Curvature Based Registration with Applications to MR-Mammography

Bernd Fischer; Jan Modersitzki

doi:10.1007/3-540-47789-6_21

Curvature Based Registration with Applications to MR-Mammography

Institute of Mathematics

Abstract

We introduce a new non-linear registration model based on a curvature type regularizer. We show that affine linear transformations belong to the kernel of this regularizer. Consequently, an additional global registration is superfluous. Furthermore, we present an implementation of the new scheme based on the numerical solution of the underlying Euler-Lagrange equations. The real discrete cosine transform is the backbone of our implementation and leads to a stable and fast backslashmathcalO(n backslashlog n)algorithm, where n denotes the number of voxels. We demonstrate the advantages of the new technique for synthetic data sets. Moreover, first convincing results for the registration of MR-mammography images are presented.

Original language	English
Title of host publication	Computational Science --- ICCS 2002
Editors	Peter M. A. Sloot, Alfons G. Hoekstra, C. J. Kenneth Tan, Jack J. Dongarra
Number of pages	5
Volume	2331
Place of Publication	Berlin, Heidelberg
Publisher	Springer Berlin Heidelberg
Publication date	10.04.2002
Pages	202-206
ISBN (Print)	978-3-540-43594-5
ISBN (Electronic)	978-3-540-47789-1
DOIs	https://doi.org/10.1007/3-540-47789-6_21
Publication status	Published - 10.04.2002
Event	International Conference on Computational Science 2002 - Amsterdam, Netherlands Duration: 21.04.2002 → 24.04.2002 Conference number: 96801

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10.1007/3-540-47789-6_21

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@inproceedings{a6c5b9a53fff4ec095b3d6c33ed62670,

title = "Curvature Based Registration with Applications to MR-Mammography",

abstract = "We introduce a new non-linear registration model based on a curvature type regularizer. We show that affine linear transformations belong to the kernel of this regularizer. Consequently, an additional global registration is superfluous. Furthermore, we present an implementation of the new scheme based on the numerical solution of the underlying Euler-Lagrange equations. The real discrete cosine transform is the backbone of our implementation and leads to a stable and fast backslashmathcalO(n backslashlog n)algorithm, where n denotes the number of voxels. We demonstrate the advantages of the new technique for synthetic data sets. Moreover, first convincing results for the registration of MR-mammography images are presented.",

author = "Bernd Fischer and Jan Modersitzki",

year = "2002",

month = apr,

day = "10",

doi = "10.1007/3-540-47789-6_21",

language = "English",

isbn = "978-3-540-43594-5",

volume = "2331",

series = " Lecture Notes in Computer Science",

publisher = "Springer Berlin Heidelberg",

pages = "202--206",

editor = "Sloot, {Peter M. A.} and Hoekstra, {Alfons G.} and Tan, {C. J. Kenneth} and Dongarra, {Jack J.}",

booktitle = "Computational Science --- ICCS 2002",

note = "International Conference on Computational Science 2002, ICCS 2002 ; Conference date: 21-04-2002 Through 24-04-2002",

}

Fischer, B & Modersitzki, J 2002, Curvature Based Registration with Applications to MR-Mammography. in PMA Sloot, AG Hoekstra, CJK Tan & JJ Dongarra (eds), Computational Science --- ICCS 2002. vol. 2331, Lecture Notes in Computer Science, vol. 2331, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 202-206, International Conference on Computational Science 2002, Amsterdam, Netherlands, 21.04.02. https://doi.org/10.1007/3-540-47789-6_21

Curvature Based Registration with Applications to MR-Mammography. / Fischer, Bernd; Modersitzki, Jan.
Computational Science --- ICCS 2002. ed. / Peter M. A. Sloot; Alfons G. Hoekstra; C. J. Kenneth Tan; Jack J. Dongarra. Vol. 2331 Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. p. 202-206 ( Lecture Notes in Computer Science; Vol. 2331).

Research output: Chapters in Books/Reports/Conference Proceedings › Conference contribution › peer-review

TY - GEN

T1 - Curvature Based Registration with Applications to MR-Mammography

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AU - Modersitzki, Jan

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N2 - We introduce a new non-linear registration model based on a curvature type regularizer. We show that affine linear transformations belong to the kernel of this regularizer. Consequently, an additional global registration is superfluous. Furthermore, we present an implementation of the new scheme based on the numerical solution of the underlying Euler-Lagrange equations. The real discrete cosine transform is the backbone of our implementation and leads to a stable and fast backslashmathcalO(n backslashlog n)algorithm, where n denotes the number of voxels. We demonstrate the advantages of the new technique for synthetic data sets. Moreover, first convincing results for the registration of MR-mammography images are presented.

AB - We introduce a new non-linear registration model based on a curvature type regularizer. We show that affine linear transformations belong to the kernel of this regularizer. Consequently, an additional global registration is superfluous. Furthermore, we present an implementation of the new scheme based on the numerical solution of the underlying Euler-Lagrange equations. The real discrete cosine transform is the backbone of our implementation and leads to a stable and fast backslashmathcalO(n backslashlog n)algorithm, where n denotes the number of voxels. We demonstrate the advantages of the new technique for synthetic data sets. Moreover, first convincing results for the registration of MR-mammography images are presented.

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SN - 978-3-540-43594-5

VL - 2331

T3 - Lecture Notes in Computer Science

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BT - Computational Science --- ICCS 2002

A2 - Sloot, Peter M. A.

A2 - Hoekstra, Alfons G.

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PB - Springer Berlin Heidelberg

CY - Berlin, Heidelberg

T2 - International Conference on Computational Science 2002

Y2 - 21 April 2002 through 24 April 2002

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Curvature Based Registration with Applications to MR-Mammography

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