Rotation invariant features are an indispensable tool for characterizing diffusion Magnetic Resonance Imaging (MRI) and in particular for brain tissue microstructure estimation. In this work, we propose a new mathematical framework for efficiently calculating a complete set of such invariants from any spherical function. Specifically, our method is based on the spherical harmonics series expansion of a given function of any order and can be applied directly to the resulting coefficients by performing a simple integral operation analytically. This enable us to derive a general closed-form equation for the invariants. We test our invariants on the diffusion MRI fiber orientation distribution function obtained from the diffusion signal both in-vivo and in synthetic data. Results show how it is possible to use these invariants for characterizing the white matter using a small but complete set of features.
CITATION STYLE
Zucchelli, M., Deslauriers-Gauthier, S., & Deriche, R. (2019). A Closed-Form Solution of Rotation Invariant Spherical Harmonic Features in Diffusion MRI. In Mathematics and Visualization (pp. 77–89). Springer Heidelberg. https://doi.org/10.1007/978-3-030-05831-9_7
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