Some geometric ideas for feature enhancement of diffusion tensor fields

Hamza Farooq, Yongxin Chen, Tryphon T. Georgiou, Christophe Lenglet

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

Abstract

Diffusion Tensor Imaging (DTI) generates a 3- dimensional 2-tensor field that encapsulates properties of diffusing water molecules. We present two complementing ideas that may be used to enhance and highlight geometric features that are present. The first is based on Ricci flow and can be understood as a nonlinear bandpass filtering technique that takes into account directionality of the spectral content. More specifically, we view the data as a Riemannian metric and, in manner reminiscent to reversing the heat equation, we regularize the Ricci flow so as to taper off the growth of the higher-frequency speckle-type of irregularities. The second approach, in which we again view data as defining a Riemannian structure, relies on averaging nearby values of the tensor field by weighing the summands in a manner which is inversely proportional to their corresponding distances of the tensors. The effect of this particular averaging is to enhance consensus among neighboring cells, regarding the principle directions and the values of the corresponding eigenvalues of the tensor field. This consensus is amplified along directions where distances in the Riemannian metric are short.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3856-3861
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

Fingerprint

Tensors
Tensor
Enhancement
Ricci Flow
Riemannian Metric
Diffusion tensor imaging
Averaging
Weighing
Speckle
Irregularity
Heat Equation
Filtering
Molecules
Directly proportional
Imaging
Eigenvalue
Water
Cell
Eigenvalues

Keywords

  • Ricci flow
  • Riemannian geometry
  • nonlinear diffusion

Cite this

Farooq, H., Chen, Y., Georgiou, T. T., & Lenglet, C. (2016). Some geometric ideas for feature enhancement of diffusion tensor fields. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 3856-3861). [7798851] (2016 IEEE 55th Conference on Decision and Control, CDC 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798851

Some geometric ideas for feature enhancement of diffusion tensor fields. / Farooq, Hamza; Chen, Yongxin; Georgiou, Tryphon T.; Lenglet, Christophe.

2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 3856-3861 7798851 (2016 IEEE 55th Conference on Decision and Control, CDC 2016).

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

Farooq, H, Chen, Y, Georgiou, TT & Lenglet, C 2016, Some geometric ideas for feature enhancement of diffusion tensor fields. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7798851, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers Inc., pp. 3856-3861, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798851
Farooq H, Chen Y, Georgiou TT, Lenglet C. Some geometric ideas for feature enhancement of diffusion tensor fields. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 3856-3861. 7798851. (2016 IEEE 55th Conference on Decision and Control, CDC 2016). https://doi.org/10.1109/CDC.2016.7798851
Farooq, Hamza ; Chen, Yongxin ; Georgiou, Tryphon T. ; Lenglet, Christophe. / Some geometric ideas for feature enhancement of diffusion tensor fields. 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 3856-3861 (2016 IEEE 55th Conference on Decision and Control, CDC 2016).
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