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Abstract

We present a method for detecting and describing features in vector flow fields. Our method models flow fields locally using a linear combination of complex monomials. These monomials form an orthogonal basis for analytic flows with respect to a correlation-based inner-product. We investigate the invariance properties of the coefficients of the approximation polynomials under both rotation and scaling operators. We then propose a descriptor for local flow patterns, and developed a method for comparing them invariantly against rigid transformations. Additionally, we propose a SIFT-like detector that can automatically detect singular flow patterns at different scales and orientations. Promising detection results are obtained on different fluid flow data.

Keywords

Singular Point Vector Flow Rotation Operator Rigid Transformation Gaussian Smoothing 
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.

References

  1. 1.
    Bronshtein, I., Semendyayev, K., Musiol, G., Muehlig, H.: Handbook of mathematics. Springer, Berlin (1997)zbMATHGoogle Scholar
  2. 2.
    Bruhn, A., Weickert, J., Schnörr, C.: Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods. Int. J. Comp. Vis. 61(3), 211–231 (2005)CrossRefGoogle Scholar
  3. 3.
    Carlier, J.: Second set of fluid mechanics image sequences. In: European Project ’Fluid image analysis and description, FLUID (2005), http://www.fluid.irisa.fr/
  4. 4.
    Corpetti, T., Mémin, E., Pérez, P.: Extraction of singular points from dense motion fields: An analytic approach. J. Math. Imaging Vis. 19(3), 175–198 (2003)zbMATHCrossRefGoogle Scholar
  5. 5.
    Davies, B.: Integral Transforms and Their Applications. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  6. 6.
    Fan, L., Wang, S., Wang, H., Guo, T.: Singular points detection based on zero-pole model in fingerprint images. Trans. Patt. Anal. Mach. Intell. 30(6), 929–940 (2008)CrossRefGoogle Scholar
  7. 7.
    Florack, L.: Scale-space theories for scalar and vector images. In: Scale-Space 2001, London, UK, 2001, pp. 193–204. Springer, London (2001)Google Scholar
  8. 8.
    Ford, R.M., Strickland, R.N., Thomas, B.A.: Image models for 2-D flow visualization and compression. Graph. Models Image Process. 56(1), 75–93 (1994)CrossRefGoogle Scholar
  9. 9.
    Forray, M.J.: Approximation Theory and Methods. Cambridge Univ. Press, Cambridge (1981)Google Scholar
  10. 10.
    Hoey, J., Little, J.J.: Bayesian clustering of optical flow fields. ICCV 2, 1086 (2003)Google Scholar
  11. 11.
    Kihl, O., Tremblais, B., Augereau, B.: Multivariate orthogonal polynomials to extract singular points. In: ICIP, pp. 857–860 (2008)Google Scholar
  12. 12.
    Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A., Eyink, G.: A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. Journal of Turbulence 9(31), 1–29 (2008)Google Scholar
  13. 13.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision 60(2), 91–110 (2004)CrossRefGoogle Scholar
  14. 14.
    Nilsson, K., Bigun, J.: Localization of corresponding points in fingerprints by complex filtering. Pattern Recogn. Lett. 24(13), 2135–2144 (2003)CrossRefGoogle Scholar
  15. 15.
    Nogawa, H., Nakajima, Y., Sato, Y., Tamura, S.: Acquisition of symbolic description from flow fields: a new approach based on a fluid model. IEEE Trans. Patt. Anal. Mach. Intell. 19(1), 58–63 (1997)CrossRefGoogle Scholar
  16. 16.
    Rao, A.R., Jain, R.C.: Computerized flow field analysis: Oriented texture fields. IEEE Trans. Pattern Anal. Mach. Intell. 14(7), 693–709 (1992)CrossRefGoogle Scholar
  17. 17.
    Schlemmer, M., Heringer, M., Morr, F., Hotz, I., Hering-Bertram, M., Garth, C., Kollmann, W., Hamann, B., Hagen, H.: Moment invariants for the analysis of 2D flow fields. IEEE Trans. on Vis. and Comp. Graph 13(6), 1743–1750 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Wei Liu
    • 1
  • Eraldo Ribeiro
    • 1
  1. 1.Computer Vision and Bio-Inspired Computing Laboratory, Department of Computer SciencesFlorida Institute of TechnologyMelbourneUSA

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