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Geodesic Image Regression with a Sparse Parameterization of Diffeomorphisms

1Scientific Computing and Imaging Institute, University of Utah, Salt lake City, UT, USA.
2INRIA/ICM, Pitié Salpêtrière Hospital, Paris, France.
Publication Date:
Geom Sci Inf
Volume Number:
Geom Sci Inf. 2013 Aug;8085:95-102.
PubMed ID:
Appears in Collections:
R01 HD055741/HD/NICHD NIH HHS/United States
U01 NS082086/NS/NINDS NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
Generated Citation:
Fishbaugh J., Prastawa M., Gerig G., Durrleman S. Geodesic Image Regression with a Sparse Parameterization of Diffeomorphisms. Geom Sci Inf. 2013 Aug;8085:95-102. PMID: 25664349. PMCID: PMC4316381.
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Image regression allows for time-discrete imaging data to be modeled continuously, and is a crucial tool for conducting statistical analysis on longitudinal images. Geodesic models are particularly well suited for statistical analysis, as image evolution is fully characterized by a baseline image and initial momenta. However, existing geodesic image regression models are parameterized by a large number of initial momenta, equal to the number of image voxels. In this paper, we present a sparse geodesic image regression framework which greatly reduces the number of model parameters. We combine a control point formulation of deformations with a L 1 penalty to select the most relevant subset of momenta. This way, the number of model parameters reflects the complexity of anatomical changes in time rather than the sampling of the image. We apply our method to both synthetic and real data and show that we can decrease the number of model parameters (from the number of voxels down to hundreds) with only minimal decrease in model accuracy. The reduction in model parameters has the potential to improve the power of ensuing statistical analysis, which faces the challenging problem of high dimensionality.

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