Geodesic Image Normalization and Temporal Parameterization in the Space of Diffeomorphisms

  • Brian B. Avants
  • C. L. Epstein
  • J. C. Gee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4091)


Medical image analysis based on diffeomorphisms (differentiable one to one and onto maps with differentiable inverse) has placed computational analysis of anatomy and physiology on firm theoretical ground. We detail our approach to diffeomorphic computational anatomy while highlighting both theoretical and practical benefits. We first introduce the metric used to locate geodesics in the diffeomorphic space. Second, we give a variational energy that parameterizes the image normalization problem in terms of a geodesic diffeomorphism, enabling a fundamentally symmetric solution. This approach to normalization is extended for optimal template population studies using general imaging data. Finally, we show how the temporal parameterization and large deformation capabilities of diffeomorphisms make them appropriate for longitudinal analysis, particularly of neurodegenerative data.


Image Registration Frontotemporal Dementia Image Match Medical Image Analysis Topology Preserve 
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-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Brian B. Avants
    • 1
  • C. L. Epstein
    • 1
  • J. C. Gee
    • 1
  1. 1.Depts. of Radiology and MathematicsUniversity of PennsylvaniaPhiladelphia

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