We design and evaluate a novel method to compute rotationally invariant features using High Angular Resolution Diffusion Imaging (HARDI) data. These measures quantify the complexity of the angular diffusion profile mod-eled using a higher order model, thereby giving more information than classi-cal diffusion tensor-derived parameters. The method is based on the spheri-cal harmonic (SH) representation of the angular diffusion information, and is generalizable to a range of HARDI reconstruction models. These scalars are obtained as homogeneous polynomials of the SH representation of a HARDI reconstruction model. We show that finding such polynomials is equiva-lent to solving a large linear system of equations, and present a numerical method based on sparse matrices to efficiently solve this system. Among the solutions, we only keep a subset of algebraically independent polynomials, using an algorithm based on a numerical implementation of the Jacobian criterion. We compute a set of 12 or 25 rotationally invariant measures rep-resentative of the underlying white matter for the rank-4 or rank-6 spherical harmonics (SH) representation of the apparent diffusion coefficient (ADC)