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I am working on Speckle reduction in ultrasound images. I read a paper (snapshot of that paper is included below) where they have used a metric called beta metric which indicates the edge preserving capability of the filters. I tried to implement it using the equation (7) provided in the below snapshot.

Beta Metrics

This is the code.

 %---Beta Calculation
    h = fspecial('laplacian');
    I1 = imfilter(Orig_Image,h);
    I2 = imfilter(Esti_Image,h);
    I_1 = mean2(I1);
    I_2 = mean2(I2);
    metrics.Beta = sum(sum((I1 - I_1).*(I2 - I_2)))./(sqrt(sum(((I1 - I_1).^2).*((I2 - I_2).^2))));

As you can see that the beta value is a single value [1x1] vector in Table 2 inside the snapshot. But when I run my code, I get beta value of size 1x256 for a 256x256 image. Is my code wrong? How to implement the given equation (7) correctly in MATLAB? Please help.

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The correct code is

metrics.Beta = sum(sum((I1 - I_1).*(I2 - I_2)))./(sqrt(sum(sum((I1 - I_1).^2))).*(sum(sum((I2 - I_2).^2))));

The reference you have shown is incorrect, reffr paper:

2013 August Gregorio - ‘A suitable threshold for speckle reduction in ultrasound images’, IEEE transactions on instrumentations and measurement

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Your implementation is correct.

As the paper says, beta metrics indicate the edge preservation. So it is supposed to have 256 beta values, with each one representing the metric for one line in the image. You may try to average the 256 values to get one beta value.

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