Statistical representation and simulation of high-dimensional deformations

Application to synthesizing brain deformations

Zhong Xue, Dinggang Shen, Bilge Karacali, Christos Davatzikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper proposes an approach to effectively representing the statistics of high-dimensional deformations, when relatively few training samples are available, and conventional methods, like PCA, fail due to insufficient training. Based on previous work on scale-space decomposition of deformation fields, herein we represent the space of "valid deformations" as the intersection of three subspaces: one that satisfies constraints on deformations themselves, one that satisfies constraints on Jacobian determinants of deformations, and one that represents smooth deformations via a Markov Random Field (MRF). The first two are extensions of PCA-based statistical shape models. They are based on a wavelet packet basis decomposition that allows for more accurate estimation of the covariance structure of deformation or Jacobian fields, and they are used jointly due to their complementary strengths and limitations. The third is a nested MRF regularization aiming at eliminating potential discontinuities introduced by assumptions in the statistical models. A randomly sampled deformation field is projected onto the space of valid deformations via iterative projections on each of these subspaces until convergence, i.e. all three constraints are met. A deformation field simulator uses this process to generate random samples of deformation fields that are not only realistic but also representative of the full range of anatomical variability. These simulated deformations can be used for validation of deformable registration methods. Other potential uses of this approach include representation of shape priors in statistical shape models as well as various estimation and hypothesis testing paradigms in the general fields of computational anatomy and pattern recognition.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages500-508
Number of pages9
Volume3750 LNCS
DOIs
StatePublished - 2005
Externally publishedYes
Event8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - Palm Springs, CA, United States
Duration: Oct 26 2005Oct 29 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3750 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005
CountryUnited States
CityPalm Springs, CA
Period10/26/0510/29/05

Fingerprint

Statistical Models
Brain
Passive Cutaneous Anaphylaxis
High-dimensional
Simulation
Anatomy
Random Field
Subspace
Valid
Decomposition
Decompose
Wavelet Packet
Scale Space
Covariance Structure
Training Samples
Hypothesis Testing
Registration
Statistical Model
Pattern Recognition
Pattern recognition

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Xue, Z., Shen, D., Karacali, B., & Davatzikos, C. (2005). Statistical representation and simulation of high-dimensional deformations: Application to synthesizing brain deformations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3750 LNCS, pp. 500-508). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3750 LNCS). https://doi.org/10.1007/11566489_62

Statistical representation and simulation of high-dimensional deformations : Application to synthesizing brain deformations. / Xue, Zhong; Shen, Dinggang; Karacali, Bilge; Davatzikos, Christos.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3750 LNCS 2005. p. 500-508 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3750 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Xue, Z, Shen, D, Karacali, B & Davatzikos, C 2005, Statistical representation and simulation of high-dimensional deformations: Application to synthesizing brain deformations. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 3750 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3750 LNCS, pp. 500-508, 8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005, Palm Springs, CA, United States, 10/26/05. https://doi.org/10.1007/11566489_62
Xue Z, Shen D, Karacali B, Davatzikos C. Statistical representation and simulation of high-dimensional deformations: Application to synthesizing brain deformations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3750 LNCS. 2005. p. 500-508. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11566489_62
Xue, Zhong ; Shen, Dinggang ; Karacali, Bilge ; Davatzikos, Christos. / Statistical representation and simulation of high-dimensional deformations : Application to synthesizing brain deformations. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3750 LNCS 2005. pp. 500-508 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{342c41eda1b547c6b4770b6dfca5f25b,
title = "Statistical representation and simulation of high-dimensional deformations: Application to synthesizing brain deformations",
abstract = "This paper proposes an approach to effectively representing the statistics of high-dimensional deformations, when relatively few training samples are available, and conventional methods, like PCA, fail due to insufficient training. Based on previous work on scale-space decomposition of deformation fields, herein we represent the space of {"}valid deformations{"} as the intersection of three subspaces: one that satisfies constraints on deformations themselves, one that satisfies constraints on Jacobian determinants of deformations, and one that represents smooth deformations via a Markov Random Field (MRF). The first two are extensions of PCA-based statistical shape models. They are based on a wavelet packet basis decomposition that allows for more accurate estimation of the covariance structure of deformation or Jacobian fields, and they are used jointly due to their complementary strengths and limitations. The third is a nested MRF regularization aiming at eliminating potential discontinuities introduced by assumptions in the statistical models. A randomly sampled deformation field is projected onto the space of valid deformations via iterative projections on each of these subspaces until convergence, i.e. all three constraints are met. A deformation field simulator uses this process to generate random samples of deformation fields that are not only realistic but also representative of the full range of anatomical variability. These simulated deformations can be used for validation of deformable registration methods. Other potential uses of this approach include representation of shape priors in statistical shape models as well as various estimation and hypothesis testing paradigms in the general fields of computational anatomy and pattern recognition.",
author = "Zhong Xue and Dinggang Shen and Bilge Karacali and Christos Davatzikos",
year = "2005",
doi = "10.1007/11566489_62",
language = "English (US)",
isbn = "3540293264",
volume = "3750 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "500--508",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

TY - GEN

T1 - Statistical representation and simulation of high-dimensional deformations

T2 - Application to synthesizing brain deformations

AU - Xue, Zhong

AU - Shen, Dinggang

AU - Karacali, Bilge

AU - Davatzikos, Christos

PY - 2005

Y1 - 2005

N2 - This paper proposes an approach to effectively representing the statistics of high-dimensional deformations, when relatively few training samples are available, and conventional methods, like PCA, fail due to insufficient training. Based on previous work on scale-space decomposition of deformation fields, herein we represent the space of "valid deformations" as the intersection of three subspaces: one that satisfies constraints on deformations themselves, one that satisfies constraints on Jacobian determinants of deformations, and one that represents smooth deformations via a Markov Random Field (MRF). The first two are extensions of PCA-based statistical shape models. They are based on a wavelet packet basis decomposition that allows for more accurate estimation of the covariance structure of deformation or Jacobian fields, and they are used jointly due to their complementary strengths and limitations. The third is a nested MRF regularization aiming at eliminating potential discontinuities introduced by assumptions in the statistical models. A randomly sampled deformation field is projected onto the space of valid deformations via iterative projections on each of these subspaces until convergence, i.e. all three constraints are met. A deformation field simulator uses this process to generate random samples of deformation fields that are not only realistic but also representative of the full range of anatomical variability. These simulated deformations can be used for validation of deformable registration methods. Other potential uses of this approach include representation of shape priors in statistical shape models as well as various estimation and hypothesis testing paradigms in the general fields of computational anatomy and pattern recognition.

AB - This paper proposes an approach to effectively representing the statistics of high-dimensional deformations, when relatively few training samples are available, and conventional methods, like PCA, fail due to insufficient training. Based on previous work on scale-space decomposition of deformation fields, herein we represent the space of "valid deformations" as the intersection of three subspaces: one that satisfies constraints on deformations themselves, one that satisfies constraints on Jacobian determinants of deformations, and one that represents smooth deformations via a Markov Random Field (MRF). The first two are extensions of PCA-based statistical shape models. They are based on a wavelet packet basis decomposition that allows for more accurate estimation of the covariance structure of deformation or Jacobian fields, and they are used jointly due to their complementary strengths and limitations. The third is a nested MRF regularization aiming at eliminating potential discontinuities introduced by assumptions in the statistical models. A randomly sampled deformation field is projected onto the space of valid deformations via iterative projections on each of these subspaces until convergence, i.e. all three constraints are met. A deformation field simulator uses this process to generate random samples of deformation fields that are not only realistic but also representative of the full range of anatomical variability. These simulated deformations can be used for validation of deformable registration methods. Other potential uses of this approach include representation of shape priors in statistical shape models as well as various estimation and hypothesis testing paradigms in the general fields of computational anatomy and pattern recognition.

UR - http://www.scopus.com/inward/record.url?scp=33744798244&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744798244&partnerID=8YFLogxK

U2 - 10.1007/11566489_62

DO - 10.1007/11566489_62

M3 - Conference contribution

SN - 3540293264

SN - 9783540293262

VL - 3750 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 500

EP - 508

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -