【图像处理】MATLAB：频域高低通滤波器

建立网格数组

  M函数dftuv，提供了距离计算及其他类似应用所需要的网格数组。

function [U, V] = dftuv(M, N)%DFTUV Computes meshgrid frequency matrices.%   [U, V] = DFTUV(M, N) computes meshgrid frequency matrices U and%   V.  U and V are useful for computing frequency-domain filter%   functions that can be used with DFTFILT.  U and V are both%   M-by-N.%   Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins%   Digital Image Processing Using MATLAB, Prentice-Hall, 2004%   $Revision: 1.3 $  $Date: 2003/04/16 22:30:34 $% Set up range of variables.u = 0:(M - 1);v = 0:(N - 1);% Compute the indices for use in meshgrid.idx = find(u > M/2);u(idx) = u(idx) - M;idy = find(v > N/2);v(idy) = v(idy) - N;% Compute the meshgrid arrays.[V, U] = meshgrid(v, u);

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低通频域滤波器

代码示例

f = imread('pattern.tif');PQ = paddedsize(size(f));[U,V] = dftuv(PQ(1),PQ(2));D0 = 0.05*PQ(2);F = fft2(f,PQ(1),PQ(2));H = exp(-(U.^2+V.^2)/(2*(D0^2)));   %低通高斯滤波器g = dftfilt(f,H);subplot(2,2,1);imshow(f);title('原图像');subplot(2,2,2);imshow(fftshift(H),[ ]);title('高斯低通滤波器');subplot(2,2,3);imshow(log(1+abs(fftshift(F))),[ ]);title('原图像的频谱');subplot(2,2,4);imshow(g,[ ]);title('处理后图像(比原图像模糊)');

运行结果

函数lpfilter用于生成低通滤波器的传递函数：

function H = lpfilter(type, M, N, D0, n)%LPFILTER Computes frequency domain lowpass filters.%   H = LPFILTER(TYPE, M, N, D0, n) creates the transfer function of%   a lowpass filter, H, of the specified TYPE and size (M-by-N). To%   view the filter as an image or mesh plot, it should be centered%   using H = fftshift(H). %%   Valid values for TYPE, D0, and n are:%%   'ideal'    Ideal lowpass filter with cutoff frequency D0. n need%              not be supplied.  D0 must be positive.%%   'btw'      Butterworth lowpass filter of order n, and cutoff%              D0.  The default value for n is 1.0.  D0 must be%              positive.%%   'gaussian' Gaussian lowpass filter with cutoff (standard%              deviation) D0.  n need not be supplied.  D0 must be%              positive. %   Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins%   Digital Image Processing Using MATLAB, Prentice-Hall, 2004%   $Revision: 1.8 $  $Date: 2004/11/04 22:33:16 $% 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 typecase 'ideal'                            %理想低通滤波器   H = double(D <= D0);case 'btw'                              %巴特沃兹低通滤波器   if nargin == 4      n = 1;       end   H = 1./(1 + (D./D0).^(2*n));case 'gaussian'                         %高斯低通滤波器   H = exp(-(D.^2)./(2*(D0^2)));otherwise   error('Unknown filter type.')end

绘制低通滤波器的线框图及表面图

% 绘制线框图H = fftshift(lpfilter('gaussian',500,500,50));  % 高斯低通滤波器mesh(H(1:10:500,1:10:500));                     % 绘制线框图axis([0 50 0 50 0 1]);                          % 坐标轴colormap([0 0 0]);                              % 通过彩色绘制网线axis on;                                        % 打开网格，axis off关闭grid on;                                        % 打开坐标轴，grid off关闭view(-25,30);                                   % 查看点（观察者）位置

% 绘制表面图H = fftshift(lpfilter('gaussian',500,500,50));  % 高斯低通滤波器surf(H(1:10:500,1:10:500));                     % 绘制表面图axis([0 50 0 50 0 1]);                          % 坐标轴colormap(gray);                                 % 通过彩色绘制网线axis pff;                                       % 关闭网格grid off;                                       % 关闭坐标轴

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高通频域滤波器

  高通滤波通过削弱傅里叶变换的低频而保持高频相对不变，会使图像变得更加清晰（锐化）。

函数hpfilter用于生成低通滤波器的传递函数：

function H = hpfilter(type, M, N, D0, n)%HPFILTER Computes frequency domain highpass filters.if nargin == 4   n = 1; % Default value of n.end% Generate highpass filter.Hlp = lpfilter(type, M, N, D0, n);H = 1 - Hlp;

代码示例

H = fftshift(hpfilter('ideal',500,500,50));mesh(H(1:10:500,1:10:500));axis([0 50 0 50 0 1]);colormap([0 0 0]);axis off;grid off;title('理想高通滤波器的透视图');figure,imshow(H,[ ]);title('理想高通滤波器相应图像');

运行结果

代码示例

f = imread('pattern.tif');PQ = paddedsize(size(f));D0 = 0.05* PQ(1);H = hpfilter('gaussian',PQ(1),PQ(2),D0);g = dftfilt(f,H);subplot(1,2,1);imshow(f);title('原图像');subplot(1,2,2);imshow(g,[ ]);title('高斯高通滤波后的结果');

运行结果

高频强调滤波

代码示例

PQ = paddedsize(size(f));D0 = 0.05*PQ(1);HBW = hpfilter('btw',PQ(1),PQ(2),D0,2);H = 0.5 + 2 * HBW;gbw = dftfilt(f,HBW);gbw = gscale(gbw);ghf = dftfilt(f,H);ghf = gscale(ghf);ghe = histeq(ghf,256);subplot(2,2,1);imshow(f);title('原图像');subplot(2,2,2);imshow(gbw);title('巴特沃兹高通滤波');subplot(2,2,3);imshow(ghf);title('高频强调滤波');subplot(2,2,4);imshow(ghe);title('高频强调滤波与直方图均衡化结合');

运行结果

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