Question

我在Matlab中创建了一个高斯滤波器。我创建了以下用于创建内核的代码。

function kernel = gaussian_filter(sigma)
    kernel_width = 3 * sigma - 1;
    [x, y] = meshgrid(-kernel_width/2:kernel_width/2, -kernel_width/2:kernel_width/2);
    normalized_constant = 1/(2 * pi * sigma * sigma);
    kernel = normalized_constant * exp(-(x.^2 + y.^2)/ (2 * sigma * sigma));
    K = mat2gray(kernel);
    imshow(K);
    title('Gaussian Kernel');
 end

我的输出是：

gaussian_filter(3)

ans =

  Columns 1 through 7

    0.0030    0.0044    0.0058    0.0069    0.0073    0.0069    0.0058
    0.0044    0.0065    0.0086    0.0101    0.0107    0.0101    0.0086
    0.0058    0.0086    0.0113    0.0134    0.0142    0.0134    0.0113
    0.0069    0.0101    0.0134    0.0158    0.0167    0.0158    0.0134
    0.0073    0.0107    0.0142    0.0167    0.0177    0.0167    0.0142
    0.0069    0.0101    0.0134    0.0158    0.0167    0.0158    0.0134
    0.0058    0.0086    0.0113    0.0134    0.0142    0.0134    0.0113
    0.0044    0.0065    0.0086    0.0101    0.0107    0.0101    0.0086
    0.0030    0.0044    0.0058    0.0069    0.0073    0.0069    0.0058

  Columns 8 through 9

    0.0044    0.0030
    0.0065    0.0044
    0.0086    0.0058
    0.0101    0.0069
    0.0107    0.0073
    0.0101    0.0069
    0.0086    0.0058
    0.0065    0.0044
    0.0044    0.0030

但是当我运行Matlab高斯滤波器时，结果略微偏离输出。

h = fspecial('gaussian', 9, 3)

h =

  Columns 1 through 7

    0.0040    0.0059    0.0077    0.0091    0.0096    0.0091    0.0077
    0.0059    0.0086    0.0114    0.0135    0.0142    0.0135    0.0114
    0.0077    0.0114    0.0150    0.0178    0.0188    0.0178    0.0150
    0.0091    0.0135    0.0178    0.0210    0.0222    0.0210    0.0178
    0.0096    0.0142    0.0188    0.0222    0.0235    0.0222    0.0188
    0.0091    0.0135    0.0178    0.0210    0.0222    0.0210    0.0178
    0.0077    0.0114    0.0150    0.0178    0.0188    0.0178    0.0150
    0.0059    0.0086    0.0114    0.0135    0.0142    0.0135    0.0114
    0.0040    0.0059    0.0077    0.0091    0.0096    0.0091    0.0077

  Columns 8 through 9

    0.0059    0.0040
    0.0086    0.0059
    0.0114    0.0077
    0.0135    0.0091
    0.0142    0.0096
    0.0135    0.0091
    0.0114    0.0077
    0.0086    0.0059
    0.0059    0.0040

我没有错过算法中的任何步骤。我想弄清楚为什么我们的结果不匹配。

Answer 1

我忘了规范化内核：

kernel = kernel/(sum(kernel(:)));

https://www.mathworks.com/help/images/ref/fspecial.html

高斯滤波器核不同于Matlab高斯滤波器核

1 个答案: