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 ? is the standard deviation.
Implementation in C++
C++
// C++ program to generate Gaussian filter #include <cmath> #include <iomanip> #include <iostream> using namespace std; // Function to create Gaussian filter void FilterCreation(double GKernel[][5]) { // 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 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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