傅立葉變換

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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')

低頻位於頻率變換影像的中心。 這些示例的變換影像顯示實心影像具有大多數低頻分量（如中心亮點所示）。 條紋轉換影像包含白色和黑色區域的低頻以及這些顏色之間的邊緣的高頻。 條紋變換影像也告訴我們這些頻率有一個主導方向; 垂直條紋由穿過頻率變換影像中心的水平線表示

# 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')

此影像包含所有頻率的分量。 你可以在變換影像的中心看到一個亮點，它告訴我們影像的很大一部分是低頻的; 這是有道理的，因為鳥類和背景的身體是純色。 變換影像還告訴我們這些頻率有兩個主導方向; 垂直邊緣（來自鳥的邊緣）由穿過頻率變換影像中心的水平線表示，水平邊緣（來自鳥頭的分支和頂部）由穿過中心的垂直線表示。