Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff

Research output: Contribution to journal › Journal article › Research › peer-review

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Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff. / Christgau, Alexander Mangulad; Arnaudon, Alexis; Sommer, Stefan.

In: Journal of Mathematical Imaging and Vision, Vol. 65, No. 4, 2023, p. 563-576.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Christgau, AM, Arnaudon, A & Sommer, S 2023, 'Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff', Journal of Mathematical Imaging and Vision, vol. 65, no. 4, pp. 563-576. https://doi.org/10.1007/s10851-022-01137-4

APA

Christgau, A. M., Arnaudon, A., & Sommer, S. (2023). Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff. Journal of Mathematical Imaging and Vision, 65(4), 563-576. https://doi.org/10.1007/s10851-022-01137-4

Vancouver

Christgau AM, Arnaudon A, Sommer S. Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff. Journal of Mathematical Imaging and Vision. 2023;65(4):563-576. https://doi.org/10.1007/s10851-022-01137-4

Author

Christgau, Alexander Mangulad ; Arnaudon, Alexis ; Sommer, Stefan. / Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff. In: Journal of Mathematical Imaging and Vision. 2023 ; Vol. 65, No. 4. pp. 563-576.

Bibtex

@article{436dcd57bf77421ca976cfb09510d6d9,
title = "Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff",
abstract = "Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random subject-specific variation. Focusing on a stochastic extension of the LDDMM models with evolutions governed by a stochastic EPDiff equation, we use moment approximations of the corresponding It{\^o} diffusion to construct estimators for statistical inference in the full stochastic model. We show that this approach, when efficiently implemented with automatic differentiation tools, can successfully estimate parameters encoding the spatial correlation of the noise fields on the image.",
keywords = "Image registration, LDDMM, Stochastic differential equations, Stochastic shape analysis",
author = "Christgau, {Alexander Mangulad} and Alexis Arnaudon and Stefan Sommer",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2023",
doi = "10.1007/s10851-022-01137-4",
language = "English",
volume = "65",
pages = "563--576",
journal = "Journal of Mathematical Imaging and Vision",
issn = "0924-9907",
publisher = "Springer",
number = "4",

}

RIS

TY - JOUR

T1 - Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff

AU - Christgau, Alexander Mangulad

AU - Arnaudon, Alexis

AU - Sommer, Stefan

N1 - Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random subject-specific variation. Focusing on a stochastic extension of the LDDMM models with evolutions governed by a stochastic EPDiff equation, we use moment approximations of the corresponding Itô diffusion to construct estimators for statistical inference in the full stochastic model. We show that this approach, when efficiently implemented with automatic differentiation tools, can successfully estimate parameters encoding the spatial correlation of the noise fields on the image.

AB - Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random subject-specific variation. Focusing on a stochastic extension of the LDDMM models with evolutions governed by a stochastic EPDiff equation, we use moment approximations of the corresponding Itô diffusion to construct estimators for statistical inference in the full stochastic model. We show that this approach, when efficiently implemented with automatic differentiation tools, can successfully estimate parameters encoding the spatial correlation of the noise fields on the image.

KW - Image registration

KW - LDDMM

KW - Stochastic differential equations

KW - Stochastic shape analysis

UR - http://www.scopus.com/inward/record.url?scp=85144680102&partnerID=8YFLogxK

U2 - 10.1007/s10851-022-01137-4

DO - 10.1007/s10851-022-01137-4

M3 - Journal article

AN - SCOPUS:85144680102

VL - 65

SP - 563

EP - 576

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

SN - 0924-9907

IS - 4

ER -

ID: 330844225