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    <p>Wikipedia has a nice explanation of <a href="http://en.wikipedia.org/wiki/Standard_deviation#Definition_of_population_values" rel="noreferrer">standard deviation</a>, which you can use to for a standard deviation filter.</p> <p>Basically, it boils down to blurring the image with a box filter, blurring the square of the image with a box filter, and taking the square root of their difference.</p> <p><strong>UPDATE:</strong> This is probably better shown with the equation from Wikipedia... <img src="https://i.stack.imgur.com/RUFQj.png" alt="enter image description here"></p> <p>You can think of the OpenCV <code>blur</code> function as representing the <a href="http://en.wikipedia.org/wiki/Expected_value" rel="noreferrer">expected value</a> (i.e., E[X] a.k.a. the sample mean) of the neighborhood of interest. The random samples X in this case are represented by image pixels in the local neighborhood. Therefore, by using the above equivalence we have something like <code>sqrt(blur(img^2) - blur(img)^2)</code> in OpenCV. Doing it this way allows you to compute the local means and standard deviations.</p> <p>Also, just in case you are curious about the mathematical proof. This equivalence is known as the <a href="http://en.wikipedia.org/wiki/Computational_formula_for_the_variance" rel="noreferrer">computational formula for variance</a>.</p> <p>Here is how you can do this in OpenCV:</p> <pre><code>#include &lt;iostream&gt; #include &lt;opencv2/core/core.hpp&gt; #include &lt;opencv2/highgui/highgui.hpp&gt; #include &lt;opencv2/imgproc/imgproc.hpp&gt; using namespace std; using namespace cv; Mat mat2gray(const Mat&amp; src) { Mat dst; normalize(src, dst, 0.0, 1.0, NORM_MINMAX); return dst; } int main() { Mat image = imread("coke-can.jpg", 0); Mat image32f; image.convertTo(image32f, CV_32F); Mat mu; blur(image32f, mu, Size(3, 3)); Mat mu2; blur(image32f.mul(image32f), mu2, Size(3, 3)); Mat sigma; cv::sqrt(mu2 - mu.mul(mu), sigma); imshow("coke", mat2gray(image32f)); imshow("mu", mat2gray(mu)); imshow("sigma",mat2gray(sigma)); waitKey(); return 0; } </code></pre> <p>This produces the following images:</p> <h2>Original</h2> <p><img src="https://i.stack.imgur.com/V8Zso.jpg" alt="enter image description here"></p> <h2>Mean</h2> <p><img src="https://i.stack.imgur.com/9e53R.jpg" alt="enter image description here"></p> <h2>Standard Deviation</h2> <p><img src="https://i.stack.imgur.com/fAclA.jpg" alt="enter image description here"></p> <p>Hope that helps!</p>
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    1. COThis is phenomenal, thank you! I was having a tough time thinking through the process of summing the squared differences as a single filter kernel, but I see that separating them could work well. One question though, don't you have to take the difference of each element vs. the local mean before you square that difference? The SD formula on the page you mention is (sum((x-mu)^2)^(1/2). I think what you wrote is (sum((x^2)-(mu^2)))^(1/2). Arguably, however, it seems your code has produced rather accurate results.
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    2. CO@gankoji Awesome! Glad you found this sample helpful. Basically, I am using the mathematical equivalence that is shown in the Wiki article. I also updated the answer to hopefully explain this in a more complete fashion.
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    3. COAhh, I see the equivalence you mentioned. Sorry, I'm not a statistics buff, I had no idea that was the case! I will try to implement this code on Monday when I return to the office, and let you know how it goes. Thanks again!
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