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Which parallel transport for the statistical analysis of longitudinal deformations?

Xavier Pennec 1, * Marco Lorenzi 2 
* Corresponding author
1 ASCLEPIOS - Analysis and Simulation of Biomedical Images
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Follow-up imaging studies require the population-wise evaluation of the anatomical changes over time for specific clinical groups. A typical example is the analysis of structural brain changes with aging in Alzheimer's disease. The longitudinal morphological changes for a specific subject can be evaluated through the non-rigid registration. However, to perform a longitudinal group-wise analysis, the subjectspecific longitudinal trajectories need to be transported in a common reference. The analysis of existing transport methods suggests that the inconsistency of the discrete approximations with composition could drown the small longitudinal deformations into the large inter-subject variability. Instead of approximating a continuous parallel transport in an inconsistent discrete setting, we propose to rely on a carefully designed discrete construction that intrinsically respects all the symmetries on the problem: the Schild's Ladder procedure. We show that the Schild's ladder procedure can be implemented extremely efficiently with great stability in the framework of diffeomorphisms parameterized by stationary velocity fields (SVF). The proposed algorithm proves to overcome other methods in terms of consistency with respect to the resampling of most scalar measures of deformations, which opens the way to stable and hopefully more powerful group-wise statistics of longitudinal deformations
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Submitted on : Friday, August 19, 2011 - 7:57:13 PM
Last modification on : Saturday, June 25, 2022 - 11:06:40 PM


  • HAL Id : inria-00616204, version 1



Xavier Pennec, Marco Lorenzi. Which parallel transport for the statistical analysis of longitudinal deformations?. Colloque GRETSI '11, 2011, Bordeaux, France. ⟨inria-00616204⟩



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