Skip to main content
SpringerLink
Log in

Toward New Spherical Harmonic Shannon Entropy for Surface Modeling

  • Conference paper
  • First Online:
Book cover Computer Analysis of Images and Patterns (CAIP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11679))

Included in the following conference series:

Abstract

Genus zero surfaces are widespread forms in real life. It is important to have adequate mathematical tools that best represent them. Spherical harmonics are special bases able to model them in a compact and a relevant way. The main problem of the spherical harmonics modeling process is how to define the optimal reconstruction order that best represent the initial surface. This paper proposed a new spherical harmonics shannon-type entropy to optimize reconstruction and to provide an accurate and efficient evaluation method of the reconstruction order.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Telesca, L., Lapenna, V., Lovallo, M.: Information entropy analysis of seismcity of umbria-marche region (Central Italy). Nat. Hazards Earth Syst. Sci. 4(5/6), 691–695 (2004)

    Article  Google Scholar 

  2. Telesca, L., Lovallo, M., Molist, J.M., Moreno, C.L., Mendelez, R.A.: Using the fisher-shannon method to characterize continuous seismic signal during volcanic eruptions: application to 20112012 El Hierro (Canary Islands) eruption. Terra Nova. 26, 425–429 (2014)

    Article  Google Scholar 

  3. Wanga, B., Chena, L.L., Chengc, J.: New result on maximum entropy threshold image segmentation based on P system. Optik 163, 81–85 (2018)

    Article  Google Scholar 

  4. Nicolis, O., Mateu, J.: 2D anisotropic wavelet entropy with an application to earthquakes in Chile. Entropy 17(6), 4155–4172 (2015)

    Article  Google Scholar 

  5. Vazquez, P.-P., Feixas, M., Sebert, M., Heidrich, W.: Viewpoint Selection using Viewpoint Entropy, pp. 21–23. Stuttgart, Germany (2001)

    Google Scholar 

  6. Shannon, C.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (2008)

    Article  MathSciNet  Google Scholar 

  7. Khelifa, W.B., Ben Abdallah, A., Ghorbel, F.: Three dimensional modeling of the left ventricle of the heart using spherical harmonic analysis. In: ISBI, pp. 1275–1278 (2008)

    Google Scholar 

  8. Arfaoui S., Rezgui, I., Ben Mabrouk, A.: Wavelet Analysis On The Sphere, Spheroidal Wavelets, Degryuter. Degruyter, ISBN 978-3-11-048188-4 (2017)

    Google Scholar 

  9. Jallouli, M., Zemni, M., Ben Mabrouk, A., Mahjoub, M.A.: Toward recursive spherical harmonics-issued bi-filters: Part I: theoretical framework. Soft Computing. Springer, Berlin (2018). https://doi.org/10.1007/s00500-018-3596-9

    Chapter  Google Scholar 

  10. Muller, I.: Entropy and energy, a universal competition. Entropy 10, 462–476 (2008)

    Article  MathSciNet  Google Scholar 

  11. Robinson, D.W.: Entropy and uncertainty. Entropy 10, 493–506 (2008)

    Article  MathSciNet  Google Scholar 

  12. Muller, I.: Extended thermodynamics: a theory of symmetric hyperbolic field equations. Entropy 10, 477–492 (2008)

    Article  MathSciNet  Google Scholar 

  13. Ruggeri, T.: The entropy principle from continuum mechanics to hyperbolic systems of balance laws: the modern theory of extended thermodynamics. Entropy 10, 319–333 (2008)

    Article  Google Scholar 

  14. Fradkov, A.: Speed-gradient entropy principle for nonstationary processes. Entropy 10, 757–764 (2008)

    Article  Google Scholar 

  15. Sello, S.: Wavelet entropy and the multi-peaked structure of solar cycle maximum. New Astron. 8, 105–117 (2003)

    Article  Google Scholar 

  16. Brechbuhler, C., Gerig, G., Kubler, O.: Parametrization of closed surfaces for 3-D shape description. Comput. Vis. Image Underst. 16, 154–170 (1996)

    Google Scholar 

  17. Chen, C., Huang, T.: Left ventricle motion analysis by hierarchical decomposition. ICASSP 3, 273–376 (1992)

    Google Scholar 

  18. Staib, L.H., Duncan, J.S.: Model-based deformable surface finding for medical imaging. IEEE Trans. Med. Imag. 15, 720–731 (1996)

    Article  Google Scholar 

  19. Ibrahim Mahmoud, M.M., Ben Mabrouk, A., Abdallah Hashim, M.H.: Wavelet multifractal models for transmembrane proteins’ series. Int. J. Wavelets Multires. Inf. Process. 14, 1650044 (2016)

    Article  Google Scholar 

  20. Makadia, A., Daniilidis, K.: Direct 3D-rotation estimation from spherical images via a generalized shift theorem. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Proceedings, pp. 18–20 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LATIS- Laboratory of Advanced Technology and Intelligent Systems, Université de Sousse, Ecole Nationale d’Ingénieurs de Sousse, 4023, Sousse, Tunisia

    Malika Jallouli, Wafa Belhadj Khalifa & Mohamed Ali Mahjoub

  2. Department of Mathematics, Faculty of Sciences, Research Unit of Algebra, Number Theory and Nonlinear Analysis UR11ES50, 5019, Monastir, Tunisia

    Anouar Ben Mabrouk

  3. Department of Mathematics, Higher Institute of Applied Mathematics and Informatics, Street of Assad Ibn Al-Fourat, 3100, Kairouan, Tunisia

    Anouar Ben Mabrouk

  4. Department of Mathematics, Faculty of Sciences, University of Tabuk, King Faisal Rd, Tabuk, Saudi Arabia

    Anouar Ben Mabrouk

Authors
  1. Malika Jallouli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wafa Belhadj Khalifa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anouar Ben Mabrouk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohamed Ali Mahjoub
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed Ali Mahjoub .

Editor information

Editors and Affiliations

  1. Department of Computer and Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy

    Mario Vento

  2. Department of Computer and Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy

    Gennaro Percannella

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jallouli, M., Khalifa, W.B., Mabrouk, A.B., Mahjoub, M.A. (2019). Toward New Spherical Harmonic Shannon Entropy for Surface Modeling. In: Vento, M., Percannella, G. (eds) Computer Analysis of Images and Patterns. CAIP 2019. Lecture Notes in Computer Science(), vol 11679. Springer, Cham. https://doi.org/10.1007/978-3-030-29891-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-29891-3_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29890-6

  • Online ISBN: 978-3-030-29891-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation