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

17 Citations (Scopus)

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
Title of host publicationMedical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - 8th International Conference, Proceedings
Pages500-508
Number of pages9
DOIs
Publication statusPublished - 2005
Externally publishedYes
Event8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - Palm Springs, CA, United States
Duration: 2005 Oct 262005 Oct 29

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3750 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005
CountryUnited States
CityPalm Springs, CA
Period05/10/2605/10/29

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Xue, Z., Shen, D., Karacali, B., & Davatzikos, C. (2005). Statistical representation and simulation of high-dimensional deformations: Application to synthesizing brain deformations. In Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - 8th International Conference, Proceedings (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