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A new two-frame particle tracking algorithm using match probability

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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.

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Abbreviations

A, B :

constants (A < 1,B > 1)

A 0 :

image area

I :

grey level distribution of flow image

d 0 :

average particle spacing

d ij :

displacement vector between x i and y j

F k :

digital image frame captured at (k-1) Δt

N :

number of points y j satisfying |d ij | <T m.

N 0 :

total number of particles in an image frame

P i * :

match probability that x i would coincide to y

P i * :

no-match probability that x j has no corresponding y j onF 2

S:

displacement vector of seeding particle during Δt

Δt :

time interval between the captured image frames

T m :

maximum movement threshold

T n :

neighborhood threshold

T q :

quasi-rigidity threshold

U m :

maximum velocity

x c :

particle centroid (x c, yc)

x i :

particle centroid on the first image frame

y j :

particle centroid on the second image frame

ρ N :

particle particle number density (=N 0/A 0)

ϕ e :

error ratio

ϕ r :

recovery ratio

Φ:

tracking parameter (=d 0/(U mΔt))

(n):

number of iteration step

\((\tilde \cdot )\) :

non-normalized probability value

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This work was supported in part by non-directed research fund, Korea Research Foundation, 1993 and Hyundai Maritime Research Institute.

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Baek, S.J., Lee, S.J. A new two-frame particle tracking algorithm using match probability. Experiments in Fluids 22, 23–32 (1996). https://doi.org/10.1007/BF01893303

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