数字图像处理课件(冈萨雷斯第三版)英文翻译课件.pptVIP

Convolution has the following properties: let F and G be Fourier transforms of f and g, respectively .Then In fact， Convolution via Fourier transform ， fast Fourier transform We derive the fast Fourier transform formula. Lets say N is the power of 2 ， That is N = 2n。Let N = 2M。 。 In the known WN conditions, calculation of each F(?) at least needs N multiplications and one division, calculation of all F(?) is required for multiplication of not less than N2.Rewriting transformation: Easy to see that WN has binary properties: define ? = 0,1,…,M-1 We also need to know the calculation value when ? = M,M+1,…,N-1。 To this end, note that ? = 0,1,…,M-1 Finally, we prove that the time complexity of the FFT algorithm is ?(NlogN)。 Setting a FFT algorithm with N points, the time complexity is T (N). According to the above formula, a FFT operation with N points is divided into two FFT operations with N/2 points, and one of them is to be multiply at a time ， A total of ourselves ?(N) multiplication ，so， T(N) = 2T(N/2) + ?(N)。 You can get it here T(N) = T(2n) = 2T(2n-1) + ?(2n) = 22T(2n-2) + 2?(2n) = …= n?(2n) = ?(NlogN)。 % open an image h=imread(butterfly.jpg); figure; imshow(h); % 因为图像的格式uint8不能做加减法,所以需要把格式uint8变成double. h=double(h); [m,n,p]=size(h); %变成黑白图像 if(p1) bw(:,:)=(h(:,:,1)+h(:,:,2)+h(:,:,3))/3; h=bw/3; end %调整灰度到0到255之间。否则 maxValue=max(max(h)); h1=h*255/maxValue; figure; imshow(uint8(h1)); % 2D Fourier变换和平移频率0到中心, 得到2D复数值图像 hf=fftshift(fft2(h)); % 画出其模的图像。如果直接用imshow(uint8(hf))将得到下面的图象. hfa=log(abs(hf)); maxValue=max(max(hfa)); h2=hfa*255/maxValue; figure; imshow(uint8(h2)); % 低通滤波器（半径平方在1000以内） a=m/2; b=n/2; for i=1:m for j=1:n if((i-a)*(i-a)+(j-b)*(j-b)1000) hf(i,j)=0; end end end hfa=log(abs(hf)); maxValue=max(max(hfa)); h3=hfa*255/maxValue; figure; imshow(uint8(h3)); ih=ifft2(fftshift(hf)); hfa=log(abs(ih)); maxValue=max(max(hfa)); h4=hfa*255/maxValue; figure; imshow(uint8(h4)); h2=h; for i=1:m-1 for j=