# Gaussian Filter Generation in C++

• Difficulty Level : Hard
• Last Updated : 16 Jun, 2021

Gaussian Filtering is widely used in the field of image processing. It is used to reduce the noise of an image. In this article we will generate a 2D Gaussian Kernel. The 2D Gaussian Kernel follows the below given Gaussian Distribution. Where, y is the distance along vertical axis from the origin, x is the distance along horizontal axis from the origin and σ is the standard deviation.

Implementation in C++

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

## C++

 // C++ prgroam to generate Gaussian filter#include #include #include using namespace std; // Function to create Gaussian filtervoid FilterCreation(double GKernel[]){    // initialising standard deviation to 1.0    double sigma = 1.0;    double r, s = 2.0 * sigma * sigma;     // sum is for normalization    double sum = 0.0;     // generating 5x5 kernel    for (int x = -2; x <= 2; x++) {        for (int y = -2; y <= 2; y++) {            r = sqrt(x * x + y * y);            GKernel[x + 2][y + 2] = (exp(-(r * r) / s)) / (M_PI * s);            sum += GKernel[x + 2][y + 2];        }    }     // normalising the Kernel    for (int i = 0; i < 5; ++i)        for (int j = 0; j < 5; ++j)            GKernel[i][j] /= sum;} // Driver program to test above functionint main(){    double GKernel;    FilterCreation(GKernel);     for (int i = 0; i < 5; ++i) {        for (int j = 0; j < 5; ++j)            cout << GKernel[i][j] << "\t";        cout << endl;    }}

Output:

0.00296902    0.0133062    0.0219382    0.0133062    0.00296902
0.0133062    0.0596343    0.0983203    0.0596343    0.0133062
0.0219382    0.0983203    0.162103    0.0983203    0.0219382
0.0133062    0.0596343    0.0983203    0.0596343    0.0133062
0.00296902    0.0133062    0.0219382    0.0133062    0.00296902

References:
https://en.wikipedia.org/wiki/Gaussian_filter
This article is contributed by Harsh Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.