Gaussian Filter Generation in C++

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.
$G(x, y)=\frac{1}{2\pi \sigma ^{2}}e^{-\frac{x^{2}+y^{2}}{2\sigma ^{2}}}$
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++

// C++ prgroam to generate Gaussian filter 
#include <cmath> 
#include <iomanip> 
#include <iostream> 
using namespace std; 
  
// Function to create Gaussian filter 
void FilterCreation(double GKernel[][5]) 
{ 
    // intialising 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 function 
int main() 
{ 
    double GKernel[5][5]; 
    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 contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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