LocalOperation01_图像滤波（壹）：mean、gauss、laplace、prewitt、sobel_laplace filter

1 均值滤波

1.1 原理

顾名思义，取平均值的滤波方法。

如上图示，对于一个3*3大小的滤波器，每次取3*3大小范围内的平均值赋值给当前像素，特别注意，滤波器应该是归一化的，对于一个n*n大小的均值滤波器，其矩阵形式为：

h m e a n = [ 1 n   1 n   ⋅ ⋅ ⋅   1 n 1 n   1 n   ⋅ ⋅ ⋅   1 n ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1 n   1 n   ⋅ ⋅ ⋅   1 n ] = 1 n [ 1   1   ⋅ ⋅ ⋅   1 1   1   ⋅ ⋅ ⋅   1 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1   1   ⋅ ⋅ ⋅   1 ] h_{mean} = \left[

$$\begin{matrix}\frac{1}{n}\space\frac{1}{n} \space···\space\frac{1}{n}\\ \frac{1}{n}\space\frac{1}{n}\space···\space\frac{1}{n}\\ ·········· \\ \frac{1}{n}\space \frac{1}{n}\space···\space\frac{1}{n} \end{matrix}$$ \right] = \frac{1}{n}\left[ $$\begin{matrix}1\space1\space···\space1\\ 1\space1 \space···\space1 \\········\\ 1\space 1\space···\space 1\end{matrix}$$ \right] hmean​=⎣⎢⎢⎡​n1​ n1​ ⋅⋅⋅ n1​n1​ n1​ ⋅⋅⋅ n1​⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅n1​ n1​ ⋅⋅⋅ n1​​⎦⎥⎥⎤​=n1​⎣⎢⎢⎡​1 1 ⋅⋅⋅ 11 1 ⋅⋅⋅ 1⋅⋅⋅⋅⋅⋅⋅⋅1 1 ⋅⋅⋅ 1​⎦⎥⎥⎤​

在Matlab中，$h_{mean}$可以通过fspecial函数生成：

h = fspecial('average',hsize) returns an averaging filter h of size hsize.
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例如：

>> h = fspecial('average', 3)

h =

    0.1111    0.1111    0.1111
    0.1111    0.1111    0.1111
    0.1111    0.1111    0.1111
    
>>
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易知，滤波器的size越大，滤波后的图像越模糊。

1.2 函数编写

function imgMean = meanfilter(img,filterSize)
% img: image
% filterSize: if=5, it means 5*5

% Generate mean filter
img = double(img);
meanFilter = fspecial('average', filterSize);
% cov
imgMean = convolutionM(img, meanFilter);
imgMean = uint8(imgMean);

end

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2 高斯滤波

2.1 原理

用高斯滤波器对图像进行滤波，例如：

h g a u s s = [ 0.075 ,   0.125 ,   0.075 0.125 ,   0.200 ,   0.125 0.075 ,   0.125 ,   0.075 ] h_{gauss} = \left[

$$\begin{matrix}0.075,\space0.125,\space0.075\\0.125,\space0.200,\space0.125\\0.075,\space0.125,\space0.075\end{matrix}$$ \right] hgauss​=⎣⎡​0.075, 0.125, 0.0750.125, 0.200, 0.1250.075, 0.125, 0.075​⎦⎤​

在Matlab中，$h_{gauss}$可以通过fspecial函数生成：

h = fspecial('gaussian',hsize,sigma) returns a rotationally symmetric Gaussian lowpass filter of size hsize with standard deviation sigma. Not recommended. Use imgaussfilt or imgaussfilt3 instead.
Standard deviation, specified as a positive number.
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例如：

>> h = fspecial('gaussian', 3, 1)

h =

    0.0751    0.1238    0.0751
    0.1238    0.2042    0.1238
    0.0751    0.1238    0.0751
    
>>
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2.2 函数编写

function imgGaussian = gaussianfilter(img,filterSize,sigma)
% img: image
% filterSize: if=5, it means 5*5
% sigma: Standard deviation, specified as a positive number.

% Generate gaussian filter
img = double(img);
gaussianFilter = fspecial('gaussian', filterSize, sigma);
% cov
imgGaussian = convolutionM(img, gaussianFilter);
imgGaussian = uint8(imgGaussian);

end

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3 laplace算子

3.1 原理

用拉普拉斯算子对图像进行滤波，例如：

h l a p l a c e = [ 0 ,      1 ,     0 1 ,   − 4 ,   1 0 ,     1 ,     0 ] h_{laplace} = \left[

$$\begin{matrix}0,\space\space\space\space1,\space\space\space0\\1,\space-4,\space1\\0,\space\space\space1,\space\space\space0\end{matrix}$$ \right] hlaplace​=⎣⎡​0,    1,   01, −4, 10,   1,   0​⎦⎤​

在Matlab中，$h_{laplace}$可以通过fspecial函数生成：

h = fspecial('laplacian',alpha) returns a 3-by-3 filter approximating the shape of the two-dimensional Laplacian operator, alpha controls the shape of the Laplacian.
Shape of the Laplacian, specified as a scalar in the range [0 1].
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例如：

>> fspecial('laplacian', 0)

ans =

     0     1     0
     1    -4     1
     0     1     0

>> 
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3.2 函数编写

function imgLaplace = laplacefilter(img,alpha)
% img: image
% filterSize: if=5, it means 5*5
% alpha: Shape of the Laplacian, specified as a scalar in the range [0 1].

% Generate laplace filter
img = double(img);
laplaceFilter = fspecial('laplacian', alpha);
% cov
imgLaplace = convolutionM(img, laplaceFilter);
imgLaplace = uint8(imgLaplace);

end

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4 prewitt算子

4.1 原理

用prewitt算子对图像进行滤波，例如：

h x p = [ − 1    0    1 − 1    0    1 − 1    0    1 ] h^{p}_{x} = \left[

$$\begin{matrix}-1\space\space0\space\space1\\-1\space\space 0\space\space 1\\ -1\space\space 0\space\space 1\end{matrix}$$ \right] hxp​=⎣⎡​−1  0  1−1  0  1−1  0  1​⎦⎤​ $h_y^p=\left[\begin{array}{c}111\\ 000\\ -1-1-1\end{array}\right]$

在Matlab中，$h_{prewitt}$可以通过fspecial函数生成：

h = fspecial('prewitt') returns a 3-by-3 filter that emphasizes horizontal edges by approximating a vertical gradient. To emphasize vertical edges, transpose the filter h'.
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例如：

>> h = fspecial('prewitt')

h =

     1     1     1
     0     0     0
    -1    -1    -1

>> h = fspecial('prewitt')' % 转置

h =

     1     0    -1
     1     0    -1
     1     0    -1

>> 
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4.2 函数编写

function imgPrewitt = prewittfilter(img)
% img: image

% Generate prewitt filter
img = double(img);
prewittFilter = fspecial('prewitt');
% cov
imgPrewitt = convolutionM(img, prewittFilter);
imgPrewitt = uint8(imgPrewitt);

end

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5 sobel算子

5.1 原理

用sobel算子对图像进行滤波，例如：

h x s = [ − 1    0    1 − 2    0    2 − 1    0    1 ] h^{s}_{x} = \left[

$$\begin{matrix}-1\space\space0\space\space1\\-2\space\space 0\space\space 2\\ -1\space\space 0\space\space 1\end{matrix}$$ \right] hxs​=⎣⎡​−1  0  1−2  0  2−1  0  1​⎦⎤​ $h_y^s=\left[\begin{array}{c}121\\ 000\\ -1-2-1\end{array}\right]$

在Matlab中，$h_{sobel}$可以通过fspecial函数生成：

h = fspecial('sobel')` returns a 3-by-3 filter that emphasizes horizontal edges using the smoothing effect by approximating a vertical gradient. To emphasize vertical edges, transpose the filter h'.
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例如：

>> h = fspecial('sobel')

h =

     1     2     1
     0     0     0
    -1    -2    -1

>> h = fspecial('sobel')' % 转置

h =

     1     0    -1
     2     0    -2
     1     0    -1

>> 
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5.2 函数编写

function imgSobel = sobelfilter(img)
% img: image

% Generate sobel filter
img = double(img);
sobelFilter = fspecial('sobel');
% cov
imgSobel = convolutionM(img, sobelFilter);
imgSobel = uint8(imgSobel);

end

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6 滤波卷积实现convolutionM函数

首先根据滤波器大小padding图像，再进行滤波：

function result=convolutionM(img, filter)

[~, ~, channel] = size(img);
pad_siz = idivide(size(filter,1), int32(2));

for k = 1:channel
    imgC = img(:, :, k);

    % pad img by 0
    pad_img = zeros(int32(size(imgC))+pad_siz*2);
    pad_img(1+pad_siz:end-pad_siz, 1+pad_siz:end-pad_siz) = imgC;

    % conv2
    out_img = zeros(size(pad_img));
    for i = 1+pad_siz:size(pad_img,1)-pad_siz
        for j = 1+pad_siz:size(pad_img,2)-pad_siz
            out_img(i,j) = sum(sum(filter.*pad_img(i+pad_siz:-1:i-pad_siz, ...
                                                    j+pad_siz:-1:j-pad_siz)));
        end
    end
    % restore original size of img
    result(:, :, k) = out_img(1+pad_siz:end-pad_siz, 1+pad_siz:end-pad_siz);
end

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7 main.m文件

调用其他函数文件的主文件为：

% imgOrg = rgb2gray(imread("peppers.png"));
imgOrg = imread("peppers.png");
subplot(2,3,1);
imshow(imgOrg);
title("Originall img");

% mean filter
imgMean = meanfilter(imgOrg, 3); % Generally, the size of a filter is an odd num
subplot(2,3,2);
imshow(imgMean);
title("Mean filter img");

% gaussian filter
imgGaussian = gaussianfilter(imgOrg, 3, 1);
subplot(2,3,3);
imshow(imgGaussian);
title("Gaussian filter img");

% laplace filter
imgSobel = laplacefilter(imgOrg, 0.2);
subplot(2,3,4);
imshow(imgSobel);
title("Laplace filter img");

% prewitt filter
imgSobel = prewittfilter(imgOrg);
subplot(2,3,5);
imshow(imgSobel);
title("Prewitt filter img");

% sobel filter
imgSobel = sobelfilter(imgOrg);
subplot(2,3,6);
imshow(imgSobel);
title("Sobel filter img");

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8 效果展示

9 源码下载

源码下载地址：点击此处