Sparse multi-scale diffeomorphic registration: the kernel bundle framework

Stefan Horst Sommer; Francois Bernard Lauze; Mads Nielsen; Xavier Pennec

doi:10.1007/s10851-012-0409-0

Sparse multi-scale diffeomorphic registration: the kernel bundle framework

Stefan Horst Sommer, Francois Bernard Lauze, Mads Nielsen, Xavier Pennec

Department of Computer Science

30 Citations (Scopus)

Abstract

In order to detect small-scale deformations during disease propagation while allowing large-scale deformation needed for inter-subject registration, we wish to model deformation at multiple scales and represent the deformation compactly at the relevant scales only. This paper presents the kernel bundle extension of the LDDMM framework that allows multiple kernels at multiple scales to be incorporated in the registration. We combine sparsity priors with the kernel bundle resulting in compact representations across scales, and we present the mathematical foundation of the framework with derivation of the KB-EPDiff evolution equations. Through examples, we illustrate the influence of the kernel scale and show that the method achieves the important property of sparsity across scales. In addition, we demonstrate on a dataset of annotated lung CT images how the kernel bundle framework with a compact representation reaches the same accuracy as the standard method optimally tuned with respect to scale.

Original language	English
Journal	Journal of Mathematical Imaging and Vision
Volume	46
Issue number	3
Pages (from-to)	292-308
Number of pages	17
ISSN	0924-9907
DOIs	https://doi.org/10.1007/s10851-012-0409-0
Publication status	Published - Jul 2013

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title = "Sparse multi-scale diffeomorphic registration: the kernel bundle framework",

abstract = "In order to detect small-scale deformations during disease propagation while allowing large-scale deformation needed for inter-subject registration, we wish to model deformation at multiple scales and represent the deformation compactly at the relevant scales only. This paper presents the kernel bundle extension of the LDDMM framework that allows multiple kernels at multiple scales to be incorporated in the registration. We combine sparsity priors with the kernel bundle resulting in compact representations across scales, and we present the mathematical foundation of the framework with derivation of the KB-EPDiff evolution equations. Through examples, we illustrate the influence of the kernel scale and show that the method achieves the important property of sparsity across scales. In addition, we demonstrate on a dataset of annotated lung CT images how the kernel bundle framework with a compact representation reaches the same accuracy as the standard method optimally tuned with respect to scale.",

keywords = "Kernel bundle, LDDKBM, LDDMM, Diffeomorphic registration, Scale space, Computational anatomy",

author = "Sommer, {Stefan Horst} and Lauze, {Francois Bernard} and Mads Nielsen and Xavier Pennec",

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T1 - Sparse multi-scale diffeomorphic registration

T2 - the kernel bundle framework

AU - Sommer, Stefan Horst

AU - Lauze, Francois Bernard

AU - Nielsen, Mads

AU - Pennec, Xavier

PY - 2013/7

Y1 - 2013/7

N2 - In order to detect small-scale deformations during disease propagation while allowing large-scale deformation needed for inter-subject registration, we wish to model deformation at multiple scales and represent the deformation compactly at the relevant scales only. This paper presents the kernel bundle extension of the LDDMM framework that allows multiple kernels at multiple scales to be incorporated in the registration. We combine sparsity priors with the kernel bundle resulting in compact representations across scales, and we present the mathematical foundation of the framework with derivation of the KB-EPDiff evolution equations. Through examples, we illustrate the influence of the kernel scale and show that the method achieves the important property of sparsity across scales. In addition, we demonstrate on a dataset of annotated lung CT images how the kernel bundle framework with a compact representation reaches the same accuracy as the standard method optimally tuned with respect to scale.

AB - In order to detect small-scale deformations during disease propagation while allowing large-scale deformation needed for inter-subject registration, we wish to model deformation at multiple scales and represent the deformation compactly at the relevant scales only. This paper presents the kernel bundle extension of the LDDMM framework that allows multiple kernels at multiple scales to be incorporated in the registration. We combine sparsity priors with the kernel bundle resulting in compact representations across scales, and we present the mathematical foundation of the framework with derivation of the KB-EPDiff evolution equations. Through examples, we illustrate the influence of the kernel scale and show that the method achieves the important property of sparsity across scales. In addition, we demonstrate on a dataset of annotated lung CT images how the kernel bundle framework with a compact representation reaches the same accuracy as the standard method optimally tuned with respect to scale.

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KW - LDDKBM

KW - LDDMM

KW - Diffeomorphic registration

KW - Scale space

KW - Computational anatomy

U2 - 10.1007/s10851-012-0409-0

DO - 10.1007/s10851-012-0409-0

M3 - Journal article

SN - 0924-9907

VL - 46

SP - 292

EP - 308

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

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ER -

Sparse multi-scale diffeomorphic registration: the kernel bundle framework

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