1 MR imaging data. This is formulated as an energy minimization problem, where energy describes shape variability and data attachment accuracy, and we derive a variational solution. A gradient descent strategy is employed in the numerical optimization. For the landmark matching case, we demonstrate the robustness of this algorithm as applied to the workflow of a large neuroanatomical study by comparing to an existing diffeomorphic landmark matching algorithm. |
| format | Article |
| id | doaj-art-5c762196517d416d89e2403c49831a5d |
| institution | Kabale University |
| issn | 1687-4188 1687-4196 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Biomedical Imaging |
| spelling | doaj-art-5c762196517d416d89e2403c49831a5d2025-02-03T01:11:04ZengWileyInternational Journal of Biomedical Imaging1687-41881687-41962013-01-01201310.1155/2013/205494205494Robust Diffeomorphic Mapping via Geodesically Controlled Active ShapesDaniel J. Tward0Jun Ma1Michael I. Miller2Laurent Younes3Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218, USADepartment of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218, USACenter for Imaging Science, Johns Hopkins University, Baltimore, MD 21218, USACenter for Imaging Science, Johns Hopkins University, Baltimore, MD 21218, USAThis paper presents recent advances in the use of diffeomorphic active shapes which incorporate the conservation laws of large deformation diffeomorphic metric mapping. The equations of evolution satisfying the conservation law are geodesics under the diffeomorphism metric and therefore termed geodesically controlled diffeomorphic active shapes (GDAS). Our principal application in this paper is on robust diffeomorphic mapping methods based on parameterized surface representations of subcortical template structures. Our parametrization of the GDAS evolution is via the initial momentum representation in the tangent space of the template surface. The dimension of this representation is constrained using principal component analysis generated from training samples. In this work, we seek to use template surfaces to generate segmentations of the hippocampus with three data attachment terms: surface matching, landmark matching, and inside-outside modeling from grayscale T1 MR imaging data. This is formulated as an energy minimization problem, where energy describes shape variability and data attachment accuracy, and we derive a variational solution. A gradient descent strategy is employed in the numerical optimization. For the landmark matching case, we demonstrate the robustness of this algorithm as applied to the workflow of a large neuroanatomical study by comparing to an existing diffeomorphic landmark matching algorithm.http://dx.doi.org/10.1155/2013/205494 |
| spellingShingle | Daniel J. Tward Jun Ma Michael I. Miller Laurent Younes Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes International Journal of Biomedical Imaging |
| title | Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes |
| title_full | Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes |
| title_fullStr | Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes |
| title_full_unstemmed | Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes |
| title_short | Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes |
| title_sort | robust diffeomorphic mapping via geodesically controlled active shapes |
| url | http://dx.doi.org/10.1155/2013/205494 |
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