A computational Framework for generating rotation invariant features and its application in diffusion MRI

• Published in: Medical image analysis Vol. 60; p. 101597
• Main Authors: Zucchelli, Mauro, Deslauriers-Gauthier, Samuel, Deriche, Rachid
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.02.2020; Elsevier BV; Elsevier
• Subjects: Algorithms; Bioengineering; Biomarkers; Computational neuroscience; Computer Science; Connectome - methods; Diffusion; Diffusion coefficient; Diffusion Magnetic Resonance Imaging - methods; Diffusion MRI; Distribution functions; Fiber orientation; Gaunt coefficients; Humans; Image Processing, Computer-Assisted - methods; Imaging; Invariants; Life Sciences; Magnetic resonance imaging; Mathematical analysis; Medical Imaging; Microstructure; Nerve Fibers, Myelinated - ultrastructure; Rotation; Rotation invariants; Series expansion; Spherical harmonics; Rotation invariants; Biomarkers; Gaunt coefficients; Diffusion MRI; Spherical harmonics; Gaunt Coefficients; Rotation Invariants; Spherical Harmonics
• DOI: 10.1016/j.media.2019.101597
• ISSN: 1361-8415; 1361-8423

•A new computational framework for the analytical generation of a complete set of algebraically independent Rotation Invariant Features (RIF) for spherical functions.•These new invariants can be linked to statistical and geometrical measures of spherical functions e.g.: the mean, the variance and the volume.•We apply our new RIF to diffusion MRI in particular to the Apparent Diffusion Coefficient, the fiber Orientation Distribution Function, and the diffusion signal itself.•Using both synthetic and real data, we assess the sensitivity of our invariants to brain tissue microstructure related changes in the diffusion signal. [Display omitted] In this work, we present a novel computational framework for analytically generating a complete set of algebraically independent Rotation Invariant Features (RIF) given the Laplace-series expansion of a spherical function. Our computational framework provides a closed-form solution for these new invariants, which are the natural expansion of the well known spherical mean, power-spectrum and bispectrum invariants. We highlight the maximal number of algebraically independent invariants which can be obtained from a truncated Spherical Harmonic (SH) representation of a spherical function and show that most of these new invariants can be linked to statistical and geometrical measures of spherical functions, such as the mean, the variance and the volume of the spherical signal. Moreover, we demonstrate their application to dMRI signal modeling including the Apparent Diffusion Coefficient (ADC), the diffusion signal and the fiber Orientation Distribution Function (fODF). In addition, using both synthetic and real data, we test the ability of our invariants to estimate brain tissue microstructure in healthy subjects and show that our framework provides more flexibility and open up new opportunities for innovative development in the domain of microstructure recovery from diffusion MRI.