Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data by Carl-Fredrik Westin Anna Vilanova & Bernhard Burgeth

Author:Carl-Fredrik Westin, Anna Vilanova & Bernhard Burgeth
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

Fig. 2Biological phantom dataset. (a) The layout of the phantom created using two excised rat spinal cords. (b) ODFs estimated from the signal as reference geometry. (c) EAPs computed from 4th order tensors estimated using the Riemannian approach. (d) EAPs computed from 4th order tensors estimated using the Ternary Quartic approach. The EAPs were evaluated at the constant probability radius of m

The results are presented in Fig. 2. The geometry of the EAPs computed from the 4th order tensors estimated using both the methods are coherent with the underlying phantom model, and also agree with the geometry of the ODFs. It is interesting to note that since the ODFs are angular marginal distributions of the true EAPs, the radial information of the true EAPs has been marginalized out by a radial integration. Therefore, although the ODFs’ angular structures resemble the angular structures of the EAPs computed from the 4th order tensors, the ODFs do not reveal anything about the magnitude of diffusion due to the heterogeneous structure of the underlying tissue. This is visible in the EAPs computed from the tensors from the size or volume of the displacement probability at a constant displacement radius. Also, by comparing (c) and (d) in Fig. 2, again the EAPs from the TQ method look sharper than the Riemannian counterparts.

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