Optimal Ratio of Lamé Moduli with Application to Motion of Jupiter Storms

  • Ramūnas Girdziušas
  • Jorma Laaksonen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3540)


Fluid dynamics models the distribution of sources, sinks and vortices in imaged motion. A variety of different flow types can be obtained by specifying a key quantity known as the ratio of the Lamé moduli λ/μ. Special cases include the weakly elliptic flow λ/μ→ –2, often utilized in the Monge-Ampère transport, the Laplacian diffusion model λ/μ =–1, and the hyper-elliptic flow λ/μ → ∞ of the Stokesian dynamics. Bayesian Gaussian process generalization of the fluid displacement estimation indicates that in the absence of the specific knowledge about the ratio of the Lamé moduli, it is better to temporally balance between the rotational and divergent motion. At each time instant the Lamé moduli should minimize the difference between the fluid displacement increment and the negative gradient of the image mismatch measure while keeping the flow as incompressible as possible. An experiment presented in this paper with the interpolation of the photographed motion of Jupiter storms supports the result.


Optimal Ratio Displacement Increment Gaussian Process Regression Motion Estimation Algorithm Gaussian Process Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    The Great Red Spot movie. NASA’s Planetary PhotoJournal, PIA02829, NASA/JPL/University of Arizona (November 2002)Google Scholar
  2. 2.
    Christensen, G.: Deformable shape models for anatomy. Phd thesis, Washington University (1994)Google Scholar
  3. 3.
    Corpetti, T., Mémin, É., Pérez, P.: Dense estimation of fluid flows. IEEE Trans. on Pattern Analysis and Machine Intelligence 24(3), 365–380 (2002)CrossRefGoogle Scholar
  4. 4.
    Cunningham, G.S., Lehovich, A., Hanson, K.M.: Bayesian estimation of regularization parameters for deformable surface models. In: SPIE, pp. 562–573 (1999)Google Scholar
  5. 5.
    Reddy, B.D.: Introductory functional analysis: with applications to boundary value problems and finite elements. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  6. 6.
    Gibbs, M.N.: Bayesian Gaussian Processes for Regression and Classification. Ph.d. thesis, Cambridge University (1997)Google Scholar
  7. 7.
    Hagemann, A.: A Biomechanical Model of the Human Head with Variable Material Properties for Intraoperative Image Correction. Logos Verlag, Berlin (2001)Google Scholar
  8. 8.
    Quiñonero-Candela, J., Rasmussen, C.E.: Analysis of some methods for reduced rank gaussian process regression. In: Shorten, R., Murray-Smith, R. (eds.) Proc. of Hamilton Summer School on Switching and Learning in Feedback systems. Springer, Heidelberg (2004)Google Scholar
  9. 9.
    Shi, P., Liu, H.: Stochastic finite element framework for simultaneous estimation of cardiac kinematic functions and material parameters. Medical Image Analysis 7, 445–464 (2003)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ramūnas Girdziušas
    • 1
  • Jorma Laaksonen
    • 1
  1. 1.Laboratory of Computer and Information ScienceHelsinki University of TechnologyEspooFinland

Personalised recommendations