imaging techniques for flow and motion measurement lecture 14 lichuan gui university of...
DESCRIPTION
= + Complex flowDistortionTanslation Complex flow that results in image distortion PIV Recording with Distorted Image Pattern - Pixel displacement = window shift + image distortion - Displacements of 9 points available with 50% window overlapping - Interpolation necessary to determine the image distortion function Image distortion function S dis (i,j) 3TRANSCRIPT
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
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