1 imaging techniques for flow and motion measurement lecture 10 lichuan gui university of...

1

Imaging Techniques for Flow and Motion Measurement

Lecture 10

Lichuan GuiUniversity of Mississippi

2011

Direct Correlation & MQD MethodDirect Correlation & MQD Method

2

Direct Correlation (w/o FFT)Direct Correlation (w/o FFT) Method 1: g2(i,j) limited in the window frame

o M

N

j

i

Adirect njmigjigA

nm ,,1, 211

g1(i,j)

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i

nN

jA

,:0n0,m1 1

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mi

nN

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,:0n0,m1 1

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mi

N

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,:0n0,m1 1

m

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g2(i+m,j+n)

A

3

Direct Correlation (w/o FFT)Direct Correlation (w/o FFT) Method 2: g2(i,j) not limited in the window frame

o M

N

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Adirect njmigjigA

nm ,,1, 212

g1(i,j)

m

n

g2(i+m,j+n)

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1 1

4

Particle Image Pattern TrackingParticle Image Pattern Tracking Tracking ensemble of particle images

1st recording

2nd recording

tracked image pattern

Image pattern at (m,n)

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5

Minimum-quadratic-difference (MQD) method

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,2,1,2,1,,

MN dimensional vectors

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1 1

2

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,,

,

Quadratic difference of the vectors

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D(m, n) (%)

nm

-20-100

1020

-20-10 0 10 20

0

20

40

60

80

100

0

20

40

60

80

100

-20-100

1020-20-1001020

0

20

40

60

80

100

0

20

40

60

80

100

D(m, n) (%)

m n

Double exposure Single exposures

Minimum-quadratic-difference (MQD) method

Particle Image Pattern TrackingParticle Image Pattern Tracking

6

Modified MQD tracking function


nmDCnmDjignmDM

i

N

j,,,,

1 1

21

*

- D*(m,n) and D(m,n) identical for determining particle image displacement- 3-point Gaussian fit directly applied to D*(m,n)

m [pixel]

n[p

ixel

]

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

1.000.900.800.700.600.500.400.300.200.100.00

D*(m,n)

m [pixel]

n[p

ixel

]

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

1.000.900.800.700.600.500.400.300.200.100.00

D(m,n)Normalized MQD tracking functions

7

Correlation-based tracking method

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21 ,,,2,,

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nmQ ,

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jtr ,,

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Correlation-based tracking function

nmNMnjmigjignm direct

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for

Particle Image Pattern TrackingParticle Image Pattern Tracking Modified correlation-based tracking function

nmQnmDnmtr ,,21, *

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2(m,n) Q(m,n) -D (m,n)*- = nmtr ,2 nmQ , nmD ,*

zero

9

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ig1(i,j)

m

n

A

g2(i+m,j+n)

0.0

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1.0

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m

-10

0

10

n

(m,n)

tr(m,n)/D*(m,n)

2

2

Tracking radius

Particle Image Pattern TrackingParticle Image Pattern Tracking Tracking area & tracking radius

10

Acceleration with FFT


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i

N

jtr njmigjignm

1 121 ,,,No periodical, no FFT:

Zero padding:

Periodical, with FFT:

* *

1 1

*2

*1

* ,,,M

i

N

jtr njmigjignm

g1(i,j) g2(i,j)

jigjigjigjig ,,*,,,* 2211

11

* *

1 1

*2

*1

* ,,,M

i

N

jtr njmigjignm for [‑ m < , ‑ n < ]

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l,,,

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rest

i

rest

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jnjmigjignjmigjig ,,,, *

2*1

1 1

*2

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*1 ,,

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1 121 ,,

nmtr ,

0

Acceleration with FFT


nmQnmnmD tr ,,2, **

12

Computation time


16 32 48 64 80 96 112 128

Side length of the squared interrogation windows [pixel]

0

500

1,000

1,500

2,000

2,500

Com

puta

tion

time

for 5

00 v

ecto

rs [s

]

Correlation without FFT

Correlation with FFTAdvanced MQD ( =10 pixel)

Correlation tracking with FFT

Test computer: IBM 6×86 P166+

[pixel]

Imaging techniques for fluid flow and insect motion experiments

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Evaluation error


Image pattern tracking methods- periodical error distribution on particle image displacement (1 pixel period)- MQD has higher accuracy for ideal PIV images, but more sensitive to noisesCorrelation algorithm- error dependent on particle image displacement, high accuracy at very small displacement

Evaluation error for ideal PIV recordings by using different algorithms with a 64x64-pixel interrogation window

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– Programming

• Compute correlation-based tracking function at the center of image01.bmp with 32x32-pixel window

– Practice with EDPIV• Evaluation settings:

- Exposure type: Double- Flow direction: E- interrogation grid: 31x31 pixels- iteration number: 0, 1- Search radius: 20 pixels

• Functions used in “Evaluation” window- create a regular evaluation grid- select a test point at the center- start an evaluation - view image samples and evaluation function- determine discrete and sub-pixel displacement

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1 imaging techniques for flow and motion measurement lecture 10 lichuan gui university of...

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