Skip to main content
SpringerLink
Log in

Tensor Method for Constructing 3D Moment Invariants

  • Conference paper
Computer Analysis of Images and Patterns (CAIP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6855))

Included in the following conference series:

Abstract

A generalization from 2D to 3D of the tensor method for derivation of both affine invariants and rotation, translation and scaling (TRS) invariants is described. The method for generation of the 3D TRS invariants of higher orders is automated and experimentally tested.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cyganski, D., Orr, J.A.: Object recognition and orientation determination by tensor methods. In: Huang, T.S. (ed.) Advances in Computer Vision and Image Processing, pp. 101–144. JAI Press, Greenwich (1988)

    Google Scholar 

  2. Department of Image Processing: 3D rotation moment invariants, http://zoi.utia.cas.cz/3DRotationInvariants

  3. Flusser, J., Suk, T., Zitová, B.: Moments and Moment Invariants in Pattern Recognition. Wiley, Chichester (2009)

    Book  MATH  Google Scholar 

  4. Lo, C.H., Don, H.S.: 3-D moment forms: Their construction and application to object identification and positioning. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(10), 1053–1064 (1989)

    Article  Google Scholar 

  5. Reiss, T.H.: Recognizing Planar Objects Using Invariant Image Features. LNCS, vol. 676. Springer, Heidelberg (1993)

    Book  MATH  Google Scholar 

  6. Sadjadi, F.A., Hall, E.L.: Three dimensional moment invariants. IEEE Transactions on Pattern Analysis and Machine Intelligence 2(2), 127–136 (1980)

    Article  MATH  Google Scholar 

  7. Suk, T., Flusser, J.: Affine moment invariants generated by graph method. Pattern Recognition 44(9), 2047–2056 (2011)

    Article  Google Scholar 

  8. Tuzikov, A.V., Sheynin, S.A., Vasiliev, P.V.: Efficient computation of body moments. In: Skarbek, W. (ed.) CAIP 2001. LNCS, vol. 2124, pp. 201–208. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Wikipedia: Einstein notation, http://en.wikipedia.org/wiki/Einsteinnotation

  10. Xu, D., Li, H.: 3-D surface moment invariants. In: Proceedings of the 18th International Conference on Pattern Recognition ICPR 2006, pp. 173–176. IEEE Computer Society, Los Alamitos (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Information Theory and Automation of the ASCR, Czech Republic

    Tomáš Suk & Jan Flusser

Authors
  1. Tomáš Suk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Flusser
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dpto. Matematica Aplicada I, Escuaela Técnica Superior de Ingeniería Informática, Universite de Sevilla, Avda. Reina Mercedes, s/n, 41012, Sevilla, Spain

    Pedro Real

  2. Departamento de Matemática Aplicada I, Escuela Técnica Superior de Ingeniería Informática, University of Seville, Avenida Reina Mercedes s/n, 41012, Sevilla, Spain

    Daniel Diaz-Pernil  & Helena Molina-Abril  & 

  3. Departamento de Didáctica de la Mathemática y de las CC.Experimentales, Escuela Universitaria de, Universidad del País Vasco-Esukal Herriko Unibertsitatea, Ramón y Cajal, 72, 48014, Bilbao, (Bizcaia), Spain

    Ainhoa Berciano

  4. Institute of Computer Graphics and Algorithms, Pattern Recognition and Image Processing Group, Vienna University of Technology, Favoritenstraße 9/186-3, 1040, Vienna, Austria

    Walter Kropatsch

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Suk, T., Flusser, J. (2011). Tensor Method for Constructing 3D Moment Invariants. In: Real, P., Diaz-Pernil, D., Molina-Abril, H., Berciano, A., Kropatsch, W. (eds) Computer Analysis of Images and Patterns. CAIP 2011. Lecture Notes in Computer Science, vol 6855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23678-5_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-23678-5_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23677-8

  • Online ISBN: 978-3-642-23678-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation