Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

  • Adrien DepeursingeEmail author
  • Julien Fageot
  • Vincent Andrearczyk
  • John Paul Ward
  • Michael Unser
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11046)


We define and investigate the Local Rotation Invariance (LRI) and Directional Sensitivity (DS) of radiomics features. Most of the classical features cannot combine the two properties, which are antagonist in simple designs. We propose texture operators based on spherical harmonic wavelets (SHW) invariants and show that they are both LRI and DS. An experimental comparison of SHW and popular radiomics operators for classifying 3D textures reveals the importance of combining the two properties for optimal pattern characterization.


Radiomics 3D texture Spherical harmonics Wavelets 



This work was supported by the Swiss National Science Foundation (grants PZ00P2_154891 and 205320_179069).


  1. 1.
    van Griethuysen, J.J.M., et al.: Computational radiomics system to decode the radiographic phenotype. Cancer Res. 77(21), e104–e107 (2017)CrossRefGoogle Scholar
  2. 2.
    Gatenby, R.A., Grove, O., Gillies, R.J.: Quantitative imaging in cancer evolution and ecology. Radiology 269(1), 8–14 (2013)CrossRefGoogle Scholar
  3. 3.
    Depeursinge, A., Al-Kadi, O.S., Mitchell, J.R.: Biomedical Texture Analysis: Fundamentals. Applications and Tools. Elsevier-MICCAI Book series. Academic Press, London (2017)Google Scholar
  4. 4.
    Daubechies, I.: Ten Lectures on Wavelets, vol. 61. SIAM, Philadelphia (1992)CrossRefGoogle Scholar
  5. 5.
    Driscoll, J.R., Healy, D.M.: Computing fourier transforms and convolutions on the 2-sphere. Adv. Appl. Math. 15(2), 202–250 (1994)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, vol. 55. Courier Corporation, New York (1964)zbMATHGoogle Scholar
  7. 7.
    Ward, J.P., Unser, M.: Harmonic singular integrals and steerable wavelets in \(L_{2}(\mathbb{R}^{d})\). Appl. Comput. Harmon. Anal. 36(2), 183–197 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dicente Cid, Y., Müller, H., Platon, A., Poletti, P.-A., Depeursinge, A.: 3-D solid texture classification using locally-oriented wavelet transforms. IEEE Trans. Image Process. 26(4), 1899–1910 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Haralick, R.M.: Statistical and structural approaches to texture. Proc. IEEE 67(5), 786–804 (1979)CrossRefGoogle Scholar
  10. 10.
    Galloway, M.M.: Texture analysis using gray level run lengths. Comput. Graph. Image Process. 4(2), 172–179 (1975)CrossRefGoogle Scholar
  11. 11.
    Thibault, G., et al.: Texture indexes and gray level size zone matrix: application to cell nuclei classification. Pattern Recognit. Inf. Process. 140–145 (2009)Google Scholar
  12. 12.
    Paulhac, L., Makris, P., Ramel, J.-Y.: A solid texture database for segmentation and classification experiments. In: 4th International Conference on Computer Vision Theory and Applications, pp. 135–141 (2009)Google Scholar
  13. 13.
    Andrearczyk, V., Depeursinge, A.: Rotational 3D texture classification using group equivariant CNNs. In submitted to SPIE Medical Imaging (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Adrien Depeursinge
    • 1
    • 2
    Email author
  • Julien Fageot
    • 1
  • Vincent Andrearczyk
    • 2
  • John Paul Ward
    • 3
  • Michael Unser
    • 1
  1. 1.Biomedical Imaging GroupEcole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  2. 2.Institute of Information Systems, University of Applied Sciences Western Switzerland (HES-SO)SierreSwitzerland
  3. 3.Department of MathematicsNorth Carolina A&T State UniversityGreensboroUSA

Personalised recommendations