Some geometric ideas for feature enhancement of diffusion tensor fields

Hamza Farooq, Yongxin Chen, Tryphon T. Georgiou, Christophe Lenglet
2016 2016 IEEE 55th Conference on Decision and Control (CDC)  
Diffusion Tensor Tomography generates a 3dimensional 2-tensor field that encapsulates properties of probed matter. 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
more » ... 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. 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.
doi:10.1109/cdc.2016.7798851 dblp:conf/cdc/FarooqCGL16 fatcat:mvzjau5tjvb2vcl4jrffcaiq4y