数字图像处理实验（7）：PROJECT 04-03 ， Lowpass Filtering

实验要求：

Objective:
To observe how the lowpass filtering smoothes an image.
Main requirements:
Ability of programming with C, C++, or Matlab.
Instruction manual:
(a) Implement the Gaussian lowpass filter in Eq. (4.3-7). You must be able to specify the size, M x N, of the resulting 2D function. In addition, you must be able to specify where the 2D location of the center of the Gaussian function.
(b) Download Fig. 4.11(a) [this image is the same as Fig. 4.18(a)] and lowpass filter it to obtain Fig. 4.18(c).

实验要求我们通过在频域的高斯低通滤波器对图像进行低通滤波。
频域滤波的处理可以参考前面的实验04-01实现。（点我打开链接）

实验代码：

% PROJECT 04-03 Lowpass Filteringclose all;clc;clear all;%img = imread('Fig4.11(a).jpg');img = mat2gray(img);figure;subplot(1,3,1);imshow(img);title('原图像');% 产生滤波函数[M, N] = size(img);P = 2 * M;Q = 2 * N;alf = 100;H = zeros(P, Q);for i = 1:P    for j = 1:Q        H(i, j) = exp(-((i-P/2)^2 + (j-Q/2)^2) / (2 * alf^2));    endend% H = ones(P, Q);subplot(1,3,2);imshow(H);title('滤波函数');% % 图像填充[M, N] = size(img);P = 2 * M;Q = 2 * N;img_fp = zeros(P, Q);img_fp(1:M, 1:N) = img(1:M, 1:N);% [X, Y] = meshgrid(1:P, 1:Q);% ones = (-1)^(X+Y);% img_f = ones .* img_fp;img_f = zeros(P, Q);for x = 1:P    for y = 1:Q        img_f(x, y) = img_fp(x, y) .* (-1)^(x+y);    endendimg_F = fft2(img_f);img_G = img_F .* H;img_g = real(ifft2(img_G));% img_g = ones .* img_g;for x = 1:P    for y = 1:Q        img_g(x, y) = img_g(x, y) .* (-1)^(x+y);    endendimg_o = img_g(1:M, 1:N);subplot(1,3,3);imshow(img_o, []);title('高斯低通滤波后的图像');

其中套用公式产生高斯滤波函数的代码如下：

[M, N] = size(img);P = 2 * M;Q = 2 * N;alf = 100;H = zeros(P, Q);for i = 1:P    for j = 1:Q        H(i, j) = exp(-((i-P/2)^2 + (j-Q/2)^2) / (2 * alf^2));    endend

其余部分就是频率域滤波的流程，不做赘述。

实验结果：

说明：
第一幅图是原始图像；
第二幅是高斯低通滤波器；
第三幅是低通滤波处理后的结果，其较原始图像明显变得更模糊。