尝试在C语言中实现高斯滤波器

您的计算不正确:过滤器应该位于原点的中心。以下是正确的版本:

#include <math.h>
#include <stdio.h>

#define smooth_kernel_size 5
#define sigma 1.0
#define K  1

int main() {
    double gauss[smooth_kernel_size][smooth_kernel_size];
    double sum = 0;
    int i, j;

    for (i = 0; i < smooth_kernel_size; i++) {
        for (j = 0; j < smooth_kernel_size; j++) {
            double x = i - (smooth_kernel_size - 1) / 2.0;
            double y = j - (smooth_kernel_size - 1) / 2.0;
            gauss[i][j] = K * exp(((pow(x, 2) + pow(y, 2)) / ((2 * pow(sigma, 2)))) * (-1));
            sum += gauss[i][j];
        }
    }
    for (i = 0; i < smooth_kernel_size; i++) {
        for (j = 0; j < smooth_kernel_size; j++) {
            gauss[i][j] /= sum;
        }
    }
    for (i = 0; i < smooth_kernel_size; i++) {
        for (j = 0; j < smooth_kernel_size; j++) {
            printf("%f ", gauss[i][j]);
        }
        printf("\n");
    }
    return 0;
}

输出:

0.002969 0.013306 0.021938 0.013306 0.002969
0.013306 0.059634 0.098320 0.059634 0.013306
0.021938 0.098320 0.162103 0.098320 0.021938
0.013306 0.059634 0.098320 0.059634 0.013306
0.002969 0.013306 0.021938 0.013306 0.002969

还要注意,主表达式可以简化:

    gauss[i][j] = K * exp(-(x * x + y * y) / (2 * sigma * sigma));

问题在于你计算高斯滤波器的方法,你应该使用对称点,我想-2-1 0 1 2,例如, 其次,我认为这是正确的公式

int length = smooth_kernel_size/2;
for (int i = -length ; i <=length ; i++)
    {
        for(int j=-length ; j <=length ; j++)
        {   //here
            gauss[i+length][j+length]= K * exp(-1*((pow((i), 2) + pow((j), 2)) / ((2 * pow(sigma, 2))))) / (M_PI * 2 * pow(sigma, 2));
            sum += gauss[i + length][j +length];
        }
    }