图像处理 之 二维快速傅里叶变换（FFT2）

 # -*- coding: utf-8 -*-

    
 """
    
 Created on Sun Jul  8 21:05:51 2018
    
   5. @author: Diko
    
 """
    
  
    
 import numpy
    
  
    
  
    
 def FFT_v1(Img,Wr):
    
     if Img.shape[0]==2:
    
     pic = numpy.zeros([2],dtype=complex)
    
     pic = pic*(1+0j)
    
     pic[0]=Img[0]+Img[1]*Wr[0]
    
     pic[1]=Img[0]-Img[1]*Wr[0]
    
     return pic
    
     else:
    
     pic = numpy.empty([Img.shape[0]],dtype=complex)
    
     pic[0:Img.shape[0]//2] = FFT_v1(Img[::2],Wr[::2])+Wr*FFT_v1(Img[1::2],Wr[::2])
    
     pic[Img.shape[0]//2:Img.shape[0]]=FFT_v1(Img[::2],Wr[::2])-Wr*FFT_v1(Img[1::2],Wr[::2])
    
     return pic;
    
  
    
  
    
 def FFT_1d(Img):
    
     Wr = numpy.ones([Img.shape[0]//2])*[numpy.cos(2*numpy.pi*i/Img.shape[0])-1j*numpy.sin(2*numpy.pi*i/Img.shape[0]) for i in numpy.arange(Img.shape[0]/2)]
    
     return FFT_v1(Img,Wr)
    
  
    
  
    
 def FFT_2d(Img):
    
     pic = numpy.zeros([Img.shape[0],Img.shape[1]],dtype=complex)
    
     for i in numpy.arange(Img.shape[0]):
    
     pic[:,i]=FFT_1d(Img[:,i])
    
     for i in numpy.arange(Img.shape[1]):
    
     pic[i,:]=FFT_1d(pic[i,:])
    
     return pic
    
  
    
  
    
 import time
    
 from skimage import io,data
    
 if __name__ == "__main__":
    
     array = numpy.zeros([512],dtype=complex)
    
     array[0],array[1],array[2],array[3],array[4],array[5],array[6],array[7],array[8]=1,5,3,2,5,6,1,6,3
    
     
    
     img = data.camera()
    
     
    
     print("numpy.fft.fft2()函数计算结果：")
    
     t_s1=time.time()
    
     print(numpy.fft.fft2(img[:16,0:16]))
    
     t_e1=time.time()
    
     print("计算时间："+str(t_e1-t_s1))
    
     
    
     print("FFT_2d()函数的计算结果：")
    
     t_s2 = time.time()
    
     print(FFT_2d(img[:16,0:16]))
    
     t_e2 =time.time()
    
     print("计算时间："+str(t_e2-t_s2))
    
    # io.imshow(numpy.log(numpy.real(numpy.fft.fft2(img))))
    
     #io.imshow(numpy.real(FFT_2d(img[0:256,0:256])))
    
     #img = data.camera()
    
     #print(numpy.fft.fft2(img))
    
     #io.imshow(FFT_2d(img))