MSE for two Vec3b images in OpenCV

Question

I have two Vec3b images and I want to find the MSE (Mean Square Error) between them. I know how to do it when you have two uchar images, but when you have two Vec3b images where there are 3 different values stored for each pixel how do you calculate it?

Answer 1

You should compute the Euclidean distance for each pair of pixels:

MSE = 0;
for(int i = 0; i < width; i++)
    for(int j = 0; j < height; j++)
        MSE += sqrt(pow(img1.at<Vec3b>(j, i)[0] - img2.at<Vec3b>(j, i)[0]), 2) + pow(img1.at<Vec3b>(j, i)[1] - img2.at<Vec3b>(j, i)[1]), 2) + pow(img1.at<Vec3b>(j, i)[2] - img2.at<Vec3b>(j, i)[2]), 2));
MSE /= width * height;

This code can be optimized and if you convert your image from BGR to HSV, you could get better results according what you want to do.

Answer 2

To calculate the Mean Square Error for 1D and 3D images in opencv, you can use this post which might be faster since image scanning takes longer times.

double getMSE(Mat& I1, Mat& I2)
{
    Mat s1;
    // save the I! and I2 type before converting to float
    int im1type = I1.type();
    int im2type = I2.type();
    // convert to float to avoid producing zero for negative numbers
    I1.convertTo(I1, CV_32F);
    I2.convertTo(I2, CV_32F);
    absdiff(I1, I2, s1);       // |I1 - I2|
    s1.convertTo(s1, CV_32F);  // cannot make a square on 8 bits
    s1 = s1.mul(s1);           // |I1 - I2|^2

    Scalar s = sum(s1);         // sum elements per channel

    double sse = s.val[0] + s.val[1] + s.val[2]; // sum channels

    if( sse <= 1e-10) // for small values return zero
        return 0;
    else
    {
        double  mse =sse /(double)(I1.channels() * I1.total());
        return mse;
        // Instead of returning MSE, the tutorial code returned PSNR (below).
        //double psnr = 10.0*log10((255*255)/mse);
        //return psnr;
    }
     // return I1 and I2 to their initial types
    I1.convertTo(I1, im1type);
    I2.convertTo(I2, im2type);

}

The above code returns zero for small mse values (under 1e-10). Terms s.val1 and s.val[2] are zero for 1D images.

If you want to check for 1D image input, use the following code to test (with random unsigned numbers):

Mat I1(12, 12, CV_8UC1), I2(12, 12, CV_8UC1);
double low = 0;
double high = 255;

cv::randu(I1, Scalar(low), Scalar(high));
cv::randu(I2, Scalar(low), Scalar(high));
double mse = getMSE(I1, I2);
cout << mse << endl;

If you want to check for 3D image input, use the following code to test (with random unsigned numbers):

Mat I1(12, 12, CV_8UC3), I2(12, 12, CV_8UC3);
double low = 0;
double high = 255;

cv::randu(I1, Scalar(low), Scalar(high));
cv::randu(I2, Scalar(low), Scalar(high));
double mse = getMSE(I1, I2);
cout << mse << endl;