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Geodesic Shape Regression in the Framework of Currents

1Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA.
2INRIA/ICM, Pitie Salpetriere Hospital, Paris, France.
Inf Process Med Imaging IPMI 2013
Publication Date:
Volume Number:
Inf Process Med Imaging. 2013 Jun; 23:718-29.
PubMed ID:
Appears in Collections:
R01 HD055741/HD/NICHD NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
Generated Citation:
Fishbaugh J., Prastawa M., Gerig G., Durrleman S. Geodesic Shape Regression in the Framework of Currents. Inf Process Med Imaging. 2013 Jun; 23:718-29. PMID: 24684012. PMCID: PMC4127488.
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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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