數字圖像處理之頻域圖像增強

數字圖像處理之頻域圖像增強

                                                        by方陽

版權聲明：本文為博主原創文章，轉載請指明轉載地址

http://www.cnblogs.com/fydeblog/p/7069942.html 

1. 前言

 

這篇博客主要講解頻域濾波增強的各類濾波器的實現，並分析不同的濾波器截止頻率對頻域濾波增強效果的影響。理論的知識還請看書和百度，這里不再復述！

 

2. 原理說明

 

（1）  圖像的增強可以通過頻域濾波來實現，頻域低通濾波器濾除高頻噪聲，頻域高通濾波器濾除低頻噪聲。

 

（2）  相同類型的濾波器的截止頻率不同，對圖像的濾除效果也會不同。

 

3. 實現內容

 

（1）     選擇任意一副圖像，對其進行傅里葉變換，在頻率域中實現二階butterworth低通濾波器的平滑作用，截止頻率任意設定。顯示原始圖像和濾波圖像。

（2）     選擇任意一副圖像，對其進行傅里葉變換，在頻率域中實現兩種不同半徑（截止頻率）的高斯高通濾波的銳化效果，顯示原始圖像和濾波圖像，及與原圖像疊加的高頻增強圖像。

 

4. 程序實現及實驗結果

 

（1）butterworth濾波器

參考代碼：

I=imread('fig620.jpg');
f=D3_To_D2(I);
PQ=paddedsize(size(f));
[U,V]=dftuv(PQ(1),PQ(2));
D0=0.05*PQ(2);
F=fft2(f,PQ(1),PQ(2));
H=1./(1+((U.^2+V.^2)/(D0^2)).^2);
g=dftfilt(f,H);
figure;
subplot(1,3,1);
imshow(f);
title('原圖');
subplot(1,3,2);
imshow(fftshift(H),[]);
title('濾波器頻譜');
subplot(1,3,3);
imshow(g,[]);
title('濾波后的圖像');

 

 D3_To_D2函數參考代碼：

 

function image_out=D3_To_D2(image_in)
[m,n]=size(image_in);
 n=n/3;%由於我的灰度圖像是185x194x3的，所以除了3，你們如果是PxQ的，就不要加了
 A=zeros(m,n);%構造矩陣
 for i=1:m
     for j=1:n
        A(i,j)= image_in(i,j);%填充圖像到A
     end
 end
image_out=uint8(A);

 

paddedsize函數參考代碼：

 

function PQ = paddedsize(AB,CD,~ )  
%PADDEDSIZE Computes padded sizes useful for FFT-based filtering.  
%   Detailed explanation goes here  
if nargin == 1  
    PQ = 2*AB;  
elseif nargin ==2 && ~ischar(CD)  
    PQ = QB +CD -1;  
    PQ = 2*ceil(PQ/2);  
elseif nargin == 2  
    m = max(AB);%maximum dimension  
      
    %Find power-of-2 at least twice m.  
    P = 2^nextpow(2*m);  
    PQ = [P,P];  
elseif nargin == 3  
    m = max([AB CD]);%maximum dimension  
    P = 2^nextpow(2*m);  
    PQ = [P,P];  
else   
    error('Wrong number of inputs');  
  
end  

 

dftuv函數參考代碼：

 

function [ U,V ] = dftuv( M, N )  
%DFTUV 實現頻域濾波器的網格函數  
%   Detailed explanation goes here  
u = 0:(M - 1);  
v = 0:(N - 1);  
idx = find(u > M/2); %找大於M/2的數據  
u(idx) = u(idx) - M; %將大於M/2的數據減去M  
idy = find(v > N/2);  
v(idy) = v(idy) - N;  
[V, U] = meshgrid(v, u);        
  
end  

 

運行結果

 

（2）高通濾波器

參考代碼：

I1=imread('lena.bmp');
f1=D3_To_D2(I1);
PQ1=paddedsize(size(f1));
D0_1=0.05*PQ(1);
D0_2=0.1*PQ(1);
H1=hpfilter('gaussian',PQ1(1),PQ1(2),D0_1);
H2=hpfilter('gaussian',PQ1(1),PQ1(2),D0_2);
g1=dftfilt(f1,H1);
g2=dftfilt(f1,H2);
H1=0.5+2*H1;
H2=0.5+2*H2;
g3=dftfilt(f1,H1);
g4=dftfilt(f1,H2);
g3=histeq(gscale(g3),256);
g4=histeq(gscale(g4),256);
figure;
subplot(2,3,1);
imshow(f1);
title('原圖');
subplot(2,3,2);
imshow(g1,[]);
title('濾波后的圖像-系數0.05');
subplot(2,3,3);
imshow(g2,[]);
title('濾波后的圖像-系數0.1');
subplot(2,3,4);
imshow(g3,[]);
title('增強后的圖像-系數0.05');
subplot(2,3,5);
imshow(g4,[]);
title('增強后的圖像-系數0.1');

 

hpfilter函數參考代碼：

 

function H = hpfilter(type, M, N, D0, n)
if nargin == 4
    n = 1;
end
hlp = lpfilter(type, M, N, D0, n);
H = 1 - hlp;

 

hpfilter中的lpfilter參考代碼：

 

function [ H, D ] = lpfilter( type,M,N,D0,n )  
%LPFILTER creates the transfer function of a lowpass filter.  
%   Detailed explanation goes here  
  
%use function dftuv to set up the meshgrid arrays needed for computing   
%the required distances.  
[U, V] = dftuv(M,N);  
   
%compute the distances D(U,V)  
D = sqrt(U.^2 + V.^2);  
  
%begin filter computations  
switch type  
    case 'ideal'  
        H = double(D <= D0);  
    case 'btw'  
        if nargin == 4  
            n = 1;  
        end  
        H = 1./(1+(D./D0).^(2*n));  
    case 'gaussian'  
        H = exp(-(D.^2)./(2*(D0^2)));  
    otherwise   
        error('Unkown filter type');  
  
end  

 

gscale函數參考代碼：

 

function g = gscale(f, varargin)
%GSCALE Scales the intensity of the input image.
%   G = GSCALE(F, 'full8') scales the intensities of F to the full
%   8-bit intensity range [0, 255].  This is the default if there is
%   only one input argument.
%
%   G = GSCALE(F, 'full16') scales the intensities of F to the full
%   16-bit intensity range [0, 65535].
%
%   G = GSCALE(F, 'minmax', LOW, HIGH) scales the intensities of F to
%   the range [LOW, HIGH]. These values must be provided, and they
%   must be in the range [0, 1], independently of the class of the
%   input. GSCALE performs any necessary scaling. If the input is of
%   class double, and its values are not in the range [0, 1], then
%   GSCALE scales it to this range before processing.
%
%   The class of the output is the same as the class of the input.
 
%   Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins
%   Digital Image Processing Using MATLAB, Prentice-Hall, 2004
%   $Revision: 1.5 $  $Date: 2003/11/21 14:36:09 $
 
if length(varargin) == 0 % If only one argument it must be f.
   method = 'full8';
else
   method = varargin{1};
end
 
if strcmp(class(f), 'double') & (max(f(:)) > 1 | min(f(:)) < 0)
   f = mat2gray(f);
end
 
% Perform the specified scaling.
switch method
case 'full8'
   g = im2uint8(mat2gray(double(f)));
case 'full16'
   g = im2uint16(mat2gray(double(f)));
case 'minmax'
   low = varargin{2}; high = varargin{3};
   if low > 1 | low < 0 | high > 1 | high < 0
      error('Parameters low and high must be in the range [0, 1].')
   end
   if strcmp(class(f), 'double')
      low_in = min(f(:));
      high_in = max(f(:));
   elseif strcmp(class(f), 'uint8')
      low_in = double(min(f(:)))./255;
      high_in = double(max(f(:)))./255;
   elseif strcmp(class(f), 'uint16')
      low_in = double(min(f(:)))./65535;
      high_in = double(max(f(:)))./65535;   
   end
   % imadjust automatically matches the class of the input.
   g = imadjust(f, [low_in high_in], [low high]);  
otherwise
   error('Unknown method.')
end

 

運行結果：

五．結果分析

（1）由第一個圖可以看出，圖像經過低通濾波器，圖像的高頻分量濾掉了，圖像變得平滑。

（2）由第二個圖可以看出，圖像不同的截止頻率，出來的圖像也不同，系數小的效果強。