We studied the symmetries of the diffusion and covariance tensors, both accessible through a general b-tensor acquisition. We showed that there is an unexplored contrast in the non-symmetric part of the covariance tensor and use it to compute the size-shape covariance of compartmental diffusion tensors. We measure all rotational invariants of the cumulant tensors in a normal volunteer, explore the novel size-shape contrast, and provide the relations between these invariants and typical diffusion contrasts.
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