Interpolation on the manifold of K component GMMs

Hyun Woo Kim, Nagesh Adluru, Monami Banerjee, Baba C. Vemuri, Vikas Singh

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

2 Citations (Scopus)

Abstract

Probability density functions (PDFs) are fundamental "objects" in mathematics with numerous applications in computer vision, machine learning and medical imaging. The feasibility of basic operations such as computing the distance between two PDFs and estimating a mean of a set of PDFs is a direct function of the representation we choose to work with. In this paper, we study the Gaussian mixture model (GMM) representation of the PDFs motivated by its numerous attractive features. (1) GMMs are arguably more interpretable than, say, square root parameterizations (2) the model complexity can be explicitly controlled by the number of components and (3) they are already widely used in many applications. The main contributions of this paper are numerical algorithms to enable basic operations on such objects that strictly respect their underlying geometry. For instance, when operating with a set of k component GMMs, a first order expectation is that the result of simple operations like interpolation and averaging should provide an object that is also a k component GMM. The literature provides very little guidance on enforcing such requirements systematically. It turns out that these tasks are important internal modules for analysis and processing of a field of ensemble average propagators (EAPs), common in diffusion weighted magnetic resonance imaging. We provide proof of principle experiments showing how the proposed algorithms for interpolation can facilitate statistical analysis of such data, essential to many neuroimaging studies. Separately, we also derive interesting connections of our algorithm with functional spaces of Gaussians, that may be of independent interest.

Original languageEnglish
Title of host publication2015 International Conference on Computer Vision, ICCV 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2884-2892
Number of pages9
ISBN (Electronic)9781467383912
DOIs
Publication statusPublished - 2015 Feb 17
Externally publishedYes
Event15th IEEE International Conference on Computer Vision, ICCV 2015 - Santiago, Chile
Duration: 2015 Dec 112015 Dec 18

Publication series

NameProceedings of the IEEE International Conference on Computer Vision
Volume2015 International Conference on Computer Vision, ICCV 2015
ISSN (Print)1550-5499

Other

Other15th IEEE International Conference on Computer Vision, ICCV 2015
CountryChile
CitySantiago
Period15/12/1115/12/18

Fingerprint

Probability density function
Interpolation
Neuroimaging
Medical imaging
Magnetic resonance
Parameterization
Set theory
Computer vision
Learning systems
Statistical methods
Imaging techniques
Geometry
Processing
Experiments

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Cite this

Kim, H. W., Adluru, N., Banerjee, M., Vemuri, B. C., & Singh, V. (2015). Interpolation on the manifold of K component GMMs. In 2015 International Conference on Computer Vision, ICCV 2015 (pp. 2884-2892). [7410687] (Proceedings of the IEEE International Conference on Computer Vision; Vol. 2015 International Conference on Computer Vision, ICCV 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICCV.2015.330

Interpolation on the manifold of K component GMMs. / Kim, Hyun Woo; Adluru, Nagesh; Banerjee, Monami; Vemuri, Baba C.; Singh, Vikas.

2015 International Conference on Computer Vision, ICCV 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2884-2892 7410687 (Proceedings of the IEEE International Conference on Computer Vision; Vol. 2015 International Conference on Computer Vision, ICCV 2015).

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

Kim, HW, Adluru, N, Banerjee, M, Vemuri, BC & Singh, V 2015, Interpolation on the manifold of K component GMMs. in 2015 International Conference on Computer Vision, ICCV 2015., 7410687, Proceedings of the IEEE International Conference on Computer Vision, vol. 2015 International Conference on Computer Vision, ICCV 2015, Institute of Electrical and Electronics Engineers Inc., pp. 2884-2892, 15th IEEE International Conference on Computer Vision, ICCV 2015, Santiago, Chile, 15/12/11. https://doi.org/10.1109/ICCV.2015.330
Kim HW, Adluru N, Banerjee M, Vemuri BC, Singh V. Interpolation on the manifold of K component GMMs. In 2015 International Conference on Computer Vision, ICCV 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 2884-2892. 7410687. (Proceedings of the IEEE International Conference on Computer Vision). https://doi.org/10.1109/ICCV.2015.330
Kim, Hyun Woo ; Adluru, Nagesh ; Banerjee, Monami ; Vemuri, Baba C. ; Singh, Vikas. / Interpolation on the manifold of K component GMMs. 2015 International Conference on Computer Vision, ICCV 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 2884-2892 (Proceedings of the IEEE International Conference on Computer Vision).
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