文章和代码以及样例图片等相关资源,已经归档至【Github仓库:digital-image-processing-matlab】或者公众号【AIShareLab】回复 数字图像处理 也可获取。

目的

  1. 了解 MATLAB 工具箱中的滤波器。
  2. 掌握空间滤波
  3. 学会对图像的空间变换

内容

A. 用滤波器祛除图象噪声

在数字图像处理中,常常会遇到图像中混杂有许多的噪声。因此,在进行图像处理中,有时要先进行祛除噪声的工作。最常用的祛除噪声的方法是用滤波器进行滤波处理。MATLAB 的图像处理工具箱里也设计了许多的滤波器。如均值滤波器、中值滤波器、维纳滤波器等。

(分别用均值滤波,中值滤波,及维纳滤波器祛除加入高斯噪声的图象)

I=imread('D:\pic\DIP3E_CH04\FigP0438(left).tif ');
J=imnoise(I,'gaussian',0,0.002);
%进行均值滤波
h=fspecial('average',3);
I2=uint8(round(filter2(h,I)));
%进行中值滤波
I3=medfilt2(J,[3,3]);
%进行维纳滤波
I4=wiener2(J,[3,3]); %进行一次维纳滤波
I5=wiener2(I4,[3,3]);%进行二次维纳滤波
subplot(2,3,1),imshow(I),title('原图象')
subplot(2,3,2),imshow(J),title('加噪声图象')
subplot(2,3,3),imshow(I2),title('均值滤波后图象')
subplot(2,3,4),imshow(I3),title('中值滤波后图象')
subplot(2,3,5),imshow(I4),title('维纳滤波后图象')
subplot(2,3,6),imshow(I5),title('两次维纳滤波后图象')

B. 空间噪声滤波器

%用函数imnoise2 生成具有表5.1 中的CDF 的随机数
function R=imnoise2(type,M,N,a,b)
if nargin ==1
    a=0;b=1;
    M=1;N=1;
elseif nargin ==3
    a=0;b=1;
end
switch lower(type)
    case 'uniform'
        R=a+(b-a)*rand(M,N);
    case 'gaussian'
        R=a+b*randn(M,N);
    case 'salt & pepper'
        if nargin <=3
            a=0.05;b=0.05;
        end
        if (a+b)>1;
            error('The sum Pa+Pb must not exceed 1.')
        end
        R(1:M, 1:N) = 0.5;
        X=rand(M,N);
        c=find(X<=a);
        R(c)=0;
        u=a+b;
        c=find(X>a & X<=u);
        R(c)=1;
    case 'rayleigh'
        R=a+(-b*log(1-rand(M,N))).^0.5;
    case 'exponential'
        if nargin <=3;
            a=1;
        end
        if a<=0
            error('Parameter a must be positive for exponential type.')
        end
        k=-1/a;
        R=k*log(1-rand(M,N));
    case 'erlang'
        if nargin<=3
            a=2;b=5;
        end
        if (b~=round(b)|b<=0)
            error('Parameter b must be a positive integer for Erlang')
        end
        k=-1/a;
        R=zeros(M,N);
        for j=1:b
            R=R+k*log(1-rand(M,N));
        end
    otherwise
        error('unknown distribution type.')
end

function image=changeclass(class,varargin)
switch class
    case 'uint8'
        image=im2uint8(varargin{:});
    case 'uint16'
        image=im2uint16(varargin{:});
    case 'double'
        image=im2double(varargin{:});
    otherwise
        error('Unsupported IPT data class.');
end
%%%%% spfilt 函数与表中列出的任何滤波器在空间域执行滤波。
function f = spfilt(g,type,m,n,parameter)
if nargin ==2
    m=3;n=3;Q=1.5;d=2;
elseif nargin == 5
    Q=parameter;d=parameter;
elseif nargin== 4
    Q=1.5; d=2;
else
    error ('wrong number of inputs');
end
switch type
    case 'amean'
    w=fspecial('average',[m,n]);
    f=imfilter(g,w, 'replicate');
    case 'gmean'
    f=gmean(g,m,n);
    case 'hmean'
    f=harmean(g,m,n);
    case 'chmean'
    %f=charmean(g,m,n,Q);
    f=charmean(g,m,n,Q);
    case 'median'
    f=medfilt2(g,[m n], 'symmetric');
    case 'max'
    f=ordfilt2(g,m*n,ones(m,n),'symmetric');
    case 'min'
    f=ordfilt2(g,1,ones(m,n), 'symmetric');
    case 'midpoint'
    f1=ordfilt2(g,1,ones(m,n), 'symmetric');
    f2=ordfilt2(g,m*n,ones(m,n), 'symmetric');
    f=imlincomb(0.5,f1,0.5,f2);
    case 'atrimmed'
    if(d<0)|(d/2~=round(d/2))
        error('d must be a nonnegative, even integer.')
    end
    f=alphatrim(g,m,n,d);
    otherwise
        error('Unknown filter type.')
end


function f=gmean(g,m,n)
inclass =class (g);
g=im2double(g);
warning off;
f=exp(imfilter(log(g),ones(m,n),'replicate')).^(1/m/n);
warning on;
f=changeclass(inclass, f);


function f=harmean(g,m,n)
inclass=class(g);
g=im2double(g);
f=m*n./imfilter(1./(g+eps),ones(m,n),'replicate');
f=changeclass(inclass,f);

function f=charmean(g,m,n,q)
inclass=class(g);
g=im2double(g);
f= imfilter(g.^(q+1),ones(m,n),'replicate');
f=f./ (imfilter(g.^q,ones(m,n),'replicate')+eps);
f=changeclass(inclass,f);

function f=alphatrim(g,m,n,d)
inclass = class(g);
g=im2double(g);
f=imfilter(g,ones(m,n),'symmetric');
for k=1:d/2
    f=imsubtract(f,ordfilt2(g,k,ones(m,n),'symmetric'));
end
for k=(m*n – (d/2)+1):m*n
    f=imsubtract(f,ordfilt2(g,k,ones(m,n),'symmetric'));
end
f=f/(m*n-d);
f=changeclass(inclass,f);

%使用函数spfilt
clear all
clc
f=imread('D:\pic\DIP3E_CH04\FigP0438(left).tif');
[M,N]=size(f);
R=imnoise2('salt & pepper',M,N,0.1,0);%被概率只有0.1 的胡椒噪声污染
c=find(R==0);
gp=f;
gp(c)=0;
figure, imshow(gp);

R=imnoise2('salt & pepper',M,N,0,0.1);
c=find(R==1);
gs=f;
gs(c)=255;
figure,imshow(gs)

fp=spfilt(gp,'chmean',3,3,1.5);%使用Q 为正值的反调和滤波器
figure, imshow(gp);
fs=spfilt(gs,'chmean',3,3,-1.5);
figure, imshow(gs);

fpmax=spfilt(gp,'max',3,3); %使用最大最小滤波器
figure, imshow(gp);
fsmin=spfilt(gs,'min',3,3);
figure, imshow(gs);

C.用滤波器祛除图象噪声

%产生一个等角变换用于测试图像
f=checkerboard(50);
s=0.8;
theta=pi/6;
T=[s*cos(theta) s*sin(theta) 0; -s*sin(theta) s*cos(theta) 0; 0 0 1];
tform=maketform('affine',T);
g=imtransform(f,tform);
figure, imshow(g);

g2=imtransform(f,tform,'nearest');
figure, imshow(g2);

g3=imtransform(f,tform,'FillValue',0.5);
figure, imshow(g3);

T2=[1 0 0;0 1 0; 50 50 1];
tform2=maketform('affine',T2);
g4=imtransform(f,tform2);
figure, imshow(g4);

g5=imtransform(f,tform2,'XData',[1 400],'YData',[1
400],'FillValue',0.5);
figure, imshow(g5);

参考文献:

[1] Rafael C. Gonzalez, Richard E. Woods, and Steven L. Eddins. 2003. Digital Image Processing Using MATLAB. Prentice-Hall, Inc., USA.

[2] 阮秋琦. 数字图像处理(MATLAB版)[M]. 北京:电子工业出版社, 2014..pdf)

[3] 冈萨雷斯. 数字图像处理(第三版)[M]. 北京:电子工业出版社, 2011..pdf)


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