Imaging Techniques for Flow and Motion Measurement
Lecture 11
Interrogation Window Shift
Lichuan Gui
University of Mississippi
2011
1
Interrogation Window Shift

Reduced working region for correlation interrogation
Evaluation error for ideal PIV recordings by using different algorithms
with a 64x64-pixel interrogation window
r < o
o
r
Reduced peak search radius
Original peak search radius usually  M/3 or N/3
2
Interrogation Window Shift

Discrete window shift (DWS)
Cross-correlation of single exposed PIV recording pair
y
G2(x,y)
M
N


g 1 i , j   G 1  x m 
 i, y m 
 j
2
2


M
N


g 2 i , j   G 2  x m 
 i, y m 
 j
2
2


j
j
f2(i,j) S
g1(i,j)
S’
ym+ys
ym
S WS  x s , y s  ( x s and y y are integer numbers)
SWS
M
N


f 2 i , j   G 2  x m  x s 
 i, y m  y s 
 j
2
2


i
o
i
o
 m , n  
M
N
  g 1 i , j   f 2 i  m , j  n 
i 1 j 1

S  m , n
o
xm
xm+xs
x
*
*


S  S   S WS  x s  m , y s  n
*
*

3
Interrogation Window Shift

Discrete window shift (DWS)
Auto correlation of double exposed PIV recording
 m , n  
M
N
  g i , j   g i  m , j  n 
i 1 j 1
g(i,j)
n
m
No secondary maximum detected
because of noises
4
Interrogation Window Shift

Discrete window shift (DWS)
Cross-correlation of double exposed PIV recording
 m , n  
M
N
  g i , j   f i  m , j  n 
i 1 j 1
g(i,j)
Sws
f(i,j)
n
m
Limited
Secondary
search
maximum
area: <x
appears
s & <ys
5
Interrogation Window Shift

Discrete window shift (DWS)
Begin
DWS Flow Chart
Determine g1(i,j)
By previous knowledge or set to zero
Determine initial window shift SWS
Determine f2(i,j)
SWS=S
Compute (m,n) from g1(i,j) and f2(i,j)
Accelerated with FFT
Maximum search to determine S’,
S=SWS+S’
S: integer number of pixels
NO
NO
S’ small enough?
YES
Too many iterations?
Usually 3 or 4 iterations
YES
Sub-pixel fit
6
End
Interrogation Window Shift

Continuous window shift (CWS)
Sws={I+x, J+y}
– I,J: integer numbers
i
– x and y: decimal numbers and 0x<1;0y< 1
f(i,j)
Binlear interpolation
d
f i , j   A  g a  B  g b  C  g c  D  g d
A  1  x   1  y 
g a  g I  i, J  j 
B  x  1  y 
g b  g  I  i  1, J  j 
C  xy
g c  g  I  i  1, J  j  1 
D  1  x   y
g d  g  I  i , J  j  1
J+j
c
B
A
C
D
a
j
y
b
g(i,j)
I+i
x
f i , j   1  x   1  y   g  I  i , J  j   x  1  y   g  I  i  1, J  j  
1  x   y  g  I
 i , J  j  1   x  y  g  I  i  1, J  j  1 
Other interpolation methods available
7
Interrogation Window Shift

Continuous window shift (CWS)
Begin
CWS Flow Chart
Determine g1(i,j)
By previous knowledge or set to zero
Determine initial window shift SWS
Determine f2(i,j)
SWS=S
Bilinear interpolation or other
Compute (m,n) from g1(i,j) and f2(i,j)
Accelerated with FFT
Maximum search and sub-pixel fit
to determine S’, S=SWS+S’
NO
NO
S’ small enough?
YES
End
Too many iterations?
Usually 4 to 6 iterations
YES
8
Interrogation Window Shift
Evaluation error distribution of DWS and CWS

Test of three different algorithms with synthetic PIV images
0.15
0.1 5
Ideal im ag es w ith rando m n oise
DWS
DWS
CW S
CW S
R M S error [pixel]
R M S error [pixel]
Ideal im ag es w itho ut no ise
C o rr-tr
0.1
0.05
0
C o rr-tr
0 .1
0.0 5
0
0
0.1
0.2
0.3
0 .4
0 .5
0 .6
0 .7
D isp lacem ent [p ixel]
0.8
0 .9
1
0
0.1
0.2
0 .3
0 .4
0 .5
0.6
0 .7
0 .8
0 .9
1
D isp lacem ent [p ixel]
 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
9
Homework
– 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
10