Riemannian nonlinear mixed effects models: Analyzing longitudinal deformations in neuroimaging

Hyun Woo Kim, Nagesh Adluru, Heemanshu Suri, Baba C. Vemuri, Sterling C. Johnson, Vikas Singh

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

8 Citations (Scopus)

Abstract

Statistical machine learning models that operate on manifold-valued data are being extensively studied in vision, motivated by applications in activity recognition, feature tracking and medical imaging. While non-parametric methods have been relatively well studied in the literature, efficient formulations for parametric models (which may offer benefits in small sample size regimes) have only emerged recently. So far, manifold-valued regression models (such as geodesic regression) are restricted to the analysis of cross-sectional data, i.e., the so-called “fixed effects” in statistics. But in most “longitudinal analysis” (e.g., when a participant provides multiple measurements, over time) the application of fixed effects models is problematic. In an effort to answer this need, this paper generalizes non-linear mixed effects model to the regime where the response variable is manifold-valued, i.e., f : Rd → M. We derive the underlying model and estimation schemes and demonstrate the immediate benefits such a model can provide - both for group level and individual level analysis - on longitudinal brain imaging data. The direct consequence of our results is that longitudinal analysis of manifold-valued measurements (especially, the symmetric positive definite manifold) can be conducted in a computationally tractable manner.

Original languageEnglish
Title of host publicationProceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5777-5786
Number of pages10
ISBN (Electronic)9781538604571
DOIs
Publication statusPublished - 2017 Nov 6
Externally publishedYes
Event30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017 - Honolulu, United States
Duration: 2017 Jul 212017 Jul 26

Publication series

NameProceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
Volume2017-January

Other

Other30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
CountryUnited States
CityHonolulu
Period17/7/2117/7/26

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ASJC Scopus subject areas

  • Signal Processing
  • Computer Vision and Pattern Recognition

Cite this

Kim, H. W., Adluru, N., Suri, H., Vemuri, B. C., Johnson, S. C., & Singh, V. (2017). Riemannian nonlinear mixed effects models: Analyzing longitudinal deformations in neuroimaging. In Proceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017 (pp. 5777-5786). (Proceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017; Vol. 2017-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CVPR.2017.612