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
Originals

Abstract

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)

A0

image area

I

grey level distribution of flow image

d0

average particle spacing

dij

displacement vector between x i and y j

Fk

digital image frame captured at (k-1) Δt

N

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

N0

total number of particles in an image frame

Pi*

match probability that x i would coincide to y

Pi*

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

S

displacement vector of seeding particle during Δt

Δt

time interval between the captured image frames

Tm

maximum movement threshold

Tn

neighborhood threshold

Tq

quasi-rigidity threshold

Um

maximum velocity

xc

particle centroid (xc, yc)

xi

particle centroid on the first image frame

yj

particle centroid on the second image frame

Greek character

ρN

particle particle number density (=N0/A0)

ϕe

error ratio

ϕr

recovery ratio

Φ

tracking parameter (=d0/(UmΔt))

Superscript

(n)

number of iteration step

\((\tilde \cdot )\)

non-normalized probability value

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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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