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Geodesic image regression with a sparse parameterization of diffeomorphisms

James Fishbaugh 1 Marcel Prastawa 1 Guido Gerig 1 Stanley Durrleman 2 
2 ARAMIS - Algorithms, models and methods for images and signals of the human brain
Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, ICM - Institut du Cerveau et de la Moëlle Epinière = Brain and Spine Institute
Abstract : 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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Contributor : Stanley Durrleman Connect in order to contact the contributor
Submitted on : Thursday, January 23, 2014 - 12:21:09 AM
Last modification on : Friday, November 18, 2022 - 9:24:44 AM


  • HAL Id : hal-00935052, version 1


James Fishbaugh, Marcel Prastawa, Guido Gerig, Stanley Durrleman. Geodesic image regression with a sparse parameterization of diffeomorphisms. Geometric Science of Information, Aug 2013, Paris, France. pp.95-102. ⟨hal-00935052⟩



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