Fabric Tensor Characterization of Tensor-Valued Directional Data: Solution, Accuracy, and Symmetrization

Table 1

Coefficients of lower order fabric tensors of the second kind using asymmetric characterization for tensor-valued ODFs (2D and 3D).

𝐬𝑚(n)	𝓢𝑚	𝓢𝑚⨁2	𝓢𝑚⨁4	𝓢𝑚⨁6	𝐚𝑚(n)	𝓐𝑚⨁1	𝓐𝑚⨁3	𝓐𝑚⨁5	𝓐𝑚⨁7
𝐒𝑚	1,1				𝐀𝑚⨁1	2,3
𝐒𝑚⨁2	3−1,−2	4,152			𝐀𝑚⨁3	−4,−152	8,352
𝐒𝑚⨁4	1,158	−12,−1054	16,3158		𝐀𝑚⨁5	6,1058	−32,−3154	32,6938
𝐒𝑚⨁6	−1,−3516	24,94516	−80,−346516	64,300316	𝐀𝑚⨁7	−8,−31516	80,346516	−192,−900916	128,643516