Brownian Warps for Non-Rigid Registration

Mads Nielsen; Peter Johansen; Andrew D. Jackson; Benny Elley Lautrup; Søren Hauberg

doi:10.1007/s10851-008-0083-4

Brownian Warps for Non-Rigid Registration

Mads Nielsen, Peter Johansen, Andrew D. Jackson, Benny Elley Lautrup, Søren Hauberg

6 Citations (Scopus)

Abstract

A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is source-destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 creates invertible warps. Using this as a least committed prior, we formulate a Partial Differential Equation for obtaining the maximally likely warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric and in an example on X-ray spine registration provides extrapolations from landmark point superior to those of spline solutions.
Udgivelsesdato: July

Original language	English
Journal	Journal of Mathematical Imaging and Vision
Volume	31
Issue number	2-3
Pages (from-to)	221-231
Number of pages	11
ISSN	0924-9907
DOIs	https://doi.org/10.1007/s10851-008-0083-4
Publication status	Published - 2008

Keywords

Faculty of Science
DIKU
Image Group
Non-rigid registration
Brownian motion
Central limit theorem
Invariance

Access to Document

10.1007/s10851-008-0083-4

Cite this

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title = "Brownian Warps for Non-Rigid Registration",

abstract = "A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is source-destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 creates invertible warps. Using this as a least committed prior, we formulate a Partial Differential Equation for obtaining the maximally likely warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric and in an example on X-ray spine registration provides extrapolations from landmark point superior to those of spline solutions. Udgivelsesdato: July",

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T1 - Brownian Warps for Non-Rigid Registration

AU - Nielsen, Mads

AU - Johansen, Peter

AU - Jackson, Andrew D.

AU - Lautrup, Benny Elley

AU - Hauberg, Søren

PY - 2008

Y1 - 2008

N2 - A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is source-destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 creates invertible warps. Using this as a least committed prior, we formulate a Partial Differential Equation for obtaining the maximally likely warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric and in an example on X-ray spine registration provides extrapolations from landmark point superior to those of spline solutions. Udgivelsesdato: July

AB - A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is source-destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 creates invertible warps. Using this as a least committed prior, we formulate a Partial Differential Equation for obtaining the maximally likely warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric and in an example on X-ray spine registration provides extrapolations from landmark point superior to those of spline solutions. Udgivelsesdato: July

KW - Faculty of Science

KW - DIKU

KW - Image Group

KW - Non-rigid registration

KW - Brownian motion

KW - Central limit theorem

KW - Invariance

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DO - 10.1007/s10851-008-0083-4

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SP - 221

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JO - Journal of Mathematical Imaging and Vision

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