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International Journal of Computer Vision

Erschienen in:

15.05.2018

Fast Diffeomorphic Image Registration via Fourier-Approximated Lie Algebras

verfasst von: Miaomiao Zhang, P. Thomas Fletcher

Erschienen in: International Journal of Computer Vision | Ausgabe 1/2019

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Abstract

This paper introduces Fourier-approximated Lie algebras for shooting (FLASH), a fast geodesic shooting algorithm for diffeomorphic image registration. We approximate the infinite-dimensional Lie algebra of smooth vector fields, i.e., the tangent space at the identity of the diffeomorphism group, with a low-dimensional, bandlimited space. We show that most of the computations for geodesic shooting can be carried out entirely in this low-dimensional space. Our algorithm results in dramatic savings in time and memory over traditional large-deformation diffeomorphic metric mapping algorithms, which require dense spatial discretizations of vector fields. To validate the effectiveness of FLASH, we run pairwise image registration on both 2D synthetic data and real 3D brain images and compare with the state-of-the-art geodesic shooting methods. Experimental results show that our algorithm dramatically reduces the computational cost and memory footprint of diffemorphic image registration with little or no loss of accuracy.

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Since a circular convolution between two bandlimited signals does not preserve the bandlimit, we define a convolution operation on zero-padded signals by truncating the output back to the bandlimits, \(n_i\), in each dimension to guarantee the Lie bracket is closed.

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Titel: Fast Diffeomorphic Image Registration via Fourier-Approximated Lie Algebras
verfasst von: Miaomiao Zhang
P. Thomas Fletcher
Publikationsdatum: 15.05.2018
Verlag: Springer US
Erschienen in: International Journal of Computer Vision / Ausgabe 1/2019
Print ISSN: 0920-5691
Elektronische ISSN: 1573-1405
DOI: https://doi.org/10.1007/s11263-018-1099-x

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