python类ifft2()的实例源码

def correlate(self, imgfft):
        #Very much related to the convolution theorem, the cross-correlation
        #theorem states that the Fourier transform of the cross-correlation of
        #two functions is equal to the product of the individual Fourier
        #transforms, where one of them has been complex conjugated:  


        if self.imgfft is not 0 or imgfft.imgfft is not 0:
            imgcj = np.conjugate(self.imgfft)
            imgft = imgfft.imgfft

            prod = deepcopy(imgcj)
            for x in range(imgcj.shape[0]):
                for y in range(imgcj.shape[0]):
                    prod[x][y] = imgcj[x][y] * imgft[x][y]

            cc = Corr( np.real(fft.ifft2(fft.fftshift(prod)))) # real image of the correlation

            # adjust to center
            cc.data = np.roll(cc.data, int(cc.data.shape[0] / 2), axis = 0)
            cc.data = np.roll(cc.data, int(cc.data.shape[1] / 2), axis = 1)
        else:
            raise FFTnotInit()
        return cc

def ift(self):
      return MyImage(np.real(fft.ifft2(fft.fftshift(self.ft))))

def ift(self):
        self.imgifft = MyImage(np.real(fft.ifft2(fft.fftshift(self.imgfft))))

def cross_corr(img1,img2,mask=None):
    '''Compute the autocorrelation of two images.
        Right now does not take mask into account.
        todo: take mask into account (requires extra calculations)
        input: 
            img1: first image
            img2: second image
            mask: a mask array
        output:
            the autocorrelation of the two images (same shape as the correlated images)

    '''
    #if(mask is not None):
    #   img1 *= mask
    #  img2 *= mask

    #img1_mean = np.mean( img1.flat )
    #img2_mean = np.mean( img2.flat )

    # imgc = fftshift( ifft2(     
    #        fft2(img1/img1_mean -1.0 )*np.conj(fft2( img2/img2_mean -1.0 ))).real )

    #imgc = fftshift( ifft2(     
    #        fft2(  img1/img1_mean  )*np.conj(fft2(  img2/img2_mean   ))).real )

    imgc = fftshift( ifft2(     
            fft2(  img1  )*np.conj(fft2(  img2  ))).real )

    #imgc /= (img1.shape[0]*img1.shape[1])**2
    if(mask is not None):
        maskc = cross_corr(mask,mask)        
        imgc /= np.maximum( 1, maskc )


    return imgc

def extractFeatures(self, img):
        "A vector of 2n elements where n is the number of theta angles"
        "and 2 is the number of frequencies under consideration"
        filters =  self.build_filters(img.shape[0],img.shape[1],5,(0.75,1.5),2,1,np.pi/2.0)
        fft_filters = [np.fft.fft2(i) for i in filters]
        img_fft = np.fft.fft2(img)
        a =  img_fft * fft_filters
        s = [np.fft.ifft2(i) for i in a]
        k = [p.real for p in s]
        return k

def fft_convolve2d(self, x,y):
        """ 2D convolution, using FFT"""
        fr = fft2(x)
        fr2 = fft2(np.flipud(np.fliplr(y)))
        m,n = fr.shape
        cc = np.real(ifft2(fr*fr2))
        cc = np.roll(cc, -m/2+1,axis=0)
        cc = np.roll(cc, -n/2+1,axis=1)
        return cc

def xcorr(imageA, imageB):
    FimageA = _fft.fft2(imageA)
    CFimageB = _np.conj(_fft.fft2(imageB))
    return _fft.fftshift(_np.real(_fft.ifft2((FimageA * CFimageB)))) / _np.sqrt(imageA.size)

def ift2(G, dfx, dfy):
    Nx = G.shape[1]
    Ny = G.shape[0]
    return ifftshift(ifft2(ifftshift(G))) * Nx * Ny * dfx * dfy

def plot_crystal2D():

    plt.figure()
    plt.subplot(221)
    plt.imshow(crystal, cmap='gray')
    plt.title('crystal')
    plt.axis('off')

    plt.subplot(223)
    test=crystal_filter2D*crystal_fourier
    plt.imshow(np.log10(abs(test)), cmap='gray')
    plt.title('log10 |FFT2| of crystal')
    plt.axis('off')

    plt.subplot(222)
    plt.imshow(crystal_skewed, cmap='gray')
    plt.xlabel(' x_s')
    plt.ylabel(' y_s')
    plt.title('crystal in skewed coordinates')
    plt.axis('off')

    plt.subplot(224)
    plt.imshow(np.log10(abs(fft_crystal_skewed)), cmap='gray')
    plt.xlabel(' 1/x_s')
    plt.ylabel(' 1/y_s')
    plt.title('log10|FFT| of crystal in skewed coordinates')
    plt.axis('off')

    # plot filtered 2D retrived crystal2D
    plt.figure
    fig,ax = plt.subplots(1)
    plt.imshow(abs((fft.ifft2(fft.ifftshift(test)))))

#plot_crystal2D()


#plt.figure()
#plt.imshow(projectedCrystal)
#plt.title('Orthoganl projection of 3D crystal into x-y-plane')
#plt.xlabel(' x')
#plt.ylabel(' y')
#savefig('test.jpg')
########################plot 3D crystal in all plane cuts