Measurements in Fluid Mechanics 058:180 (ME:5180) Time & Location: 2:30P - 3:20P MWF 3315 SC Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui Phone: (Lab), (Cell)

2 Lecture 35. Particle image identification & tracking

3 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 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

6 Particle Image Specifics - Particle image position (x s,y s ) 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/(  R 2 max ) FH 

7 Particle Image Specifics - Insect image identification example nXYFH 

8 Create Phase Mask 1. Original2. Binary3. Big particles 4. Expanded5. Inverted

9 Tracking of Big Particle images Tow-frame tracking of big particles - Information from particle image identification Recording pair:1 st frame2 nd frame Particle image number: l 1 =1,2,···, L 1 l 2 =1,2,···, L 2 Size in pixels of particle imagesF 1 (l 1 )F 2 (l 2 ) Average brightnessH 1 (l 1 )H 2 (l 2 ) Shape coefficient  1 (l 1 )  2 (l 2 ) Position of particle imagex 1 (l 1 ),y 1 (l 1 ) x 2 (l 2 ),y 2 (l 2 ) - Tracking function - Weighting coefficients:  F +  H +   =1

10 Tracking of Big Particle images Tow-frame tracking of big particles - Pairing criterion: - Particle image displacement: - Deformation limits:

11 Tracking of Big Particle images Example Tracking results1 st frame2 nd frame

12 Tracking of Insect Motion Example: Tracking fire ant in successive image frames Fire ant trace Fire ant speed time history

13 Position of LID particle images Maxima search B B C C Erosion B C Combine One pixel for one particle

14 Evaluation of LID recordings LID recordingsEvaluation with large window Evaluation at identified particles LID recordings with small interrogation window Individual particle image pattern tracking

15 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: 2  4 pixels Particle image displacement: S x =2.3, S y =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

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

17 Matlab function for 4-P CDIC function[g]=sample4P(G,M,N,Xm,Ym,Sx,Sy,C) %INPUT PARAMETERS % G - gray value distribution of the PIV recording % M - interrogation sample width % N - interrogation sample height % Xm,Ym - interrogation sample location % Sx,Sy - displacements at 9 points % C=-1 for f1(i,j), C=1 for f2(i,j) % OUTPUT PARAMETERS % g - gray value distribution of the evaluation sample [nx ny]=size(G); % image size Xws=Sx(5);% window shift Yws=Sy(5); Xdis=Sx-(Sx(1)+Sx(3)+Sx(7)+Sx(9))/4; % distortion function Ydis=Sy-(Sy(1)+Sy(3)+Sy(7)+Sy(9))/4; % at 9 points Xpix=C*(Xws+Xdis)/2; % pixel displacement Ypix=C*(Yws+Ydis)/2; % at 9 points - Window shift determined with displacement in the window center, i.e. S ws =S 5 - Image distortion at the 4 points determined as - Particle image sisplacements at center and 4 corners (i.e. S 1, S 3, S 5, S 7, S 9 ) determined according to a previus evaluation C=-1:C=+1:

18 Matlab function for 4-P CDIC gm=0; % initial average gray value nr=0; % initial number of effective pixels for i=1:M% column loop start for j=1:N % row loop start A=(M-i)*(N-j)/double((M-1)*(N-1)); % weighting coefficient for point 1 B=(i-1)*(N-j)/double((M-1)*(N-1)); % weighting coefficient for point 3 C=(M-i)*(j-1)/double((M-1)*(N-1)); % weighting coefficient for point 7 D=(i-1)*(j-1)/double((M-1)*(N-1)); % weighting coefficient for point 9 x_pix=Xpix(1)*A+Xpix(3)*B+Xpix(7)*C+Xpix(9)*D; % pixel displacement at current pixel y_pix=Ypix(1)*A+Ypix(3)*B+Ypix(7)*C+Ypix(9)*D; % pixel displacement at current pixel X=Xm+x_pix-M/2+i; % corresponding x position of current pixel in the PIV recording Y=Ym+y_pix-N/2+j; % corresponding y position of current pixel in the PIV recording I=int16(X);% integer portion of x-position J=int16(Y); % integer portion of y-position x=double(X)-double(I); % decimal portion of x-position y=double(Y)-double(J); % decimal portion of y-position if x<0 % adjust values so that x≥0, y≥0 I=I-1; x=x+1; end if y<0 J=J-1; y=y+1; end A C B D i=1 j=1 j=N i=M

19 Matlab function for 4-P CDIC if I>=1 & I =1 & J<ny % limited in the image frame Ga=double(G(I,J));% gray value at integer pixels Gb=double(G(I+1,J)); Gc=double(G(I,J+1)); Gd=double(G(I+1,J+1)); A=(1-x)*(1-y);% weighting coefficients for interpolation B=x*(1-y); C=(1-x)*y; D=x*y; g(i,j)=A*Ga+B*Gb+C*Gc+D*Gd; % bilinear interpolation gm=gm+g(i,j); % sum of gray values for averaging nr=nr+1; % count number of effective pixels else g(i,j)=-1; % temporary value for pixel out of image frame end end % row loop end end % column loop end gm=gm/double(nr); % average gray value of effective pixels for i=1:M for j=1:N if g(i,j)<0 g(i,j)=gm; % fill with average value for pixel out of image frame end A C B D I J J+1 I+1 Ga Gb GcGd

20 Matlab program for 4-P CDIC clear; % clear variables A1=imread('A001_1.bmp'); % input 1st image in the recording pair A2=imread('A001_2.bmp'); % input 2nd image file G1=img2xy(A1); % convert image to gray value distribution G2=img2xy(A2); % convert image to gray value distribution Mg=16; % interrogation grid width Ng=16; % interrogation grid height M=2*Mg; % interrogation window width w. 50% overlap N=2*Ng; % interrogation window height w. 50% overlap sr1=12; % initial search radius sr2=6; % final search radius NN=6; % iteration number dU=[ ]; % parameters for error detection dV=[ ]; % parameters for error detection [nx ny]=size(G1); % determine size of the image col=400/Mg; % number of grid rows in limited area of 400-pixel in height row=400/Ng; % number of grid columns in limited area of 400-pixel in width

21 Matlab program for 4-P CDIC for i=1:col for j=1:row X(i,j)=double((i-1)*Mg+400); % x-position of interrogation point Y(i,j)=double((j-1)*Ng+300); % y-position of interrogation point U(i,j)=double(0); % initial particle image displacement in x-direction V(i,j)=double(0); % initial particle image displacement in y-direction end for nn=1:NN % iteration begin sr=int16((nn-1)*(sr2-sr1)/(NN-1)+sr1); % determine search radius if nn>1 [U V valid]=interpolation(U,V, valid); % interpolation for at wrong vectors [U V valid]=interpolation(U,V, valid); % second pass of interpolation end % iteration may be necessary in complicated case

22 Matlab program for 4-P CDIC for i=1:col % column loop start for j=1:row % row loop start if nn==1 wsx=0; % set window shift to 0 in the first run wsy=0; else if valid(i,j)>0 wsx=U(i,j); % window shift determined with previous evaluation wsy=V(i,j); end nr=0; % determining particle image displacement at 9 points in the window begin for q=-1:1 for p=-1:1 nr=nr+1; % number of grid point in the window if i>1 & i 1 & j 1 % after the first run & when all the 9 pints have valid vectors sx(nr)=U(i+p,j+q); % determine displacements at 9 points in the window sy(nr)=V(i+p,j+q); % with results of previous evaluation else sx(nr)=wsx; % ignore image distortion sy(nr)=wsy; end end % determining particle image displacement at 9 points in the window end

23 Matlab program for 4-P CDIC x=X(i,j); % determine horizontal coordinate of interrogation point y=Y(i,j); % determine vertical coordinate of interrogation point g1=sample4P(G1,M,N,x,y, sx, sy, -1); % evaluation sample with backward image correction g2=sample4P(G2,M,N,x,y, sx, sy, 1); % evaluation sample with forward image correction [C m n]=correlation(g1,g2); % calculating correlation function [cm vx vy]=peaksearch(C,m,n,sr,0,0); % determine particle image displacement U(i,j)=vx+wsx; % adjust particle image displacement with window shift V(i,j)=vy+wsy; % adjust particle image displacement with window shift end % row loop end end % column loop end valid=errordetection(U,V,dU,dV); % detect evaluation errors end % iteration end quiver(X,Y,U,V); % plot vector map