Python图像处理:频域滤波降噪和图像增强

 import cv2 import numpy as np from matplotlib import pyplot as plt img = cv2.imread('sample.png',0) # Using 0 to read image in grayscale mode plt.imshow(img, cmap='gray')  #cmap is used to specify imshow that the image is in greyscale plt.xticks([]), plt.yticks([])  # remove tick marks plt.show()

 f = np.fft.fft2(img)  #the image 'img' is passed to np.fft.fft2() to compute its 2D Discrete Fourier transform f mag = 20*np.log(np.abs(f)) plt.imshow(mag, cmap = 'gray') #cmap='gray' parameter to indicate that the image should be displayed in grayscale. plt.title('Magnitude Spectrum') plt.xticks([]), plt.yticks([]) plt.show()

 fshift = np.fft.fftshift(f) mag = 20*np.log(np.abs(fshift)) plt.imshow(mag, cmap = 'gray') plt.title('Centered Spectrum'), plt.xticks([]), plt.yticks([]) plt.show()

 import math def distance(point1,point2):     return math.sqrt((point1[0]-point2[0])**2 + (point1[1]-point2[1])**2)
 def idealFilterLP(D0,imgShape):     base = np.zeros(imgShape[:2])     rows, cols = imgShape[:2]     center = (rows/2,cols/2)     for x in range(cols):         for y in range(rows):             if distance((y,x),center) < D0:                 base[y,x] = 1     return base
 def idealFilterHP(D0,imgShape):     base = np.ones(imgShape[:2])     rows, cols = imgShape[:2]     center = (rows/2,cols/2)     for x in range(cols):         for y in range(rows):             if distance((y,x),center) < D0:                 base[y,x] = 0     return base

 import math def distance(point1,point2):     return math.sqrt((point1[0]-point2[0])**2 + (point1[1]-point2[1])**2)
 def gaussianLP(D0,imgShape):     base = np.zeros(imgShape[:2])     rows, cols = imgShape[:2]     center = (rows/2,cols/2)     for x in range(cols):         for y in range(rows):             base[y,x] = math.exp(((-distance((y,x),center)**2)/(2*(D0**2))))     return base
 def gaussianHP(D0,imgShape):     base = np.zeros(imgShape[:2])     rows, cols = imgShape[:2]     center = (rows/2,cols/2)     for x in range(cols):         for y in range(rows):             base[y,x] = 1 - math.exp(((-distance((y,x),center)**2)/(2*(D0**2))))     return base

 fig, ax = plt.subplots(2, 2) # create a 2x2 grid of subplots fig.suptitle('Filters') # set the title for the entire figure
 # plot the first image in the top-left subplot im1 = ax[0, 0].imshow(np.abs(idealFilterLP(50, img.shape)), cmap='gray') ax[0, 0].set_title('Low Pass Filter of Diameter 50 px') ax[0, 0].set_xticks([]) ax[0, 0].set_yticks([])
 # plot the second image in the top-right subplot im2 = ax[0, 1].imshow(np.abs(idealFilterHP(50, img.shape)), cmap='gray') ax[0, 1].set_title('High Pass Filter of Diameter 50 px') ax[0, 1].set_xticks([]) ax[0, 1].set_yticks([])
 # plot the third image in the bottom-left subplot im3 = ax[1, 0].imshow(np.abs(gaussianLP(50 ,img.shape)), cmap='gray') ax[1, 0].set_title('Gaussian Filter of Diameter 50 px') ax[1, 0].set_xticks([]) ax[1, 0].set_yticks([])
 # plot the fourth image in the bottom-right subplot im4 = ax[1, 1].imshow(np.abs(gaussianHP(50 ,img.shape)), cmap='gray') ax[1, 1].set_title('Gaussian Filter of Diameter 50 px') ax[1, 1].set_xticks([]) ax[1, 1].set_yticks([])
 # adjust the spacing between subplots fig.subplots_adjust(wspace=0.5, hspace=0.5)
 # save the figure to a file fig.savefig('filters.png', bbox_inches='tight')

 fig, ax = plt.subplots() im = ax.imshow(np.log(1+np.abs(fftshifted_image * idealFilterLP(50,img.shape))), cmap='gray') ax.set_title('Filtered Image in Frequency Domain') ax.set_xticks([]) ax.set_yticks([])
 fig.savefig('filtered image in freq domain.png', bbox_inches='tight')

 fig, ax = plt.subplots() im = ax.imshow(np.log(1+np.abs(np.fft.ifftshift(fftshifted_image * idealFilterLP(50,img.shape)))), cmap='gray') ax.set_title('Filtered Image inverse fft shifted') ax.set_xticks([]) ax.set_yticks([])
 fig.savefig('filtered image inverse fft shifted.png', bbox_inches='tight')

 fig, ax = plt.subplots() im = ax.imshow(np.log(1+np.abs(np.fft.ifft2(np.fft.ifftshift(fftshifted_image * idealFilterLP(50,img.shape))))), cmap='gray') ax.set_title('Final Filtered Image In Spatial Domain') ax.set_xticks([]) ax.set_yticks([])
 fig.savefig('final filtered image.png', bbox_inches='tight')

 def Freq_Trans(image, filter_used):     img_in_freq_domain = np.fft.fft2(image)      # Shift the zero-frequency component to the center of the frequency spectrum     centered = np.fft.fftshift(img_in_freq_domain)      # Multiply the filter with the centered spectrum     filtered_image_in_freq_domain = centered * filter_used      # Shift the zero-frequency component back to the top-left corner of the frequency spectrum     inverse_fftshift_on_filtered_image = np.fft.ifftshift(filtered_image_in_freq_domain)      # Apply the inverse Fourier transform to obtain the final filtered image     final_filtered_image = np.fft.ifft2(inverse_fftshift_on_filtered_image)      return img_in_freq_domain,centered,filter_used,filtered_image_in_freq_domain,inverse_fftshift_on_filtered_image,final_filtered_image

 fig, axs = plt.subplots(12, 7, figsize=(30, 60))  filters = [(f, d) for f in [idealFilterLP, idealFilterHP, gaussianLP, gaussianHP] for d in [50, 100, 150]]  for row, (filter_name, filter_diameter) in enumerate(filters):     # Plot each filter output on a separate subplot     result = Freq_Trans(img, filter_name(filter_diameter, img.shape))      for col, title, img_array in zip(range(7),    ["Original Image", "Spectrum", "Centered Spectrum", f"{filter_name.__name__} of Diameter {filter_diameter} px",     f"Centered Spectrum multiplied by {filter_name.__name__}", "Decentralize", "Processed Image"],    [img, np.log(1+np.abs(result[0])), np.log(1+np.abs(result[1])), np.abs(result[2]), np.log(1+np.abs(result[3])),      np.log(1+np.abs(result[4])), np.abs(result[5])]):                  axs[row, col].imshow(img_array, cmap='gray')         axs[row, col].set_title(title)  plt.tight_layout() plt.savefig('all_processess.png', bbox_inches='tight') plt.show()