Measurements in Fluid Mechanics058:180:001 (ME:5180:0001)

Time & Location: 2:30P - 3:20P MWF 218 MLH

Office Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan Guilichuan-gui@uiowa.edu

http://lcgui.net

Students are encouraged to attend the class. You may not be able to understand by just reading the lecture notes.

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Lecture 35. Particle image identification & tracking

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Particle Image Identification

Purposes

- To determined image specifics for particle tracking

- To analyze particle size and distribution in flows

- To separated phases according to image size

- To mask unexpected objects in the flow field

- To mask flow boundaries

- Others

4

Particle Image Identification

Original Norm alization Regional normalization Binarization

Step 1: Preprocess particle images

- Increase contrast of the PIV recording

- Increase brightness of dark images

- Binarize particle images

5

Particle Image Identification

Step 2: Identify particle images (method in EDPIV)

- Number every image pixel and give a large number to background pixels

- Reconstruct number field with minimum in 3×3 neighborhood of image pixels

- Iterate until no changes can be made

1 111

5 6 75 6 78 9 1 08 9

1 6 1 6 1 8 1 8 1 91 6 1 6 1 6 1 8 1 92 1 2 1 2 4 2 4 2 5

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Particle Image Specifics

- Particle image position (xs,ys) determined at center of mass

- Particle size in pixels (F)

- Average brightness of all pixels belong to one image (H)

- Particle shape coefficient, e.g. roundness =F/(R2max)

x s

y s

R m ax

F H

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Particle Image Specifics

- Insect image identification example

X [pixel]

Y[p

ixel

]

0 4 8 12 160

4

8

12

16

ri

(Xn ,Yn)

re

Equivalent circle

Ie= 0.5Snre2

= 0.5Sn2 /

In= ri2

=In / Ie

Roundness () & Orientation angle ()

n X Y F H 1 30.33 4.33 15 170.1 1.86 -1.27

2 84.29 28.11 17 171.1 2.25 -0.37

3 176.43 45.68 16 166.7 2.39 -1.25

4 103.00 46.50 16 167.7 2.55 -0.62

5 149.56 56.81 16 172.9 2.95 1.23

6 133.53 55.66 15 163.9 2.60 0.05

7 167.62 83.31 39 169.4 2.69 -0.47

8 241.65 85.94 17 172.4 2.15 0.15

9 85.21 110.00 14 190.6 2.26 -1.20

10 89.50 114.00 20 176.4 2.00 1.41

11 155.50 122.25 16 171.5 2.63 1.55

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Create Phase Mask

1. Original 2. Binary 3. Big particles

4. Expanded 5. Inverted

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Painting Tools

Paste – help for generating masksOriginal Mask Effect

Mask EffectPasted

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Painting Tools

Line - help for identifying big particles

Original Line cut

Effect Effect

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Painting Tools

Fill – Used to create a boundary mask

Fill flow field with 250Original Fill boundary with 0

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Tracking of Big Particle images

Tow-frame tracking of big particles

- Information from particle image identificationRecording pair: 1st frame 2nd frame

Particle image number: l1=1,2,···, L1 l2=1,2,···, L2

Size in pixels of particle images F1(l1) F2(l2)

Average brightness H1(l1) H2(l2)

Shape coefficient 1(l1) 2(l2)

Position of particle image x1 (l1),y1 (l1) x2 (l2),y2 (l2)

2

11

2211

2

11

2211

2

11

221121,

l

ll

lH

lHlH

lF

lFlFll HFg

- Tracking function

- Weighting coefficients: F +H +=1

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Tracking of Big Particle images

Tow-frame tracking of big particles

- Pairing criterion: 21*21

1*2

,3,2,1,,min,when

asparticlesamethetorelatedisimageParticle

Lkklll

ll

gg

11

*22

11*22

lylyS

lxlxS

y

x

- Particle image displacement:

- Deformation limits:

11

*2211

11

*2211

11

*2211 ,,

l

ll

lH

lHlH

lF

lFlFHF

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Tracking of Big Particle images

Example

Tracking results1st frame 2nd frame

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Tracking of Insect Motion

Example: Tracking fire ant in successive image frames

x [mm]y

[mm

]

-60 -50 -40 -30 -20 -10 0 10 20 30 40-20

-10

0

10

20

30

40

50

(a)

Time [s]

Spe

ed[m

m/s

]

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

(b)

Fire ant trace

Fire ant speed time history

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Position of LID particle images

Maxima search

B

B

C

C

ErosionB

C

Combine

One pixel for one particle

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Evaluation of LID recordings

LID recordings Evaluation with large window

Evaluation at identified particles

LID recordings with small interrogation window

Individual particle image pattern tracking

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Tracking of small particle images

- Nearest displacement criterion (distance between particles >> displacement)

- Pairing with help of neighbor particle images (e.g. Okamoto et al. 1995)

- Multi-frame tracking (e.g. Hassan & Canaan 1991 )

- Displacement determined according to particle image center positions

Simulated PIV recording pair of uniform flow

Particle image diameter: 24 pixels

Particle image displacement: Sx=2.3, Sy=1.5 pixels

Particle tracking results

RMS error=0.25 pixels

Pattern tracking results

4x4-pixel pattern

RMS error=0.06 pixels

- Individual particle image pattern tracking recommended for LID PIV

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• Gui L, Merzkirch W, Shu JZ (1997) Evaluation of low image density PIV recordings with the MQD method and application to the flow in a liquid bridge. Journal of Flow Visualization and Image Processing, vol. 4: 333-343 

• Gui L and Seiner JM (2009) Application of an Image Tracking Algorithm in Fire Ant Motion Experiment. Algorithms 2, no. 2:735-749

References

Fast computation of unsharp mask

A

sm jyixGA

yxG ,1

,

𝑛𝑦−

2𝑟

𝑛𝑥− 2𝑟

A

- Compute Gsm(x,y) close to the edges of the image

for x r+1 or x> nx -r or y< r+1 or y>ny-r

20

CyxGyxGCjyixGrr

yxGyxG sm

r

ri

r

rj

,,,1212

1,,

r

rjsmsm jyrxGjyrxG

rryxGyxG ,1,

1212

1,1,

Fast computation of unsharp mask

21

𝑛𝑦−

2𝑟

𝑛𝑥− 2𝑟

𝑦

𝑥−1𝑥

- Compute Gsm(x,y) away from the edges of the image

CyxGyxGCjyixGrr

yxGyxG sm

r

ri

r

rj

,,,1212

1,,

Fast computation of unsharp maskfunction [F]=unsharpmask(G,fr) % G - gray value distribution of the image [nx ny]=size(G); % fr - radius of the filterG=double(G);

for y=1:ny for x=1:nx nr=0; % used to count pixels in effective area A Gm(x,y)=0; for i=-fr:fr for j=-fr:fr if x+i>0 & x+i<=nx & y+j>0 & y+j<=ny % limit calculation in the image Gm(x,y)=Gm(x,y)+double(G(x+i,y+j)); nr=nr+1; end end end Gm(x,y)=Gm(x,y)/nr; % average gray value endendF=double(G)-double(Gm); % remove unsharp mask

nx

ny

A

x

y

23

Fast computation of unsharp mask

𝑛𝑦

r+1

function [F]=unsharpmask2(G,fr) % G - gray value distribution of the image [nx ny]=size(G); % fr - radius of the filterG=double(G);

for y=1:ny for x=1:fr+1 nr=0; Gsm(x,y)=0; for i=-fr:fr for j=-fr:fr if x+i>0 & x+i<=nx & y+j>0 & y+j<=ny Gsm(x,y)=Gsm(x,y)+G(x+i,y+j); nr=nr+1; end end end Gsm(x,y)=Gsm(x,y)/nr; end end

function [F]=unsharpmask2(G,fr) % G - gray value distribution of the image [nx ny]=size(G); % fr - radius of the filterG=double(G);

for y=1:ny for x=1:fr+1 nr=0; Gsm(x,y)=0; for i=-fr:fr for j=-fr:fr if x+i>0 & x+i<=nx & y+j>0 & y+j<=ny Gsm(x,y)=Gsm(x,y)+G(x+i,y+j); nr=nr+1; end end end Gsm(x,y)=Gsm(x,y)/nr; end Endfor y=1:ny for x=nx-fr:nx nr=0; Gm(x,y)=0; for i=-fr:fr for j=-fr:fr if x+i>0 & x+i<=nx & y+j>0 & y+j<=ny Gm(x,y)=Gm(x,y)+G(x+i,y+j); nr=nr+1; end end end Gm(x,y)=Gm(x,y)/nr; end end

Fast computation of unsharp mask

𝑛𝑦

r+1 nx-r

Fast computation of unsharp mask

r+2

for y=1:fr for x=fr+2:nx-fr-1 nr=0; Gm(x,y)=0; for i=-fr:fr for j=-fr:fr if x+i>0 & x+i<=nx & y+j>0 & y+j<=ny Gm(x,y)=Gm(x,y)+G(x+i,y+j); nr=nr+1; end end end Gm(x,y)=Gm(x,y)/nr; end end

nx-r-1

r

for y=1:fr for x=fr+2:nx-fr-1 nr=0; Gm(x,y)=0; for i=-fr:fr for j=-fr:fr if x+i>0 & x+i<=nx & y+j>0 & y+j<=ny Gm(x,y)=Gm(x,y)+G(x+i,y+j); nr=nr+1; end end end Gm(x,y)=Gm(x,y)/nr; end end

for y=ny-fr:ny for x=fr+2:nx-fr-1 nr=0; Gm(x,y)=0; for i=-fr:fr for j=-fr:fr if x+i>0 & x+i<=nx & y+j>0 & y+j<=ny Gm(x,y)=Gm(x,y)+G(x+i,y+j); nr=nr+1; end end end Gm(x,y)=Gm(x,y)/nr; end end

Fast computation of unsharp mask

r+2 nx-r-1

r

nr=(2*fr+1)*(2*fr+1);for y=fr+1:ny-fr-1 for x=fr+2:nx-fr-1 D=0; x1=x-fr-1; x2=x+fr; for j=-fr:fr D=D-G(x1,y+j)+G(x2,y+j); end Gm(x,y)=Gm(x-1,y)+D/nr; endEnd

F=G-Gm; % function output

Fast computation of unsharp mask

r+2 nx-r-1

ny-r-1

r+1

Fast computation of unsharp maskTest program clear;A=imread('D001_1.bmp'); % input image file G=img2xy(A); % convert image to gray value distributionfr=5;F=unsharpmask2(G,fr);

D=xy2img(F);imshow(D);