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Abstract

We consider geodesic regression with parametric time-warps. This allows, for example, to capture saturation effects as typically observed during brain development or degeneration. While highly-flexible models to analyze time-varying image and shape data based on generalizations of splines and polynomials have been proposed recently, they come at the cost of substantially more complex inference. Our focus in this paper is therefore to keep the model and its inference as simple as possible while allowing to capture expected biological variation. We demonstrate that by augmenting geodesic regression with parametric time-warp functions, we can achieve comparable flexibility to more complex models while retaining model simplicity. In addition, the time-warp parameters provide useful information of underlying anatomical changes as demonstrated for the analysis of corpora callosa and rat calvariae. We exemplify our strategy for shape regression on the Grassmann manifold, but note that the method is generally applicable for time-warped geodesic regression.

Keywords

Mean Square Error Corpus Callosum Synthetic Data Geodesic Equation Grassmann Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yi Hong
    • 1
  • Nikhil Singh
    • 1
  • Roland Kwitt
    • 3
  • Marc Niethammer
    • 1
    • 2
  1. 1.University of North Carolina (UNC)Chapel HillUSA
  2. 2.Biomedical Research Imaging CenterUNCChapel HillUSA
  3. 3.Department of Computer ScienceUniversity of SalzburgAustria

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