與Matlab不同的高斯濾波器內核高斯濾波器內核

Question

我在Matlab中創建了一個高斯濾波器。我創建了以下用於創建內核的代碼。

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 

而且我的輸出是：

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 

但是當我運行了Matlab高斯濾波器，其結果是稍微偏離我的輸出。

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 

我不缺少算法中的任何步驟。我想弄清楚爲什麼我們的結果不匹配。

Answer 1

我忘了標準化內核：

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

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