傅里叶变换

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import numpy as np
import matplotlib.pyplot as plt
import cv2

%matplotlib inline

# Read in the images
image_stripes = cv2.imread('images/stripes.jpg')
# Change color to RGB (from BGR)
image_stripes = cv2.cvtColor(image_stripes, cv2.COLOR_BGR2RGB)

# Read in the images
image_solid = cv2.imread('images/pink_solid.jpg')
# Change color to RGB (from BGR)
image_solid = cv2.cvtColor(image_solid, cv2.COLOR_BGR2RGB)


# Display the images
f, (ax1,ax2) = plt.subplots(1, 2, figsize=(10,5))

ax1.imshow(image_stripes)
ax2.imshow(image_solid)

# convert to grayscale to focus on the intensity patterns in the image
gray_stripes = cv2.cvtColor(image_stripes, cv2.COLOR_RGB2GRAY)
gray_solid = cv2.cvtColor(image_solid, cv2.COLOR_RGB2GRAY)

# normalize the image color values from a range of [0,255] to [0,1] for further processing
norm_stripes = gray_stripes/255.0
norm_solid = gray_solid/255.0

# perform a fast fourier transform and create a scaled, frequency transform image
def ft_image(norm_image):
    '''This function takes in a normalized, grayscale image
       and returns a frequency spectrum transform of that image. '''
    f = np.fft.fft2(norm_image)
    fshift = np.fft.fftshift(f)
    frequency_tx = 20*np.log(np.abs(fshift))
    
    return frequency_tx
# Call the function on the normalized images
# and display the transforms
f_stripes = ft_image(norm_stripes)
f_solid = ft_image(norm_solid)

# display the images
# original images to the left of their frequency transform
f, (ax1,ax2,ax3,ax4) = plt.subplots(1, 4, figsize=(20,10))

ax1.set_title('original image')
ax1.imshow(image_stripes)
ax2.set_title('frequency transform image')
ax2.imshow(f_stripes, cmap='gray')

ax3.set_title('original image')
ax3.imshow(image_solid)
ax4.set_title('frequency transform image')
ax4.imshow(f_solid, cmap='gray')

低频位于频率变换图像的中心。 这些示例的变换图像显示实心图像具有大多数低频分量（如中心亮点所示）。 条纹转换图像包含白色和黑色区域的低频以及这些颜色之间的边缘的高频。 条纹变换图像也告诉我们这些频率有一个主导方向; 垂直条纹由穿过频率变换图像中心的水平线表示

# Read in an image
image = cv2.imread('images/birds.jpg')
# Change color to RGB (from BGR)
image = cv2.cvtColor(image, cv2.COLOR_BGR2RGB)

# convert to grayscale
gray = cv2.cvtColor(image, cv2.COLOR_RGB2GRAY)
# normalize the image
norm_image = gray/255.0

f_image = ft_image(norm_image)

# Display the images
f, (ax1,ax2) = plt.subplots(1, 2, figsize=(20,10))

ax1.imshow(image)
ax2.imshow(f_image, cmap='gray')

此图像包含所有频率的分量。 你可以在变换图像的中心看到一个亮点，它告诉我们图像的很大一部分是低频的; 这是有道理的，因为鸟类和背景的身体是纯色。 变换图像还告诉我们这些频率有两个主导方向; 垂直边缘（来自鸟的边缘）由穿过频率变换图像中心的水平线表示，水平边缘（来自鸟头的分支和顶部）由穿过中心的垂直线表示。