【图像处理】MATLAB：频域高低通滤波器

建立网格数组

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);

低通频域滤波器

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)');

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 type
case '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

高通频域滤波器

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;

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');

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');

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');