Kernel bundle EPDiff: evolution equations for multi-scale diffeomorphic image registration

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

doi:10.1007/978-3-642-24785-9_57

Kernel bundle EPDiff: evolution equations for multi-scale diffeomorphic image registration

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

Datalogisk Institut

1 Citationer (Scopus)

Abstract

In the LDDMM framework, optimal warps for image registration are found as end-points of critical paths for an energy functional, and the EPDiff equations describe the evolution along such paths. The Large Deformation Diffeomorphic Kernel Bundle Mapping (LDDKBM) extension of LDDMM allows scale space information to be automatically incorporated in registrations and promises to improve the standard framework in several aspects. We present the mathematical foundations of LDDKBM and derive the KB-EPDiff evolution equations, which provide optimal warps in this new framework. To illustrate the resulting diffeomorphism paths, we give examples showing the decoupled evolution across scales and how the method automatically incorporates deforma-
tion at appropriate scales.

Originalsprog	Engelsk
Titel	Scale Space and Variational Methods in Computer Vision : Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers
Redaktører	Alfred Bruckstein, Bart M. ter Haar Romeny, Alexander M. Bronstein, Michael M. Bronstein
Antal sider	12
Forlag	Springer
Publikationsdato	2012
Sider	677-688
ISBN (Trykt)	978-3-642-24784-2
ISBN (Elektronisk)	978-3-642-24785-9
DOI	https://doi.org/10.1007/978-3-642-24785-9_57
Status	Udgivet - 2012
Begivenhed	3rd International Conference on Scale Space and Variational Methods in Computer Vision - Ein-Gedi, Israel Varighed: 29 maj 2011 → 2 jun. 2011 Konferencens nummer: 3

Konference

Konference	3rd International Conference on Scale Space and Variational Methods in Computer Vision
Nummer	3
Land/Område	Israel
By	Ein-Gedi
Periode	29/05/2011 → 02/06/2011

Navn	Lecture notes in computer science
Vol/bind	6667
ISSN	0302-9743

Adgang til dokumentet

10.1007/978-3-642-24785-9_57

Citationsformater

Sommer, S. H., Lauze, F. B., Nielsen, M., & Pennec, X. (2012). Kernel bundle EPDiff: evolution equations for multi-scale diffeomorphic image registration. I A. Bruckstein, B. M. ter Haar Romeny, A. M. Bronstein, & M. M. Bronstein (red.), Scale Space and Variational Methods in Computer Vision : Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers (s. 677-688). Springer. Lecture notes in computer science Bind 6667 https://doi.org/10.1007/978-3-642-24785-9_57

Kernel bundle EPDiff : evolution equations for multi-scale diffeomorphic image registration. / Sommer, Stefan Horst ; Lauze, Francois Bernard ; Nielsen, Mads et al.

Scale Space and Variational Methods in Computer Vision : Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers. red. / Alfred Bruckstein; Bart M. ter Haar Romeny; Alexander M. Bronstein; Michael M. Bronstein. Springer, 2012. s. 677-688 (Lecture notes in computer science, Bind 6667).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Sommer, SH , Lauze, FB , Nielsen, M & Pennec, X 2012, Kernel bundle EPDiff: evolution equations for multi-scale diffeomorphic image registration. i A Bruckstein, BM ter Haar Romeny, AM Bronstein & MM Bronstein (red), Scale Space and Variational Methods in Computer Vision : Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers. Springer, Lecture notes in computer science, bind 6667, s. 677-688, 3rd International Conference on Scale Space and Variational Methods in Computer Vision, Ein-Gedi, Israel, 29/05/2011. https://doi.org/10.1007/978-3-642-24785-9_57

Sommer SH , Lauze FB , Nielsen M, Pennec X. Kernel bundle EPDiff: evolution equations for multi-scale diffeomorphic image registration. I Bruckstein A, ter Haar Romeny BM, Bronstein AM, Bronstein MM, red., Scale Space and Variational Methods in Computer Vision : Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers. Springer. 2012. s. 677-688. (Lecture notes in computer science, Bind 6667). doi: 10.1007/978-3-642-24785-9_57

Sommer, Stefan Horst ; Lauze, Francois Bernard ; Nielsen, Mads et al. / Kernel bundle EPDiff : evolution equations for multi-scale diffeomorphic image registration. Scale Space and Variational Methods in Computer Vision : Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers. red. / Alfred Bruckstein ; Bart M. ter Haar Romeny ; Alexander M. Bronstein ; Michael M. Bronstein. Springer, 2012. s. 677-688 (Lecture notes in computer science, Bind 6667).

@inproceedings{438aa80e196d4fe6a47c5cdd5c265f38,

title = "Kernel bundle EPDiff: evolution equations for multi-scale diffeomorphic image registration",

abstract = "In the LDDMM framework, optimal warps for image registration are found as end-points of critical paths for an energy functional, and the EPDiff equations describe the evolution along such paths. The Large Deformation Diffeomorphic Kernel Bundle Mapping (LDDKBM) extension of LDDMM allows scale space information to be automatically incorporated in registrations and promises to improve the standard framework in several aspects. We present the mathematical foundations of LDDKBM and derive the KB-EPDiff evolution equations, which provide optimal warps in this new framework. To illustrate the resulting diffeomorphism paths, we give examples showing the decoupled evolution across scales and how the method automatically incorporates deforma-tion at appropriate scales.",

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

year = "2012",

doi = "10.1007/978-3-642-24785-9_57",

language = "English",

isbn = "978-3-642-24784-2",

series = "Lecture notes in computer science",

publisher = "Springer",

pages = "677--688",

editor = "{ Bruckstein}, Alfred and { ter Haar Romeny}, {Bart M.} and Bronstein, {Alexander M.} and Bronstein, {Michael M.}",

booktitle = "Scale Space and Variational Methods in Computer Vision",

note = "3rd International Conference on Scale Space and Variational Methods in Computer Vision ; Conference date: 29-05-2011 Through 02-06-2011",

}

TY - GEN

T1 - Kernel bundle EPDiff

T2 - 3rd International Conference on Scale Space and Variational Methods in Computer Vision

AU - Sommer, Stefan Horst

AU - Lauze, Francois Bernard

AU - Nielsen, Mads

AU - Pennec, Xavier

N1 - Conference code: 3

PY - 2012

Y1 - 2012

N2 - In the LDDMM framework, optimal warps for image registration are found as end-points of critical paths for an energy functional, and the EPDiff equations describe the evolution along such paths. The Large Deformation Diffeomorphic Kernel Bundle Mapping (LDDKBM) extension of LDDMM allows scale space information to be automatically incorporated in registrations and promises to improve the standard framework in several aspects. We present the mathematical foundations of LDDKBM and derive the KB-EPDiff evolution equations, which provide optimal warps in this new framework. To illustrate the resulting diffeomorphism paths, we give examples showing the decoupled evolution across scales and how the method automatically incorporates deforma-tion at appropriate scales.

AB - In the LDDMM framework, optimal warps for image registration are found as end-points of critical paths for an energy functional, and the EPDiff equations describe the evolution along such paths. The Large Deformation Diffeomorphic Kernel Bundle Mapping (LDDKBM) extension of LDDMM allows scale space information to be automatically incorporated in registrations and promises to improve the standard framework in several aspects. We present the mathematical foundations of LDDKBM and derive the KB-EPDiff evolution equations, which provide optimal warps in this new framework. To illustrate the resulting diffeomorphism paths, we give examples showing the decoupled evolution across scales and how the method automatically incorporates deforma-tion at appropriate scales.

U2 - 10.1007/978-3-642-24785-9_57

DO - 10.1007/978-3-642-24785-9_57

M3 - Article in proceedings

SN - 978-3-642-24784-2

T3 - Lecture notes in computer science

SP - 677

EP - 688

BT - Scale Space and Variational Methods in Computer Vision

A2 - Bruckstein, Alfred

A2 - ter Haar Romeny, Bart M.

A2 - Bronstein, Alexander M.

A2 - Bronstein, Michael M.

PB - Springer

Y2 - 29 May 2011 through 2 June 2011

ER -