Experiments in Fluids

, Volume 22, Issue 1, pp 23–32 | Cite as

A new two-frame particle tracking algorithm using match probability

  • S. J. Baek
  • S. J. Lee


A new particle tracking algorithm using the concept of match probability between two consequent image frames has been developed to obtain an instantaneous 2-dimensional velocity field. Our proposed algorithm for correctly tracking particle paths from only two image frames is based on iterative estimation of match probability and no-match probability as a measure of the matching degree. A computer simulation has been carried out to study the performance of the developed algorithm by comparing with the conventional 4-frame Particle Tracking Velocimetry (PTV) method. The effect of various thresholds used in the developed algorithm on the recovery ratio and the error ratio were also investigated. Although the new algorithm relies on the iterative updating process of match probability which is time consuming, computation time is relatively short compared to that of the 4-frame PTV method. Additionally, the new 2-frame PTV algorithm recovers more velocity vectors and has a higher dynamic range and a lower error ratio.

List of symbols

A, B

constants (A < 1,B > 1)


image area


grey level distribution of flow image


average particle spacing


displacement vector between x i and y j


digital image frame captured at (k-1) Δt


number of points y j satisfying |d ij | <Tm.


total number of particles in an image frame


match probability that x i would coincide to y


no-match probability that x j has no corresponding y j onF2


displacement vector of seeding particle during Δt


time interval between the captured image frames


maximum movement threshold


neighborhood threshold


quasi-rigidity threshold


maximum velocity


particle centroid (xc, yc)


particle centroid on the first image frame


particle centroid on the second image frame

Greek character


particle particle number density (=N0/A0)


error ratio


recovery ratio


tracking parameter (=d0/(UmΔt))



number of iteration step

\((\tilde \cdot )\)

non-normalized probability value


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  1. Ballard DH; Brown CM (1982) Computer vision. pp 195–225. New Jersey: Prentice-HallGoogle Scholar
  2. Buchhave P (1992) Particle image velocimetry-status and trends. Exp Thermal and Fluid Sci 5: 586–604CrossRefGoogle Scholar
  3. Chang TPK; Watson AT; Tatterson GB (1985) Image processing of tracer particle motions as applied to mixing and turbulent flow - Part I: The technique. Chem Eng Sci 40: 269–275CrossRefGoogle Scholar
  4. Hassan YA; Canaan RE (1991) Full-field bubbly flow velocity measurements using a multi-frame particle tracking technique. Exp Fluids 12: 49–60CrossRefGoogle Scholar
  5. Kasagi N; Nishino K (1991) Probing turbulence with three-dimensional particle-tracking velocimetry. Exp Thermal and Fluid Sci 4: 601–612CrossRefGoogle Scholar
  6. Keane RD; Adrian RI (1991) Cross-correlation analysis of particle image fields for velocity measurement. In: Experimental and Numerical Flow Visualization (Ed. Khalighia B et al.). ASME FED 128: 1–8Google Scholar
  7. Keane RD; Adrian RJ; Zhang Y (1995) Super-resolution particle imaging velocimetry. Meas Sci Technol 6: 754–768CrossRefGoogle Scholar
  8. Kobayashi T; Ishihara T; Sasaki N (1983) Automatic analysis of photographs of trace particles by microcomputer system. In: Flow Visualization III (Ed. Yang WJ). pp 231–235. Ann Arbor: New YorkGoogle Scholar
  9. Kobayashi T; Saga T; Segawa S (1986) Some considerations on automated image processing of pathline photographs. In: Flow Visualization IV (Ed. Véret C). pp 241–246. Paris: Springer-VerlagGoogle Scholar
  10. Kobayashi T; Saga T; Haeno T; Tsuda N (1991) Development of a real-time velocity measurement system for high Reynolds fluid flow using a digital image processing technique. In: Experimental and Numerical Flow Visualization (Ed. Khalighia B et al.). ASME FED 128: 9–14Google Scholar
  11. Malik NA; Dracos T; Papantoniou DA (1993) Particle tracking velocimetry in three-dimensional flows. Exp Fluids 15: 279–294CrossRefGoogle Scholar
  12. Shigeru M; Hiroshi S (1992) Measurement of unsteady separated flows on a blunt plate by a Fourier transform method. In: Flow Visualization VI (Ed. Tanida T; Miyashiro H). pp 710–714. Yokohama: Springer-VerlagGoogle Scholar
  13. Wernet MP; Pline A (1993) Particle displacement tracking technique and Cramer-Rao lower bound error in centroid estimates from CCD imagery. Exp Fluids 15: 295–307CrossRefGoogle Scholar
  14. Willert CE; Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10: 181–193CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • S. J. Baek
    • 1
  • S. J. Lee
    • 1
  1. 1.Department of Mechanical Engineering Advanced Fluids Engineering Research CenterPohang University of Science and TechnologySouth Korea

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