A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis

Monami Banerjee, Rudrasis Chakraborty, Edward Ofori, Michael S. Okun, David E. Vaillancourt, Baba C. Vemuri

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

20 Scopus citations

Abstract

Regression is an essential tool in Statistical analysis of data with many applications in Computer Vision, Machine Learning, Medical Imaging and various disciplines of Science and Engineering. Linear and nonlinear regression in a vector space setting has been well studied in literature. However, generalizations to manifold-valued data are only recently gaining popularity. With the exception of a few, most existing methods of regression for manifold valued data are limited to geodesic regression which is a generalization of the linear regression in vector-spaces. In this paper, we present a novel nonlinear kernel-based regression method that is applicable to manifold valued data. Our method is applicable to cases when the independent and dependent variables in the regression model are both manifold-valued or one is manifold-valued and the other is vector or scalar valued. Further, unlike most methods, our method does not require any imposed ordering on the manifold-valued data. The performance of our model is tested on a large number of real data sets acquired from Alzhiemers and movement disorder (Parkinsons and Essential Tremor) patients. We present an extensive set of results along with statistical validation and comparisons.

Original languageEnglish (US)
Title of host publicationProceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
PublisherIEEE Computer Society
Pages4424-4432
Number of pages9
ISBN (Electronic)9781467388504
DOIs
StatePublished - Dec 9 2016
Externally publishedYes
Event29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 - Las Vegas, United States
Duration: Jun 26 2016Jul 1 2016

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume2016-December
ISSN (Print)1063-6919

Conference

Conference29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
CountryUnited States
CityLas Vegas
Period6/26/167/1/16

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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  • Cite this

    Banerjee, M., Chakraborty, R., Ofori, E., Okun, M. S., Vaillancourt, D. E., & Vemuri, B. C. (2016). A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis. In Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 (pp. 4424-4432). [7780848] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; Vol. 2016-December). IEEE Computer Society. https://doi.org/10.1109/CVPR.2016.479