A stochastic large deformation model for computational anatomy

Alexis Arnaudon; Darryl D. Holm; Akshay Sadananda Uppinakudru Pai; Stefan Horst Sommer

doi:10.1007/978-3-319-59050-9_45

A stochastic large deformation model for computational anatomy

Alexis Arnaudon, Darryl D. Holm, Akshay Sadananda Uppinakudru Pai, Stefan Horst Sommer^*

^*Corresponding author for this work

Department of Computer Science

4 Citations (Scopus)

Abstract

In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. By accounting for randomness in a particular setup which is crafted to fit the geometrical properties of LDDMM, we formulate the template estimation problem for landmarks with noise and give two methods for efficiently estimating the parameters of the noise fields from a prescribed data set. One method directly approximates the time evolution of the variance of each landmark by a finite set of differential equations, and the other is based on an Expectation-Maximisation algorithm. In the second method, the evaluation of the data likelihood is achieved without registering the landmarks, by applying bridge sampling using a stochastically perturbed version of the large deformation gradient flow algorithm. The method and the estimation algorithms are experimentally validated on synthetic examples and shape data of human corpora callosa.

Original language	English
Title of host publication	Information Processing in Medical Imaging : 25th International Conference, IPMI 2017, Boone, NC, USA, June 25-30, 2017, Proceedings
Number of pages	12
Publisher	Springer
Publication date	2017
Pages	571-582
ISBN (Print)	978-3-319-59049-3
ISBN (Electronic)	978-3-319-59050-9
DOIs	https://doi.org/10.1007/978-3-319-59050-9_45
Publication status	Published - 2017
Event	25th International Conference on Information Processing in Medical Imaging - Boone, United States Duration: 25 Jun 2017 → 30 Jun 2017 Conference number: 25

Conference

Conference	25th International Conference on Information Processing in Medical Imaging
Number	25
Country/Territory	United States
City	Boone
Period	25/06/2017 → 30/06/2017

Series	Lecture notes in computer science
Volume	10265
ISSN	0302-9743

Keywords

Computational anatomy
Large deformations
LDDMM
Stochastic processes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1007/978-3-319-59050-9_45

https://arxiv.org/pdf/1612.05323.pdf

Cite this

A stochastic large deformation model for computational anatomy. / Arnaudon, Alexis; Holm, Darryl D.; Pai, Akshay Sadananda Uppinakudru et al.
Information Processing in Medical Imaging: 25th International Conference, IPMI 2017, Boone, NC, USA, June 25-30, 2017, Proceedings. Springer, 2017. p. 571-582 (Lecture notes in computer science, Vol. 10265).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Arnaudon, A, Holm, DD, Pai, ASU & Sommer, SH 2017, A stochastic large deformation model for computational anatomy. in Information Processing in Medical Imaging: 25th International Conference, IPMI 2017, Boone, NC, USA, June 25-30, 2017, Proceedings. Springer, Lecture notes in computer science, vol. 10265, pp. 571-582, 25th International Conference on Information Processing in Medical Imaging, Boone, North Carolina, United States, 25/06/2017. https://doi.org/10.1007/978-3-319-59050-9_45

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abstract = "In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. By accounting for randomness in a particular setup which is crafted to fit the geometrical properties of LDDMM, we formulate the template estimation problem for landmarks with noise and give two methods for efficiently estimating the parameters of the noise fields from a prescribed data set. One method directly approximates the time evolution of the variance of each landmark by a finite set of differential equations, and the other is based on an Expectation-Maximisation algorithm. In the second method, the evaluation of the data likelihood is achieved without registering the landmarks, by applying bridge sampling using a stochastically perturbed version of the large deformation gradient flow algorithm. The method and the estimation algorithms are experimentally validated on synthetic examples and shape data of human corpora callosa.",

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N2 - In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. By accounting for randomness in a particular setup which is crafted to fit the geometrical properties of LDDMM, we formulate the template estimation problem for landmarks with noise and give two methods for efficiently estimating the parameters of the noise fields from a prescribed data set. One method directly approximates the time evolution of the variance of each landmark by a finite set of differential equations, and the other is based on an Expectation-Maximisation algorithm. In the second method, the evaluation of the data likelihood is achieved without registering the landmarks, by applying bridge sampling using a stochastically perturbed version of the large deformation gradient flow algorithm. The method and the estimation algorithms are experimentally validated on synthetic examples and shape data of human corpora callosa.

AB - In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. By accounting for randomness in a particular setup which is crafted to fit the geometrical properties of LDDMM, we formulate the template estimation problem for landmarks with noise and give two methods for efficiently estimating the parameters of the noise fields from a prescribed data set. One method directly approximates the time evolution of the variance of each landmark by a finite set of differential equations, and the other is based on an Expectation-Maximisation algorithm. In the second method, the evaluation of the data likelihood is achieved without registering the landmarks, by applying bridge sampling using a stochastically perturbed version of the large deformation gradient flow algorithm. The method and the estimation algorithms are experimentally validated on synthetic examples and shape data of human corpora callosa.

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A stochastic large deformation model for computational anatomy

Abstract

Conference

Keywords

UN SDGs

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