数字图像处理实验（6）：PROJECT 04-02，Fourier Spectrum and Average Value

实验要求：

Objective:
To observe the Fourier spectrum by FFT and the average value of an image.
Main requirements:
Ability of programming with C, C++, or Matlab.
Instruction manual:
(a) Download Fig. 4.18(a) and compute its (centered) Fourier spectrum.
(b) Display the spectrum.
(c) Use your result in (a) to compute the average value of the image.

实验中我们要观察图像进行FFT后的傅里叶频谱图，并且输出其均值。

代码：

%%
close all;
clc;
clear all;

%%
img = imread('gray_image.jpg');
imshow(img);
title('original image');

% 计算傅里叶变换
img_F = fft2(img);

[M, N] = size(img);
s = sum(abs(img_F(1:M, 1:N)));  % 行求和
s = sum(s);     % 列求和
ave = s / (M * N);
disp(['average value of image is: ',num2str(ave)]);

S = log(1 + abs(img_F));
% figure;
% plot(S);
% title('二维图像显示幅度谱');

x = 0:1:255;
y = 0:1:255;
[x, y] = meshgrid(x, y);
figure;
mesh(S);
title('三维图像显示幅度谱');

img_Q = angle(img_F);
% figure;
% plot(img_Q);
% title('二维图像显示相位谱');

x = 0:1:255;
y = 0:1:255;
[x, y] = meshgrid(x, y);
figure;
mesh(img_Q);
title('三维图像显示相位谱');

实验结果：

上图是原始图像。

上图是FFT之后3维幅度谱。

上图是FFT之后3维幅度谱。

均值。