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Geodesic Shape Regression in the Framework of Currents

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 : Shape regression is emerging as an important tool for the statistical analysis of time dependent shapes. In this paper, we develop a new generative model which describes shape change over time, by extending simple linear regression to the space of shapes represented as currents in the large deformation diffeomorphic metric mapping (LDDMM) framework. By analogy with linear regression, we estimate a baseline shape (intercept) and initial momenta (slope) which fully parameterize the geodesic shape evolution. This is in contrast to previous shape regression methods which assume the baseline shape is fixed. We further leverage a control point formulation, which provides a discrete and low dimensional parameterization of large diffeomorphic transformations. This flexible system decouples the parameterization of deformations from the specific shape representation, allowing the user to define the dimensionality of the deformation parameters. We present an optimization scheme that estimates the baseline shape, location of the control points, and initial momenta simultaneously via a single gradient descent algorithm. Finally, we demonstrate our proposed method on synthetic data as well as real anatomical shape complexes.
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Submitted on : Thursday, January 23, 2014 - 12:27:24 AM
Last modification on : Friday, November 18, 2022 - 9:26:13 AM
Long-term archiving on: : Wednesday, April 23, 2014 - 11:25:10 PM


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James Fishbaugh, Marcel Prastawa, Guido Gerig, Stanley Durrleman. Geodesic Shape Regression in the Framework of Currents. Information Processing in Medical Imaging, Jul 2013, Asilomar, United States. pp.718-729. ⟨hal-00935053⟩



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