A new algorithm for the computation of the group logarithm of diffeomorphisms

Abstract : There is an increasing interest on computing statistics of spa- tial transformations, in particular diffeomorphisms. In the Log-Euclidean framework proposed recently the group exponential and logarithm are essential operators to map elements from the tangent space to the man- ifold and vice versa. Currently, one of the main bottlenecks in the Log- Euclidean framework applied on diffeomorphisms is the large computa- tion times required to estimate the logarithm. Up to now, the fastest ap- proach to estimate the logarithm of diffeomorphisms is the Inverse Scal- ing and Squaring (ISS) method. This paper presents a new method for the estimation of the group logarithm of diffeomorphisms, based on a se- ries in terms of the group exponential and the Baker-Campbell-Hausdorff formula. The proposed method was tested on 3D MRI brain images as well as on random diffeomorphisms. A performance comparison showed a significant improvement in accuracy-speed trade-off vs. the ISS method.
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Communication dans un congrès
Xavier Pennec. 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, Oct 2008, New-York, United States. 2008
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Matias Bossa, Salvador Olmos. A new algorithm for the computation of the group logarithm of diffeomorphisms. Xavier Pennec. 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, Oct 2008, New-York, United States. 2008. 〈inria-00629873〉

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