OpenCV Mean/SD filter

In case you want to use this in more general way this can produce nan values

Values close to zero can be sometimes "negative".

Mat sigma;
cv::sqrt(mu2 - mu.mul(mu), sigma);

correct way should be

Mat sigma;
cv::sqrt(cv::abs(mu2 - mu.mul(mu)), sigma);

Wikipedia has a nice explanation of standard deviation, which you can use to for a standard deviation filter.

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.

UPDATE: This is probably better shown with the equation from Wikipedia...

You can think of the OpenCV blur function as representing the expected value (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 sqrt(blur(img^2) - blur(img)^2) in OpenCV. Doing it this way allows you to compute the local means and standard deviations.

Also, just in case you are curious about the mathematical proof. This equivalence is known as the computational formula for variance.

Here is how you can do this in OpenCV:

#include <iostream>
#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/imgproc/imgproc.hpp>

using namespace std;
using namespace cv;

Mat mat2gray(const Mat& 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;
}

This produces the following images:

Original

Mean

Standard Deviation

Hope that helps!