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

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