P. [. Axler, W. Bourdon, and . Ramey, Harmonic function theory, Graduate Texts in Mathematics, vol.137, 2001.
DOI : 10.1007/b97238

K. Atkinson, W. Hanar95-]-s, W. Axler, and . Ramey, Spherical harmonics and approximations on the unit sphere: an introduction, volume 2044 of Lecture Notes in Mathematics Harmonic polynomials and Dirichlet-type problems, Proc. Amer, pp.3765-3773, 1995.

P. Basser, S. [. Pajevic, B. C. Barmpoutis, J. R. Vemuri, and . Forder, Spectral decomposition of a 4th-order covariance tensor : Applications to diffusion tensor mri Fast displacement probability profile approximation from hardi using 4th-order tensors The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group), Proceedings of ISBI: IEEE International Symposium on Biomedical Imaging Algebraic groups and homogeneous spaces, pp.220-236, 2007.

E. Caruyer and R. Verma, On facilitating the use of HARDI in population studies by creating rotation-invariant markers, Medical Image Analysis, vol.20, issue.1, pp.87-96, 2015.
DOI : 10.1016/j.media.2014.10.009
URL : https://hal.archives-ouvertes.fr/hal-01090154

G. [. Derksen and . Kemper, Computational invariant theory Invariant Theory and Algebraic Transformation Groups, I, Encyclopaedia of Mathematical Sciences, 130. [DK15] H. Derksen and G. Kemper. Computational invariant theory, 2002.
DOI : 10.1007/978-3-662-04958-7

C. Delmaire, M. Vidailhet, D. Wassermann, M. Descoteaux, R. Valabregue et al., Diffusion abnormalities in the primary sensorimotor pathways in writer's cramp Computation of cubic harmonics Characterization of anisotropy in high angular resolution diffusion-weighted MRI, Archives of Neurology J. Computational Phys. Magnetic Resonance in Medicine, vol.66, issue.2546, pp.386-408, 1977.

A. Ghosh, T. Papadopoulo, and R. Deriche, Biomarkers for HARDI: 2nd & 4th order tensor invariants, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), 2012.
DOI : 10.1109/ISBI.2012.6235475
URL : https://hal.archives-ouvertes.fr/hal-00667905

A. Ghosh, T. Papadopoulo, R. [. Deriche, C. Golub, and . Van-loan, Generalized Invariants of a 4th order tensor: Building blocks for new biomarkers in dMRI, Computational Diffusion MRI Workshop (CDMRI), MICCAI Matrix computations. Johns Hopkins Studies in the Mathematical SciencesGW09] R. Goodman and N. R. Wallach. Symmetry, representations, and invariants, pp.165-173, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00789763

J. Grace and A. Young, The algebra of invariants. Cambridge Library Collection, 2010.

E. Hubert and I. Kogan, Rational invariants of a group action. Construction and rewriting, Journal of Symbolic Computation, vol.42, issue.1-2, pp.203-217, 2007.
DOI : 10.1016/j.jsc.2006.03.005
URL : https://hal.archives-ouvertes.fr/hal-00839283

E. Hubert, I. Koganhl12-]-e, G. Hubert, . Labahnhl13-]-e, G. Hubert et al., Smooth and algebraic invariants of a group action. Local and global constructions Rational invariants of scalings from Hermite normal forms Scaling invariants and symmetry reduction of dynamical systems, ISSAC 2012, pp.355-393, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00198857

E. Hubert, G. Labahnhub12-]-e, and . Hubert, Computation of invariants of finite abelian groups, Foundations of computational mathematics number 403 in London Mathematical Society Lecture Note SeriesKre05] D. Kressner. Numerical methods for general and structured eigenvalue problems of Lecture Notes in Computational Science and Engineering, pp.3029-3050, 2005.
DOI : 10.1090/mcom/3076

]. X. Lmm-+-10, A. Li, G. Messé, M. Marrelec, H. Pélégrini-issac et al., An enhanced voxel-based morphometry method to investigate structural changes: application to alzheimer's disease, Neuroradiology, vol.52, issue.3, pp.203-213, 2010.

J. Muggli, Cubic harmonics as linear combinations of spherical harmonics, Zeitschrift f??r angewandte Mathematik und Physik ZAMP, vol.41, issue.2, pp.311-317, 1972.
DOI : 10.1007/BF01593094

M. Olive, B. Kolev, and N. Auffray, A minimal integrity basis for the elasticity tensor. Archive for Rational Mechanics and Analysis, p.2017
URL : https://hal.archives-ouvertes.fr/hal-01467996

M. Olive, About Gordan???s Algorithm for Binary Forms, Foundations of Computational Mathematics, vol.161, issue.2, pp.1-60, 2016.
DOI : 10.1007/978-0-387-89498-0
URL : http://arxiv.org/abs/1403.2283

T. Papadopoulo, A. Ghosh, and R. Deriche, Complete Set of Invariants of a 4 th Order Tensor: The 12 Tasks of HARDI from Ternary Quartics, Medical Image Computing and Computer-Assisted Intervention ? MICCAI 2014, pp.233-240, 2014.
DOI : 10.1007/978-3-319-10443-0_30
URL : https://hal.archives-ouvertes.fr/hal-01092492

M. Rosenlicht, Some basic theorems on algebraic groups Algebraic quotients of compact group actions On a theorem of Weitzenböck in invariant theory, Stu08] B. Sturmfels. Algorithms in invariant theory. Texts and Monographs in Symbolic Computation. SpringerWien- NewYork, pp.401-443365, 1956.

D. S. Tuch, T. G. Reese, M. R. Weigel, and V. J. Wedeen, Diffusion MRI of Complex Neural Architecture, Neuron, vol.40, issue.5, pp.885-895, 2003.
DOI : 10.1016/S0896-6273(03)00758-X
URL : http://doi.org/10.1016/s0896-6273(03)00758-x

S. David, . Tuchveg00-]-g, and . Vegter, Diffusion MRI of Complex Tissue Structure The apolar bilinear form in geometric modeling, Math. Comp, vol.69, issue.230, pp.691-720, 2000.

È. Vinberg, V. Popov, and I. R. Shafarevich, Invariant theory, volume 55 of Encyclopaedia of Mathematical Sciences A translation of ?t Algebraic geometry, Akad. Nauk SSSR Vsesoyuz, 1989.