傅里叶变换分离高频低频信息

傅里叶变换高通滤波与低通滤波例子

    img = cv2.imread(r'C:\Users\root\Desktop\1.jpg') #读取图像
    plt.imshow(img, cmap=plt.cm.gray)  #展示图像
    plt.axis('off') #显示时不显示坐标轴
    plt.show() #展示原图

    img = img.mean(axis=-1) #把RGB分量均分叠加到一个通道
    #plt.imsave('gray_raccoon.jpg', np.dstack((img.astype(np.uint8), img.astype(np.uint8), img.astype(np.uint8))))
    img = np.fft.fft2(img)#对图像进行傅里叶变换
    img = np.fft.fftshift(img)#将低频区域移向中心
    fourier = np.abs(img)#取频谱图幅度
    magnitude_spectrum = np.log(fourier)#对幅度取对数，映射到0-255之间方便作图


    plt.imshow(magnitude_spectrum.astype(np.uint8), cmap=plt.cm.gray)#展示频谱图
    plt.axis('off')
    plt.show()  # image after fourier transform
    #plt.imsave('fourier_raccoon.jpg', 14*np.dstack((magnitude_spectrum.astype(np.uint8),magnitude_spectrum.astype(np.uint8),magnitude_spectrum.astype(np.uint8))))

    x,y = img.shape #提取图像尺寸
    lowF = np.zeros((x, y)) #进行低通滤波
    lowF = lowF.astype(np.complex128) #将图像矩阵转复数
    window_shape = (10, 10) #滤波空间大小设置
    lowF[int(x / 2) - window_shape[0]:int(x / 2) + window_shape[0],int(y / 2) - window_shape[1]:int(y / 2) + window_shape[1]] = \
        img[int(x / 2) - window_shape[0]:int(x / 2) + window_shape[0],int(y / 2) - window_shape[1]:int(y / 2) + window_shape[1]] #保留原图低频区域
    lowF_im = np.fft.ifft2(lowF) #傅里叶反变换
    lowF_im = np.abs(lowF_im) #取幅度大小
    lowF_im[lowF_im > 255] = 255 #截断大于255的像素点
    plt.imshow(lowF_im.astype(np.uint8), cmap='gray') #展示图像
    plt.axis('off')
    plt.show()
    #plt.imsave('LowF_raccoon.jpg', np.dstack((lowF_im.astype(np.uint8), lowF_im.astype(np.uint8), lowF_im.astype(np.uint8))))

    highF = np.zeros((x, y)) #进行高通滤波
    highF = highF.astype(np.complex128)
    window_shape = (10, 10) #高通滤波空间大小
    highF[0:window_shape[0], :] = img[0:window_shape[0], :] #保留原图高频区域
    highF[x - window_shape[0]:x, :] = img[x - window_shape[0]:x, :] #保留原图高频区域
    highF[:, 0:window_shape[1]] = img[:, 0:window_shape[1]]#保留原图高频区域
    highF[:, y - window_shape[1]:y] = img[:, y - window_shape[1]:y]#保留原图高频区域
    highF_im = np.fft.ifft2(highF)#傅里叶反变换
    highF_im = np.abs(highF_im)
    highF_im[highF_im > 255] = 255
    plt.imshow(highF_im.astype(np.uint8), cmap='gray')
    plt.axis('off')
    plt.show()