apracticalguidetobiospecklelaseranalysis - non-gnu · apracticalguidetobiospecklelaseranalysis...

A Practical Guide to Biospeckle Laser Analysis

Theory and Software

Fernando Pujaico Rivera1 and Roberto Alves Braga1

1Universidade Federal de Lavras

Aula-1 2016

Fernando A Practical Guide

Datapack

Datapack


Datapack

Loading a Datapack

1.bmp 2.bmp 3.bmp ... 9.bmp

10.bmp 11.bmp 12.bmp ... 128.bmp

Loading a Datapack

IMAGESDIR='~/data/cafe-biospeckle/sem1';

DATA=datapack(IMAGESDIR,'',1,128,'bmp');


Datapack

Loading a Datapack

cafe1.bmp cafe2.bmp cafe3.bmp ... cafe9.bmp


Loading a Datapack (Pg. 69)


DATA=datapack(IMAGESDIR,'cafe',1,128,'bmp');


Datapack

Loading a Datapack



Loading a Datapack (Pg. 69)


DATA=datapack(IMAGESDIR,'cafe%03d',1,128,'bmp');


Datapack

Saving a datapack

1.bmp 2.bmp 3.bmp ... 9.bmp ... cafe128.bmp

Saving a datapack (Pg. 70)



Frames=20;

Ts=0.5;

datapack_to_gif(DATA,'datapack.gif',Frames,gray,Ts);

colormap(’list’)

autumn bone gray ... jet ... winter


Numerical

Numerical


Numerical

THSP

Creating a THSP (Pg. 71)



THSP=thsp(DATA,'column',240);

imagesc(THSP);colormap gray;

20 40 60 80 100 120

100

200

300

400


Numerical

COM

Creating a COM (Pg. 72)



THSP=thsp(DATA,'line',240);

COM=coom(THSP);

imagesc(COM);colormap gray;

50 100 150 200 250

50

100

150

200

250


Numerical

IM

Where the IM moment [3] (IM1) is:

E [(i − j)2] =∑

ij

COM(i , j)∑

lm COM(l ,m)(i − j)2. (1)

And, the IM moment following [2] (IM2) is presented as in theEquation (2),

EAriz .[(i − j)2] =∑

ij

COM(i , j)∑

m COM(i ,m)(i − j)2. (2)


Numerical

IM

Calculating the IM value (Pg. 75)




COM=coom(THSP);

[IM1 IM2]=inertiamoment(COM,2)

IM1 = 359.36IM2 = 1.0547e + 05


Numerical

AVD

Where the AVD first moment [3] (AVD1) is:

E [|i − j |] =∑

ij

COM(i , j)∑

lm COM(l ,m)|i − j | (3)

The AVD second moment (AVD2) is:

E [(i − j)2] =∑

ij

COM(i , j)∑

lm COM(l ,m)(i − j)2 (4)

The AVD second central moment (AVD3) is:

Var [|i − j |] = E [(i − j)2]− E [|i − j |]2 (5)

And the AVD first moment following [2] (AVD4) is:

EAriz .[|i − j |] =∑

ij

COM(i , j)∑

m COM(i ,m)|i − j | (6)


Numerical

AVD

Calculating the AVD value (Pg. 76)




COM=coom(THSP);

[AVD1 AVD2 AVD3 AVD4]=avd(COM,2,3,4)

AVD1 = 13.780AVD2 = 359.36AVD3 = 169.48AVD4 = 3210.4


Numerical

NUMAD

Where the first moment (NUMAD1) is:

E

[

|i − j |

i + j

]

=∑

ij

COM(i , j)∑

lm COM(l ,m)

|i − j |

i + j(7)

And the second moment (NUMAD2) is:

E

[

(

|i − j |

i + j

)2]

=∑

ij

COM(i , j)∑

lm COM(l ,m)

(

|i − j |

i + j

)2

(8)


Numerical

NUMAD

Calculating the NUMAD value (Pg. 80)




COM=coom(THSP);

[NUMAD1 NUMAD2]=numad(COM,2)

NUMAD1 = 0.084686NUMAD2 = 0.013135


Numerical

Correlation

The correlation Cil [10] (Equation 9) is calculated between allpixels THSP(:, i) in the instant i and the pixels THSP(:, i + j) inthe instant i + j ,

Cil = corr(THSP(:, i),THSP(:, i + l)). (9)

The function finally returns, Cl (Equation 10), the mean value ofthis correlations for a lag of l ,

Cl =1

NTIMES/2

NTIMES/2∑

i=1

Cil . (10)


Numerical

Correlation

Calculating the correlation value (Pg. 81)




[C1 L1] = thsp2corr(THSP,1);

plot(L1,C1,'-o');grid;xlabel('L1');ylabel('C1');

0 10 20 30 40 50 60 700.96

0.97

0.98

0.99

1

L1

C1


Numerical

Spatial-Temporal Correlation

The correlation C lτk0

[11] (Equation 11) is calculated between theimage Ik0 and the image Ik0+l , ∀ 1 ≤ k0 + l ≤ NTIMES. Here it isassumed that the images were taken with sampling rate equal to τ .

C lτk0

= corr(Ik0 , Ik0+l ), (11)


Numerical

Spatial-Temporal Correlation

Calculating the spatial-temporal correlation value [11] (Pg. 82)



tau=1;

[C T]=stscorr(DATA,tau,42);

-40 -20 0 20 40 60 800.75

0.8

0.85

0.9

0.95

1

k tau

Cor

rela

tion

coef

ficie

nts

Spatial-Temporal Speckle Correlation Technique: k0=42


Graphical

Graphical


Graphical

Fujii


The function in Equation (12) [7, 6] is normalized to Equation(13):

FUJII =

NTIMES−1∑

k=1

|Ik − Ik+1|

Ik + Ik+1 + eps, (12)

Y = FUJII2× 100

NTIMES− 1. (13)

Where NTIMES=128.


Graphical

Fujii

Fujii [7, 6] (Pg. 83)



FUJII=fujii(DATA);

Fujii Method

100 200 300 400

100

200

300

400

0

10

20

30

40


Graphical

GD


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 Ik ≡ DATA(:, :, k),1 ≤ k ≤ NTIMES ≡ 128.

GD =

NTIMES−1∑

k=1

NTIMES−k∑

l=1

|Ik − Ik+l | (14)

The function is normalized to Y (Equation 15) with the number ofelements in the sum.

Y =GD

(

NTIMES

2

) (15)


Graphical

GD

Generalized Difference (GD) [1] (Pg. 83)



Y = gendiff(DATA);

Generalized Difference Method

100 200 300 400

100

200

300

400

0

10

20

30

40


Graphical

C D E

To get the temporal speckle contrast image [9], first it is necessaryto get the temporal speckle mean matrix (Equation 16), µ, as

µ = E [Ik ] =1

NTIMES

NTIMES∑

k=1

Ik , (16)

Then the temporal speckle standard deviation (Equation 17), σ, iscalculates as

σ =√

E [(Ik − µ)2] =

√

√

√

√

1

NTIMES

NTIMES∑

k=1

(Ik − E [Ik ])2. (17)

The temporal speckle contrast image can be calculated as

Contrast =σ

µ(18)


Graphical

C D E

temporal speckle contrast image [9] (Pg. 84)



[C D E] = stdcont(DATA);

Images: Speckle Mean

100 200 300 400

100

200

300

400

50

100

150

200

Images: Speckle Standard Deviation

100 200 300 400

100

200

300

400

0

10

20

30

40

Images: Speckle Contrast

100 200 300 400

100

200

300

400

0

0.2

0.4

0.6


Graphical

Graphic IM


The function graphim() uses, as input data, a 3D matrix (DATA)created by grouping intensity matrices Ik ≡ DATA(:, :, k),1 ≤ k ≤ NTIMES = 128.

GIM = E [(Ik − Ik+1)2] =

1

NTIMES− 1

NTIMES−1∑

k=1

(Ik − Ik+1)2 (19)


Graphical

Graphic IM

Calculating the IM in graphic mode (Pg. 85)



GIM = graphim(DATA);

Graphic IM Method

100 200 300 400

100

200

300

400

0

500

1000

1500

2000


Graphical

Graphic AVD


The function graphavd() uses, as input data, a 3D matrix (DATA)created by grouping intensity matrices Ik ≡ DATA(:, :, k),1 ≤ k ≤ NTIMES = 128.

GAVD = E [|Ik − Ik+1|] =1

NTIMES− 1

NTIMES−1∑

k=1

|Ik − Ik+1| (20)


Graphical

Graphic AVD

Calculating the AVD in graphic mode (Pg. 85)



GIM = graphavd(DATA);

Graphic AVD Method

100 200 300 400

100

200

300

400

0

10

20

30


Graphical

MHI

The calculus of MHI matrix [8, 5], that is the result of applying theMHI technique, can be seen in the Equations (21-24).

Sk = Ik − Ik−1. (21)

Tk(i , j) =

{

1 if |Sk(i , j)| > U

0 if |Sk(i , j)| ≤ U(22)

MHI = 255NTIMES−2∑

i=0

TNTIMES−i hi , (23)

being that

hi =NTIMES− 1− i

M(24)

where NTIMES = 128 and M = NTIMES(NTIMES− 1)/2.


Graphical

MHI

Motion History Image [8, 5] (Pg. 90)



MHI=graphmhi(DATA,11);

Motion History Image

100 200 300 400

100

200

300

400


Quality Test

Quality Test


Quality Test

Saturation

Saturated and dark zones [4] (Pg. 91)



IMAGE1=DATA(:,:,1);

WIDTH=8; HEIGHT=8; MINL=20; MAXL=150; PERCENT=50;

[Img S D]=satdark(IMAGE1,WIDTH,HEIGHT,MINL,MAXL,PERCENT);

Preview

100 200 300 400

100

200

300

400

0

50

100

150

200

250

Saturation Zone Image

100 200 300 400

100

200

300

400

0

0.2

0.4

0.6

0.8

1

Dark Zone Image

100 200 300 400

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200

300

400

0

0.2

0.4

0.6

0.8

1


Quality Test

Contrast

All the pixels in analysis windows are filled with the contrast valueC l [4],

C l =σl

µl, (25)

whereµl =< W l > (26)

and

σl =√

< (W l − µl)2 >. (27)


Quality Test

Contrast

Contrast [4] (Pg. 92)



IMAGE1=DATA(:,:,1);

WIDTH=8; HEIGHT=8;

[C mC]=sscont(IMAGE1,WIDTH,HEIGHT);

Spatial speckle contrast method - 0.232431.

100 200 300 400

100

200

300

400

0.1

0.2

0.3

0.4


Quality Test

Homogeneity

H(i , j) = 100

(

1−C (i , j)

Cmax

)

, (28)

where the value C (i , j) is calculated as in the Equations (29), (30),(31), and (32),

C (i , j) =σZ (i,j)

µZ (i,j)

, (29)

µZ (i,j) =1

5

∑

l

Z (i ,j)(l), (30)

σ2Z (i,j) =

1

5

∑

l

(Z (i ,j)(l)− µZ (i,j))2, (31)

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)


Quality Test

Homogeneity

Homogeneity [4] (Pg. 92)



WIDTH=8; HEIGHT=8;

[Y X]=homogeneity(DATA,WIDTH,HEIGHT,0);% 0 - IM

Activity indicator: Inertia Moment

100 200 300 400

100

200

300

400

200

400

600

800

1000

Homogeneity test in analysis windows

100 200 300 400

100

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400

0

20

40

60

80

100


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):287–294.

[2] Arizaga, R., Trivi, M., and Rabal, H. J. (1999). Speckle timeevolution characterization by the co-occurrence matrix analysis.Optics & Laser Technology, 31(2):163 – 169.

[3] Cardoso, R. R. and Braga, R. A. (2014). Enhancement of therobustness on dynamic speckle laser numerical analysis. Opticsand Lasers in Engineering, 63:19–24.

[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.


Quality Test

References II

[5] Davis, J. W. (2001). Hierarchical motion history images forrecognizing human motion. In Detection and Recognition of

Events in Video, 2001. Proceedings. IEEE Workshop on, pages39–46.

[6] Fujii, H. and Asakura, T. (1975). Statistical properties ofimage speckle patterns in partially coherent light. NouvelleRevue 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):5321–5325.

[8] Godinho, R., Silva, M. M., Nozela, J. R., and Braga, R. A.(2012). Online biospeckle assessment without loss of definitionand resolution by motion history image. Optics and Lasers in

Engineering, 50:366–372.


Quality Test

References III

[9] Nothdurft, R. and Yao, G. (2005). Imaging obscuredsubsurface inhomogeneity using laser speckle. Optics Express,13(25):10034–10039.

[10] Xu, Z., Joenathan, C., and Khorana, B. M. (1995). Temporaland spatial properties of the time-varying speckles of botanicalspecimens. Optical Engineering, 34(5):1487–1502.

[11] Zdunek, A., Muravsky, L. I., Frankevych, L., andKonstankiewicz, K. (2007). New nondestructive method basedon spatial-temporal speckle correlation technique for evaluationof apples quality during shelf-life. International Agrophysics,21(3):305–310.


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