Imaging Techniques for Flow and Motion Measurement

Lecture 14

Lichuan GuiUniversity of Mississippi

2011

Central Central DifferenceDifference Image Image

CorrectionCorrection

PIV Recording with Distorted Image Pattern

Correlation interrogation without window shift

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

Correlation function of distorted image patterns

M

i

N

jnjmigjignm

1 121 ,,,

jNyiMxGjig mm 2

,2

, 11

jNyiMxGjig mm 2

,2

, 22

No correlation high peak at the particle image displacement2

10 pixels 10 pixels20 pixels

= +

Complex flow DistortionTanslation

Complex flow that results in image distortion

PIV Recording with Distorted Image Pattern

- Pixel displacement = window shift + image distortion

},,,{,,S jiyyjixxjiSSji diswsdiswsdiswspix 0,0ji,Sfor dis

- Displacements of 9 points available with 50% window overlapping

- Interpolation necessary to determine the image distortion function

Image distortion function Sdis(i,j)

3

Correlation interrogation with central difference window shift

PIV Recording with Distorted Image Pattern

jNyyiMx

xGjif wsm

wsm 22

,22

, 11

jNyyiMx

xGjif wsm

wsm 22

,22

, 22

M

i

N

jnjmifjifnm

1 121 ,,,

Low contrast among correlation function high peaks

f1(i,j) f2(i,j)

Correlation function improved with window shift 4

Central difference window shift & image corection

PIV Recording with Distorted Image Pattern

jNjiyyiMjixxGjif pixmpixm 2

,,2

,, 1111

jNjiyyiMjixxGjif pixmpixm 2

,,2

,, 2222

M

i

N

jnjmifjifnm

1 121 ,,,

Clear correlation function high peak at the particle image displacement

f1(i,j) f2(i,j)

Correlation function improved with window shift (red) & image correction (blue)

5

Central Difference Image Correction (CDIC)

Pixel displacement functions

jixxjix diswspix ,21

21,1

jiyyjiy diswspix ,21

21,1

jixxjix diswspix ,21

21,2

jiyyjiy diswspix ,21

21,2

jijiji pixpixpix ,S,S,S 21

2/,,S 1 jiSSji diswspix

2/,,S 2 jiSSji diswspix

0,1 1

N

j

M

idis jix 0,

1 1

N

j

M

idis jiy

6

9-point image corection method

- Window shift determined with displacement

in the window center, i.e. Sws=S5

- Image distortion at the 9 points determined as

,91,2,kfor wskdis SSkS

- Sdis(i,j) determined with interpolation according to Sdis(k)

- f(i,j) determined with interpolation according to Sws and Sdis(i,j)

- Particle image sisplacements at 9 points (S1 S9) determined according to a previus estimation

1 2 3

4 6

7 8 9

5

Interrogation window

Central Difference Image Correction (CDIC)

- Mutipass interrogation with iterated number around 6.

7

4-point image corection method

- Window shift determined with displacement

in the window center, i.e. Sws=S5

- Image distortion at the 4 points determined as

1,3,7,9kfor4

9731

SSSSSkS kdis

- Sdis(i,j) determined with bilinear interpolation according to Sdis(k)

- f(i,j) determined with bilinear interpolation according to Sws and Sdis(i,j)

- Particle image sisplacements at center and 4 corners (i.e. S1,

S3, S5, S7, S9) determined according to a previus evaluation

1 2 3

4 6

7 8 9

5

Interrogation window

Central Difference Image Correction (CDIC)

- Mutipass interrogation with iterated number aropund 6.

8

Central Difference Image Correction (CDIC)

Tests on image corection methods

Tested with synthetic PIV recordings of simulated 4-roll-mill flow

- Mutipass interrogation conveges after 6 iterations

- 9-piont method better with given (ideal) displacements

- 4-piont method better with with nulti-pass interations

- RMS evaluation error reduction more than 50% 9

10

Test of CDIC with Four-Roll Mill Flow

Top view

x [mm]

y[m

m]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

0.05 mm/s

Velocity field

Radius [pixel]

RM

Ser

rors

[pix

el]

0 100 200 300 400 500 6000

0.1

0.2

0.3

0.4

0.5

Bias errorPrecision errorTotal error

FDI

( a ) Radius [pixel]

RM

Ser

rors

[pix

el]

0 100 200 300 400 500 6000

0.1

0.2

0.3

0.4

0.5

Bias errorPrecision errorTotal error

CDI

( b )

Without image correction

Radius [pixel]

RM

Ser

rors

[pix

el]

0 100 200 300 400 500 6000

0.1

0.2

0.3

0.4

0.5

Bias errorPrecision errorTotal error

FDI

( a ) Radius [pixel]

RM

Ser

rors

[pix

el]

0 100 200 300 400 500 6000

0.1

0.2

0.3

0.4

0.5

Bias errorPrecision errorTotal error

CDI

( b )

With image correction

10

9-Point CDIC: Adjust Window Shift

Possible 9-point image corection methods

9

1:0Method

nnws SS

491:1Method 8642

5

9

1

SSSSSSS

nnws

491:2Method 9731

5

9

1

SSSSSSS

nnws

591:3Method 86542

5

9

1

SSSSSSSS

nnws

591:4Method 97531

5

9

1

SSSSSSSS

nnws

5:5Method SSws

wskdis SSkS

1 2 3

4 6

7 8 9

5

Interrogation window

- Different ways to determine window shift Sws

11

Tests on image corection methods

/L

/A

4 5 6 7 8 9 10 11 12 13 14 15 160.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

9P algorithm 09P algorithm 19P algorithm 29P algorithm 39P algorithm 49P algorithm 5

Tests with known displacements

/L/

A

4 5 6 7 8 9 10 11 12 13 14 15 160.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

9P algorithm 09P algorithm 19P algorithm 29P algorithm 39P algorithm 49P algorithm 5

Tests with 10 iterations

- Best in the ideal cases: 9P algorithm 0, i.e.

9

1nnws SS

- Best in iterated cases: 9P algorithm 3, i.e. 59

1 865425

9

1

SSSSSSSS

nnws

Tested with synthetic PIV recordings of simulated periodical flow of wave length (L: window width)

9-Point CDIC: Adjust Window Shift12

Different Base-algorithms for CDIC

Correlation interrogation better than correlation tracking for CDIC

Particle image diameter [pix]

RM

Ser

ror[

pix]

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50.00

0.05

0.10

0.15

0.20CDIC with correlation-based interrogationCDIC with correlation-based trackingCorrelation-based tracking

Side length of interrogation window [pix]R

MS

erro

r[pi

x]

0 8 16 24 32 40 48 56 64 720.00

0.05

0.10

0.15

0.20

0.25

0.30CDIC with correlation-based interrogationCDIC with correlation-based tracking

Test results with synthetic PIV recordings of simulated periodical flow

13

14

Image Pattern Correction Options

1. Central difference window shift & central difference image correction (CDIC)

jixxjix disspix ,21

21,1

jiyyjiy disspix ,21

21,1

jixxjix disspix ,21

21,2

jiyyjiy disspix ,21

21,2

Image interpolation required for both the two evaluation samples

2. Central difference window shift & forward difference image correction (FDIC)

spix xjix21,1

spix yjiy21,1

jixxxjix dispixspix ,, 12

jiyyyjiy dispixspix ,, 12

When xpix1 and ypix1 are set to integer numbers, image interpolation only required for

the second evaluation sample

– Reading• Wereley ST, Gui L (2003) A correlation-based central difference image

correction (CDIC) method and application in a four-roll-mill flow PIV measurement. Exp. Fluids 34, 42-51

• Gui L, Seiner JM (2004) An improvement in the 9-point central difference image correction method for digital particle image velocimetry recording evaluation. Meas. Sci. Technol. 15, 1598-1964

– Practice with EDPIV• Application example #1

- follow instruction #1- change evaluation settings to compare different results

• Application example #2- follow instruction #2- change evaluation settings to compare different results

HomeworkHomework

15