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A Closed-Form Solution of Rotation Invariant Spherical Harmonic Features in Diffusion MRI

Abstract : 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.
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https://hal.inria.fr/hal-01912148
Contributor : Mauro Zucchelli <>
Submitted on : Monday, November 5, 2018 - 11:04:38 AM
Last modification on : Monday, October 12, 2020 - 10:28:55 AM
Long-term archiving on: : Wednesday, February 6, 2019 - 2:49:40 PM

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  • HAL Id : hal-01912148, version 1

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Mauro Zucchelli, Samuel Deslauriers-Gauthier, Rachid Deriche. A Closed-Form Solution of Rotation Invariant Spherical Harmonic Features in Diffusion MRI. MICCAI - Computational Diffusion MRI Workshop 2018, Sep 2018, Granada, Spain. ⟨hal-01912148⟩

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