TY - GEN
T1 - Some geometric ideas for feature enhancement of diffusion tensor fields
AU - Farooq, Hamza
AU - Chen, Yongxin
AU - Georgiou, Tryphon T.
AU - Lenglet, Christophe
N1 - Publisher Copyright:
© 2016 IEEE.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2016/12/27
Y1 - 2016/12/27
N2 - 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.
AB - 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.
KW - Ricci flow
KW - Riemannian geometry
KW - nonlinear diffusion
UR - http://www.scopus.com/inward/record.url?scp=85010764341&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2016.7798851
DO - 10.1109/CDC.2016.7798851
M3 - Conference contribution
AN - SCOPUS:85010764341
T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
SP - 3856
EP - 3861
BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 55th IEEE Conference on Decision and Control, CDC 2016
Y2 - 12 December 2016 through 14 December 2016
ER -