Skip to Main content Skip to Navigation
Conference papers

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.
Document type :
Conference papers
Complete list of metadata

Cited literature [12 references]  Display  Hide  Download

https://hal.inria.fr/inria-00629873
Contributor : Alain Monteil <>
Submitted on : Thursday, October 6, 2011 - 5:27:41 PM
Last modification on : Thursday, February 14, 2019 - 3:32:10 PM
Long-term archiving on: : Tuesday, November 13, 2012 - 3:16:45 PM

File

mfca08_1_2.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00629873, version 1

Collections

Citation

Matias Bossa, Salvador Olmos. A new algorithm for the computation of the group logarithm of diffeomorphisms. 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, Oct 2008, New-York, United States. ⟨inria-00629873⟩

Share

Metrics

Record views

162

Files downloads

212