André V. Saúde, Fortunato S. de Menezes, Patricia L. S. Freitas, Giovanni F. Rabelo, and Roberto A. Braga, "Alternative measures for biospeckle image analysis," J. Opt. Soc. Am. A 29, 1648-1658 (2012)

Biospeckle is a technique whose purpose is to observe and study the underlying activity of some material. It has its roots in optical physics, and its first step is an image acquisition process that produces a video sequence of the reflection of a laser. The video content can be analyzed to have an interpretation of the activity of the observed material. The literature on this subject presents several different measures for analyzing the video sequence. Three of the most popular measures are the generalized difference (GD), the weighted generalized difference (WGD), and Fujii’s method. These measures have drawbacks such as high computation time or limited visual quality of the results. In this paper, we propose (i) an alternative $O(n)$ algorithm for the computation of the GD, (ii) an alternative measure based on the GD, (iii) an alternative measure based on the WGD, and (iv) a generalized definition of the Fujii’s method with better visual quality. We discuss the similarities between the new measures and the existent ones, showing when they are applicable. We prove the gain in time computation. The proposed measures will help researchers to gain time during their research and to be able to develop faster tools based on biospeckle application.

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Numerical Comparison between the MWD Eq. (17) and the ${\mathrm{MWD}}^{\prime}$ Eq. (18) for $w=4$, 8, 12, 16, and 20, Where $X=\mathrm{MWD}$ and ${X}^{\prime}={\mathrm{MWD}}^{\prime}$, $\mathrm{max}(y)$ Is the Maximum Value in $y$, $\mathrm{min}(y)$ Is the Minimum Value in $y$, $\mathrm{mean}(y)$ Is the Mean Value in $y$, $\mathrm{stddev}(y)$ Is the Standard Deviation in $y$, $\mathrm{peakratio}(y,{y}^{\prime})=\mathrm{mean}(y-{y}^{\prime})/\mathrm{max}(\{y,{y}^{\prime}\})$ Is the Percentage of the Mean Difference over the Peak Value of the Samples Union, and $\mathrm{peakstdratio}(y,{y}^{\prime})=\mathrm{stddev}(y-{y}^{\prime})/\mathrm{max}(\{y,{y}^{\prime}\})$ Is the Percentage of the Mean Standard Deviation over the Peak Value of the Samples Uniona

$w$

4

8

12

16

20

$\mathrm{max}(X)$

8855

24562

45971

66958

83014

$\mathrm{max}({X}^{\prime})$

8157

22996

42399

59744

73734

$\mathrm{min}(X)$

0

0

0

0

0

$\mathrm{min}({X}^{\prime})$

0

0

0

0

0

$\mathrm{max}(X-{X}^{\prime})$

1264

3382

6620

11304

16166

$\mathrm{min}(X-{X}^{\prime})$

0

0

0

0

0

$\text{mean}(X-{X}^{\prime})$

421.5922

995.8408

1627.044

2313.8139

3035.4388

$\text{stddev}(X-{X}^{\prime})$

187.3067

444.7653

775.0706

1202.6929

1711.5886

$\text{peakratio}(X,{X}^{\prime})$

4.76%

4.05%

3.54%

3.46%

3.66%

$\text{peakstdratio}(X,{X}^{\prime})$

2.12%

1.81%

1.69%

1.80%

2.06%

All values are signed integers or real numbers, except $\text{peakratio}(y,{y}^{\prime})$ and $\text{peakstdratio}(y,{y}^{\prime})$, which are represented as percentages.

Table 2.

Numerical Comparison between the MWD and the ${\mathrm{MWD}}^{\prime}$ for $w=4$, 8, 12, 16, and 20, Where $X=\mathrm{MWD}$ and ${X}^{\prime}={\mathrm{MWD}}^{\prime}$, Both Normalized to the Interval 0…255, $\mathrm{max}(y)$ Is the Maximum Value in $y$, $\mathrm{min}(y)$ Is the Minimum Value in $y$, $\mathrm{mean}(y)$ Is the Mean Value in $y$, $\mathrm{stddev}(y)$ Is the Standard Deviation in $y$, $\mathrm{peakratio}(y,{y}^{\prime})=\mathrm{mean}(y-{y}^{\prime})/\mathrm{max}(\{y,{y}^{\prime}\})$ Is the Percentage of the Mean Difference over the Peak Value of the Samples Union, and $\mathrm{peakstdratio}(y,{y}^{\prime})=\mathrm{stddev}(y-{y}^{\prime})/\mathrm{max}(\{y,{y}^{\prime}\})$ Is the Percentage of the Mean Standard Deviation over the Peak Value of the Samples Uniona

$w$

4

8

12

16

20

$\mathrm{max}(X)$

255

255

255

255

255

$\mathrm{max}({X}^{\prime})$

255

255

255

255

255

$\mathrm{min}(X)$

0

0

0

0

0

$\mathrm{min}({X}^{\prime})$

0

0

0

0

0

$\mathrm{max}(X-{X}^{\prime})$

27

25

27

29

34

$\mathrm{min}(X-{X}^{\prime})$

$-9$

$-7$

$-8$

$-13$

$-16$

$\text{mean}(X-{X}^{\prime})$

6.8933

6.9504

5.3844

3.8202

3.9682

$\text{stddev}(X-{X}^{\prime})$

4.1065

3.6829

3.1243

3.0465

3.2947

$\text{peakratio}(X,{X}^{\prime})$

2.70%

2.73%

2.11%

1.50%

1.56%

$\text{peakstdratio}(X,{X}^{\prime})$

1.61%

1.44%

1.23%

1.19%

1.29%

All values are signed integers or real numbers, except $\text{peakratio}(y,{y}^{\prime})$ and $\text{peakstdratio}(y,{y}^{\prime})$ which are represented as percentages.

Tables (2)

Table 1.

Numerical Comparison between the MWD Eq. (17) and the ${\mathrm{MWD}}^{\prime}$ Eq. (18) for $w=4$, 8, 12, 16, and 20, Where $X=\mathrm{MWD}$ and ${X}^{\prime}={\mathrm{MWD}}^{\prime}$, $\mathrm{max}(y)$ Is the Maximum Value in $y$, $\mathrm{min}(y)$ Is the Minimum Value in $y$, $\mathrm{mean}(y)$ Is the Mean Value in $y$, $\mathrm{stddev}(y)$ Is the Standard Deviation in $y$, $\mathrm{peakratio}(y,{y}^{\prime})=\mathrm{mean}(y-{y}^{\prime})/\mathrm{max}(\{y,{y}^{\prime}\})$ Is the Percentage of the Mean Difference over the Peak Value of the Samples Union, and $\mathrm{peakstdratio}(y,{y}^{\prime})=\mathrm{stddev}(y-{y}^{\prime})/\mathrm{max}(\{y,{y}^{\prime}\})$ Is the Percentage of the Mean Standard Deviation over the Peak Value of the Samples Uniona

$w$

4

8

12

16

20

$\mathrm{max}(X)$

8855

24562

45971

66958

83014

$\mathrm{max}({X}^{\prime})$

8157

22996

42399

59744

73734

$\mathrm{min}(X)$

0

0

0

0

0

$\mathrm{min}({X}^{\prime})$

0

0

0

0

0

$\mathrm{max}(X-{X}^{\prime})$

1264

3382

6620

11304

16166

$\mathrm{min}(X-{X}^{\prime})$

0

0

0

0

0

$\text{mean}(X-{X}^{\prime})$

421.5922

995.8408

1627.044

2313.8139

3035.4388

$\text{stddev}(X-{X}^{\prime})$

187.3067

444.7653

775.0706

1202.6929

1711.5886

$\text{peakratio}(X,{X}^{\prime})$

4.76%

4.05%

3.54%

3.46%

3.66%

$\text{peakstdratio}(X,{X}^{\prime})$

2.12%

1.81%

1.69%

1.80%

2.06%

All values are signed integers or real numbers, except $\text{peakratio}(y,{y}^{\prime})$ and $\text{peakstdratio}(y,{y}^{\prime})$, which are represented as percentages.

Table 2.

Numerical Comparison between the MWD and the ${\mathrm{MWD}}^{\prime}$ for $w=4$, 8, 12, 16, and 20, Where $X=\mathrm{MWD}$ and ${X}^{\prime}={\mathrm{MWD}}^{\prime}$, Both Normalized to the Interval 0…255, $\mathrm{max}(y)$ Is the Maximum Value in $y$, $\mathrm{min}(y)$ Is the Minimum Value in $y$, $\mathrm{mean}(y)$ Is the Mean Value in $y$, $\mathrm{stddev}(y)$ Is the Standard Deviation in $y$, $\mathrm{peakratio}(y,{y}^{\prime})=\mathrm{mean}(y-{y}^{\prime})/\mathrm{max}(\{y,{y}^{\prime}\})$ Is the Percentage of the Mean Difference over the Peak Value of the Samples Union, and $\mathrm{peakstdratio}(y,{y}^{\prime})=\mathrm{stddev}(y-{y}^{\prime})/\mathrm{max}(\{y,{y}^{\prime}\})$ Is the Percentage of the Mean Standard Deviation over the Peak Value of the Samples Uniona

$w$

4

8

12

16

20

$\mathrm{max}(X)$

255

255

255

255

255

$\mathrm{max}({X}^{\prime})$

255

255

255

255

255

$\mathrm{min}(X)$

0

0

0

0

0

$\mathrm{min}({X}^{\prime})$

0

0

0

0

0

$\mathrm{max}(X-{X}^{\prime})$

27

25

27

29

34

$\mathrm{min}(X-{X}^{\prime})$

$-9$

$-7$

$-8$

$-13$

$-16$

$\text{mean}(X-{X}^{\prime})$

6.8933

6.9504

5.3844

3.8202

3.9682

$\text{stddev}(X-{X}^{\prime})$

4.1065

3.6829

3.1243

3.0465

3.2947

$\text{peakratio}(X,{X}^{\prime})$

2.70%

2.73%

2.11%

1.50%

1.56%

$\text{peakstdratio}(X,{X}^{\prime})$

1.61%

1.44%

1.23%

1.19%

1.29%

All values are signed integers or real numbers, except $\text{peakratio}(y,{y}^{\prime})$ and $\text{peakstdratio}(y,{y}^{\prime})$ which are represented as percentages.