1 Imaging Techniques for Flow and Motion Measurement Lecture 11 Lichuan Gui University of Mississippi 2011 Interrogation Window Shift

1

Imaging Techniques for Flow and Motion Measurement

Lecture 11

Lichuan Gui

University of Mississippi

2011

Interrogation Window ShiftInterrogation Window Shift

2

Reduced working region for correlation interrogation


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

Original peak search radius usually M/3 or N/3

Reduced peak search radius

o

r

r < o

3

Discrete window shift (DWS)


G2(x,y)

o

y

xxm

ym

o

j

i

g1(i,j) SWS

numbers)integerareyandx(,S ysssWS yx

xm+xs

ym+ys

f2(i,j)

o

j

i

j

Nyyi

MxxGjif smsm 2

,2

, 22

M

i

N

j

njmifjignm1 1

21 ,,,

**,S nm

S’

**WS ,SSS nymx ss

S

j

Nyi

MxGjig mm 2

,2

, 22

j

Nyi

MxGjig mm 2

,2

, 11

Cross-correlation of single exposed PIV recording pair

4



mn

Auto correlation of double exposed PIV recording

M

i

N

j

njmigjignm1 1

,,,

No secondary maximum detected because of noises

g(i,j)

5

mn

Cross-correlation of double exposed PIV recording

Secondary maximum appears

Sws

Limited search area: <xs & <ys

mn



M

i

N

j

njmifjignm1 1

,,,

g(i,j)

f(i,j)

6



Determine initial window shift SWS

Determine g1(i,j)

Determine f2(i,j)

Compute (m,n) from g1(i,j) and f2(i,j)

Maximum search to determine S’, S=SWS+S’

S’ small enough?

SWS=S

YES

NOToo many iterations?

NO

YES

Begin

By previous knowledge or set to zero

Usually 3 or 4 iterations

Accelerated with FFT

Sub-pixel fit

End

S: integer number of pixels

DWS Flow Chart

7

Continuous window shift (CWS)


Sws={I+x, J+y}

– I,J: integer numbers

– x and y: decimal numbers and 0x<1;0y< 1

B A

DC

a b

cd

g(i,j)I+i

J+j

i

j

f(i,j)

x

y

yxD

yxC

yxB

yxA

1

1

11

Binlear interpolation

dcba gDgCgBgAjif ,

1,

1,1

,1

,

jJiIgg

jJiIgg

jJiIgg

jJiIgg

d

c

b

a

1,11,1

,11,11,

jJiIgyxjJiIgyx

jJiIgyxjJiIgyxjif

Other interpolation methods available

8

Continuous window shift (CWS)


Determine initial window shift SWS

Determine g1(i,j)

Determine f2(i,j)

Compute (m,n) from g1(i,j) and f2(i,j)

Maximum search and sub-pixel fitto determine S’, S=SWS+S’

S’ small enough?

SWS=S

YES

NOToo many iterations?

NO

YES

Begin

By previous knowledge or set to zero

Usually 4 to 6 iterations

Accelerated with FFT

End

Bilinear interpolation or other

CWS Flow Chart

9

Evaluation error distribution of DWS and CWS


Displacement [pixel]R

MS

erro

r[p

ixel

]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

DWSCWSCorr-tr

Ideal images with random noise

Displacement [pixel]

RM

Ser

ror

[pix

el]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

DWSCWSCorr-tr

Ideal images without noise

Test of three different algorithms with synthetic PIV images

Periodical functions of particle image displacement of 1-pixel period; DWS better than correlation tracking around integer-pixel displacements but worse around mid-pixel displacements CWS has much lower error level than DWS and correlation-based tracking

10

– Practice with EDPIV

• Evaluate PIV recording D001_1.bmp with evaluation settings as- Exposure type: Double - Flow direction: E- Interrogation grid: 32x32 - Error limits: Dx=4, Dy=2- interrogation window: 64x64 - Iteration number: 0,1- Search radius: 20 - Range limit: 20, 4, Absolute

• Remove erroneous vectors with 3x3 median filter- click menu “Edit \ Vector filtering \ regular” to select median filter

• Interpolate vectors- click menu “Edit \ Vector interpolation \ With data in M0”

• Smooth vector map with 3x3 filter- click menu “Edit \ Vector filtering \ regular” to select smooth filter

• Save vectors into memory #1- click menu “Edit \ Save vectors into \ M1”

• Clear vectors and change evaluation settings as- Exposure type: Single - Window shift: M1- Iteration number: 0,3 - Search radius: 4

• Evaluate the PIV recording with the interrogation window shift

HomeworkHomework

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1 Imaging Techniques for Flow and Motion Measurement Lecture 11 Lichuan Gui University of Mississippi 2011 Interrogation Window Shift