A Practical Guide to Biospeckle Laser Analysis

Transcription

1 to Biospeckle Laser Analysis Theory and Software Pujaico Rivera 1 and Roberto Alves Braga 1 1 Universidade Federal de Lavras Aula

2 Datapack Datapack

3 Datapack Loading a Datapack Loading a Datapack 1.bmp 2.bmp 3.bmp... 9.bmp 10.bmp 11.bmp 12.bmp bmp IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp');

4 Datapack Loading a Datapack cafe1.bmp cafe2.bmp cafe3.bmp... cafe9.bmp cafe10.bmp cafe11.bmp cafe12.bmp... cafe128.bmp Loading a Datapack (Pg. 69) IMAGESDIR='~/data/cafe-biospeckle/sem2'; DATA=datapack(IMAGESDIR,'cafe',1,128,'bmp');

5 Datapack Loading a Datapack cafe001.bmp cafe002.bmp cafe003.bmp... cafe009.bmp cafe010.bmp cafe011.bmp cafe012.bmp... cafe128.bmp Loading a Datapack (Pg. 69) IMAGESDIR='~/data/cafe-biospeckle/sem3'; DATA=datapack(IMAGESDIR,'cafe%03d',1,128,'bmp');

6 Datapack Saving a datapack 1.bmp 2.bmp 3.bmp... 9.bmp... cafe128.bmp Saving a datapack (Pg. 70) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); Frames=20; Ts=0.5; datapack_to_gif(data,'datapack.gif',frames,gray,ts); colormap( list ) autumn bone gray... jet... winter

7 Numerical Numerical

8 THSP Numerical Creating a THSP (Pg. 71) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); THSP=thsp(DATA,'column',240); imagesc(thsp);colormap gray;

9 COM Numerical Creating a COM (Pg. 72) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); THSP=thsp(DATA,'line',240); COM=coom(THSP); imagesc(com);colormap gray;

10 IM Numerical Where the IM moment [3] (IM 1 ) is: E[(i j) 2 ] = ij COM(i,j) lm COM(l,m)(i j)2. (1) And, the IM moment following [2] (IM 2 ) is presented as in the Equation (2), E Ariz. [(i j) 2 ] = ij COM(i,j) m COM(i,m)(i j)2. (2)

11 IM Numerical Calculating the IM value (Pg. 75) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); THSP=thsp(DATA,'line',240); COM=coom(THSP); [IM1 IM2]=inertiamoment(COM,2) IM1 = IM2 = e +05

12 AVD Numerical Where the AVD first moment [3] (AVD 1 ) is: E[ i j ] = ij lm The AVD second moment (AVD 2 ) is: E[(i j) 2 ] = ij COM(i,j) j (3) COM(l,m) i COM(i,j) lm COM(l,m)(i j)2 (4) The AVD second central moment (AVD 3 ) is: Var[ i j ] = E[(i j) 2 ] E[ i j ] 2 (5) And the AVD first moment following [2] (AVD 4 ) is: E Ariz. [ i j ] = ij m COM(i,j) j (6) COM(i,m) i

13 AVD Numerical Calculating the AVD value (Pg. 76) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); THSP=thsp(DATA,'line',240); COM=coom(THSP); [AVD1 AVD2 AVD3 AVD4]=avd(COM,2,3,4) AVD1 = AVD2 = AVD3 = AVD4 =

14 NUMAD Numerical Where the first moment (NUMAD 1 ) is: [ ] i j E = COM(i,j) i j i +j ij lm COM(l,m) i +j (7) And the second moment (NUMAD 2 ) is: [ ( i ) ] j 2 E = i +j ij COM(i,j) lm COM(l,m) ( ) i j 2 (8) i +j

15 NUMAD Numerical Calculating the NUMAD value (Pg. 80) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); THSP=thsp(DATA,'line',240); COM=coom(THSP); [NUMAD1 NUMAD2]=numad(COM,2) NUMAD1 = NUMAD2 =

16 Numerical Correlation The correlation C il [10] (Equation 9) is calculated between all pixels THSP(:,i) in the instant i and the pixels THSP(:,i +j) in the instant i +j, C il = corr(thsp(:,i),thsp(:,i +l)). (9) The function finally returns, C l (Equation 10), the mean value of this correlations for a lag of l, C l = NTIMES/2 1 C il. (10) NTIMES/2 i=1

17 Numerical Correlation Calculating the correlation value (Pg. 81) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); THSP=thsp(DATA,'line',240); [C1 L1] = thsp2corr(thsp,1); plot(l1,c1,'-o');grid;xlabel('l1');ylabel('c1'); C L1

18 Numerical Spatial-Temporal Correlation The correlation C lτ k 0 [11] (Equation 11) is calculated between the image I k0 and the image I k0 +l, 1 k 0 +l NTIMES. Here it is assumed that the images were taken with sampling rate equal to τ. C lτ k 0 = corr(i k0,i k0 +l), (11)

19 Numerical Spatial-Temporal Correlation Calculating the spatial-temporal correlation value [11] (Pg. 82) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); tau=1; [C T]=stscorr(DATA,tau,42); 1 Spatial-Temporal Speckle Correlation Technique: k0= Correlation coefficients k tau

20 Graphical Graphical

21 Fujii Graphical 1.bmp 2.bmp 3.bmp... 9.bmp... cafe128.bmp The function in Equation (12) [7, 6] is normalized to Equation (13): Where NTIMES=128. FUJII = NTIMES 1 k=1 Y = FUJII I k I k+1 I k +I k+1 +eps, (12) NTIMES 1. (13)

22 Fujii Graphical Fujii [7, 6] (Pg. 83) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); FUJII=fujii(DATA); Fujii Method

23 GD Graphical 1.bmp 2.bmp 3.bmp... 9.bmp... cafe128.bmp This function implements the Generalized Difference (GD) technique (Equation 14) [1]. It uses, as input data, a 3D matrix (DATA) created by grouping intensity matrices I k DATA(:,:,k), 1 k NTIMES 128. GD = NTIMES 1 k=1 NTIMES k l=1 I k I k+l (14) The function is normalized to Y (Equation 15) with the number of elements in the sum. Y = GD ) (15) ( NTIMES 2

24 GD Graphical Generalized Difference (GD) [1] (Pg. 83) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); Y = gendiff(data); Generalized Difference Method

25 C D E Graphical To get the temporal speckle contrast image [9], first it is necessary to get the temporal speckle mean matrix (Equation 16), µ, as NTIMES 1 µ = E[I k ] = I k, (16) NTIMES k=1 Then the temporal speckle standard deviation (Equation 17), σ, is calculates as σ = E[(I k µ) 2 ] = 1 NTIMES (I k E[I k ]) NTIMES 2. (17) k=1 The temporal speckle contrast image can be calculated as Contrast = σ µ (18)

26 C D E Graphical temporal speckle contrast image [9] (Pg. 84) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); [C D E] = stdcont(data); Images: Speckle Mean Images: Speckle Standard Deviation Images: Speckle Contrast

27 Graphical Graphic IM 1.bmp 2.bmp 3.bmp... 9.bmp... cafe128.bmp The function graphim() uses, as input data, a 3D matrix (DATA) created by grouping intensity matrices I k DATA(:,:,k), 1 k NTIMES = 128. GIM = E[(I k I k+1 ) 2 ] = NTIMES 1 1 (I k I k+1 ) 2 (19) NTIMES 1 k=1

28 Graphical Graphic IM Calculating the IM in graphic mode (Pg. 85) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); GIM = graphim(data); Graphic IM Method

29 Graphical Graphic AVD 1.bmp 2.bmp 3.bmp... 9.bmp... cafe128.bmp The function graphavd() uses, as input data, a 3D matrix (DATA) created by grouping intensity matrices I k DATA(:,:,k), 1 k NTIMES = 128. GAVD = E[ I k I k+1 ] = NTIMES 1 1 I k I k+1 (20) NTIMES 1 k=1

30 Graphical Graphic AVD Calculating the AVD in graphic mode (Pg. 85) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); GIM = graphavd(data); Graphic AVD Method

31 MHI Graphical The calculus of MHI matrix [8, 5], that is the result of applying the MHI technique, can be seen in the Equations (21-24). being that S k = I k I k 1. (21) T k (i,j) = { 1 if S k (i,j) > U 0 if S k (i,j) U (22) NTIMES 2 MHI = 255 T NTIMES i h i, (23) i=0 h i = NTIMES 1 i M where NTIMES = 128 and M = NTIMES(NTIMES 1)/2. (24)

32 MHI Graphical Motion History Image [8, 5] (Pg. 90) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); MHI=graphmhi(DATA,11); Motion History Image

33 Quality Test Quality Test

34 Quality Test Saturation Saturated and dark zones [4] (Pg. 91) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); IMAGE1=DATA(:,:,1); WIDTH=8; HEIGHT=8; MINL=20; MAXL=150; PERCENT=50; [Img S D]=satdark(IMAGE1,WIDTH,HEIGHT,MINL,MAXL,PERCENT); Preview Saturation Zone Image Dark Zone Image

35 Contrast Quality Test All the pixels in analysis windows are filled with the contrast value C l [4], where and σ l = C l = σl µ l, (25) µ l =< W l > (26) < (W l µ l ) 2 >. (27)

36 Contrast Quality Test Contrast [4] (Pg. 92) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); IMAGE1=DATA(:,:,1); WIDTH=8; HEIGHT=8; [C mc]=sscont(image1,width,height); Spatial speckle contrast method

37 Quality Test Homogeneity ( H(i,j) = C(i,j) ), (28) C max where the value C(i,j) is calculated as in the Equations (29), (30), (31), and (32), C(i,j) = σ Z (i,j), (29) µ Z (i,j) µ Z (i,j) = 1 Z (i,j) (l), (30) 5 l σ 2 = 1 (Z (i,j) (l) µ Z (i,j) 5 Z (i,j)) 2, (31) l Z (i,j) = {A(i,j 1) A(i 1,j) A(i,j) A(i +1,j) A(i,j +1)} {Z (i,j) (0) Z (i,j) (1) Z (i,j) (2) Z (i,j) (3) Z (i,j) (4)} (32)

38 Quality Test Homogeneity Homogeneity [4] (Pg. 92) IMAGESDIR='~/data/cafe-biospeckle/sem1'; DATA=datapack(IMAGESDIR,'',1,128,'bmp'); WIDTH=8; HEIGHT=8; [Y X]=homogeneity(DATA,WIDTH,HEIGHT,0);% 0 - IM Activity indicator: Inertia Moment Homogeneity test in analysis windows

39 Quality Test References I [1] Arizaga, R., Cap, N. L., Rabal, H. J., and Trivi, M. (2002). Display of local activity using dynamical speckle patterns. Optical Engineering, 41(2): [2] Arizaga, R., Trivi, M., and Rabal, H. J. (1999). Speckle time evolution characterization by the co-occurrence matrix analysis. Optics & Laser Technology, 31(2): [3] Cardoso, R. R. and Braga, R. A. (2014). Enhancement of the robustness on dynamic speckle laser numerical analysis. Optics and Lasers in Engineering, 63: [4] Cardoso, R. R., Braga, R. A., and Rabal, H. J. (2012). Alternative protocols on dynamic speckle laser analysis. Proc. SPIE, 8413:84131F 84131F 6.

40 Quality Test References II [5] Davis, J. W. (2001). Hierarchical motion history images for recognizing human motion. In Detection and Recognition of Events in Video, Proceedings. IEEE Workshop on, pages [6] Fujii, H. and Asakura, T. (1975). Statistical properties of image speckle patterns in partially coherent light. Nouvelle Revue d Optique, 6(1):5. [7] Fujii, H., Nohira, K., Yamamoto, Y., Ikawa, H., and Ohura, T. (1987). Evaluation of blood flow by laser speckle image sensing. part 1. Applied Optics, 26(24): [8] Godinho, R., Silva, M. M., Nozela, J. R., and Braga, R. A. (2012). Online biospeckle assessment without loss of definition and resolution by motion history image. Optics and Lasers in Engineering, 50:

41 Quality Test References III [9] Nothdurft, R. and Yao, G. (2005). Imaging obscured subsurface inhomogeneity using laser speckle. Optics Express, 13(25): [10] Xu, Z., Joenathan, C., and Khorana, B. M. (1995). Temporal and spatial properties of the time-varying speckles of botanical specimens. Optical Engineering, 34(5): [11] Zdunek, A., Muravsky, L. I., Frankevych, L., and Konstankiewicz, K. (2007). New nondestructive method based on spatial-temporal speckle correlation technique for evaluation of apples quality during shelf-life. International Agrophysics, 21(3):