Python 이미지 처리: 주파수 도메인 필터링, 노이즈 감소 및 이미지 향상

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()