Skip to main content

Nonlinear Multiscale Analysis of Motion Trajectories

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6374))

Abstract

Multiscale analysis initially proposed in image processing domain, turned out to be an effective tool in many other areas. It has been also proposed for motion data trajectories parametrized in quaternion space. In this paper we introduce novel approach, which is the framework for non-linear scale space analysis of quaternion trajectories. In the paper theoretical basis has been proposed and numerical validation has been presented.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barr, A.H., Currin, B., Gabriel, S., Hughes, J.F.: Smooth Interpolation of Orientations with Angular Velocity Constraints using Quaternions. Computer Graphics 26(2) (1992)

    Google Scholar 

  2. Burt, P.J., Adelson, E.H.: The Laplacian Pyramid as a Compact Image Code. IEEE Trans. on Communications 31(4), 532–542 (1983)

    Article  Google Scholar 

  3. Jablonski, B.: Anisotropic filtering of multidimensional rotational trajectories as a generalization of 2D diffusion process. Multidimensional Systems and Signal Processing 19(3-4), 379–399 (2008)

    Article  MathSciNet  Google Scholar 

  4. Kim, T., Lee, J., Shin, S.Y.: Robust Motion Watermarking based on Multiresolution Analysis. Computer Graphics Forum 19(3) (2000)

    Google Scholar 

  5. Laptev, C., Lindeberg, T.: Interest point detection and scale selection in space-time. In: Proc. Scale-Space Methods in Computer Vision, pp. 372–387. Springer, Heidelberg (1994)

    Google Scholar 

  6. Lee, J., Shin, S.Y.: Motion Fairing. Computer Animation,136–143 (1996)

    Google Scholar 

  7. Lee, J., Shin, S.Y.: Multiresolution Motion Analysis with Applications. In: International Workshop on Human Modeling and Animation, Seoul, pp. 131–143 (2000)

    Google Scholar 

  8. Lindeberg, T.: Scale-Space Theory in Computer Vision. Kluwer Academic Publishers, Netherlands (1994)

    Google Scholar 

  9. McCarthy, J.M.: Introduction to Theoretical Kinematics. MIT Press, Cambridge (1990)

    Google Scholar 

  10. Perona, P., Malik, J.: Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Trans. On Pattern Analysis and Machine Intelligence 12(7) (1990)

    Google Scholar 

  11. Weickert, J.: Anisotropic Diffusion in Image Processing. B.G. Teubner, Stuttgart (1998)

    MATH  Google Scholar 

  12. Witkin, A.: Scale-Space Filtering. In: IJCAI, pp. 1019–1022 (1983)

    Google Scholar 

  13. Witkin, A., Popovic, Z.: Motion Warping. In: Proc. SIGGRAPH 1995, Los Angeles (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jabłoński, B., Kulbacki, M. (2010). Nonlinear Multiscale Analysis of Motion Trajectories. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds) Computer Vision and Graphics. ICCVG 2010. Lecture Notes in Computer Science, vol 6374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15910-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15910-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15909-1

  • Online ISBN: 978-3-642-15910-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics