初探FFT在数字图像处理中的应用

一般FFT在通信等领域都做的一维变换就可以了，但是在图像处理方面，需要做二维变换，这个时候就需要用到FFT2.

在利用Octave(或者matlab)里面的fft2()函数的时候，观察频率领域的图像还是要点额外的技巧的.下面的图像是我们想要的，也是我们人类才可以理解的(图片的中心表示低频区域，越是远离中心，频率越高，这里下面图片中，中心区域很亮，value很高，中心周围越来越暗，表示低频信号强，高频信号慢慢减弱)

>> result = fft2(dark_channel);

>> imshow(uint8(real(result)));

直接输出fft2的结果如下(正常人应该看不出什么吧~)

怎么得到之前我们给出的结果呢？

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% code writer 	:	EOF
% code date	    :	2014.09.27
% code file	    :	fft2_demo.m
% e-mail	      :	[email protected]
%
%	If there is something wrong with my code, please
% touch me by e-mail. Thank you :)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all
clc

Original_img = imread('/home/jasonleaster/Picture/hand.png');

float_Orignal_img = double(Original_img);

F64_WHITE = 255.0;
F64_BLACK = 0.000;

Original_img_row 	= size(Original_img,1);
Original_img_col 	= size(Original_img,2);
Original_img_channel 	= size(Original_img,3);

for row = 1:Original_img_row

	for col = 1:Original_img_col

		min_piexl = F64_WHITE;
		for channel = 1: Original_img_channel 

			if(min_piexl > Original_img(row,col,channel))

				min_piexl = Original_img(row,col,channel);
			end
		end

		dark_channel(row,col) = min_piexl;
	end
end

result = fft2(dark_channel);

%spectrum = fftshift(abs(result));
spectrum = result;
figure(1);

spectrum = spectrum*255/max(spectrum(:));

imshow(spectrum);

这里一定记得fftshift，不然会出现下面的结果，低频结果分散在四个角落

正确结果如下