94 lines
3.2 KiB
Python
94 lines
3.2 KiB
Python
import numpy as np
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import cv2
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import math
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def dct(a: np.ndarray):
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a_freq = np.zeros_like(a)
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N, M = a_freq.shape[1], a_freq.shape[0]
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# Iteriere über jeden Koeffizienten
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for k in range(N):
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for m in range(M):
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dct_k_m = 0
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# Iteriere über jede Position im Ortsraum
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for x in range(N):
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for y in range(M):
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dct_k_m += a[y, x] * np.cos(k*np.pi*(2*x+1)/(2*N)) * np.cos(m*np.pi*(2*y+1)/(2*M))
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dct_k_m = 4 * dct_k_m / (np.sqrt(2*N) * np.sqrt(2*M))
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a_freq[m, k] = dct_k_m
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return a_freq
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def idct(a_freq: np.ndarray):
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a = np.zeros_like(a_freq)
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N, M = a_freq.shape[1], a_freq.shape[0]
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a_freq = (np.sqrt(2*N) * np.sqrt(2*M)) * a_freq / 16
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a_freq[0, :] = a_freq[0, :] / 2
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a_freq[:, 0] = a_freq[:, 0] / 2
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# Iteriere über jeden Koeffizienten
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for x in range(N):
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for y in range(M):
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f_x_y = 0 #a_freq[0, 0] / (4)# * np.sqrt(2))
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# Iteriere über jede Position im Ortsraum
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for k in range(N):
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for m in range(M):
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f_x_y += a_freq[m, k] * np.cos(k*np.pi*(2*x+1)/(2*N)) * np.cos(m*np.pi*(2*y+1)/(2*M))
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f_x_y = f_x_y / 4
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a[y, x] = f_x_y
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return a
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def remove_dct(img, rate):
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"""
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Diese Implementierung wendet die diskrete Fourier Transformation auf das Bild img an. Daraufhin werden die hoch-
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frequenten Anteile anteilig der Rate rate entfernt. Am Ende wird das Bild wieder in den Bildbereich transformiert.
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:param img:
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:param rate:
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:return:
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"""
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assert rate <= 1, "Die Rate muss kleiner gleich 1 sein!"
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height, width = img.shape
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for i in range(math.ceil(width / 8)):
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for j in range(math.ceil(height / 8)):
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# Block extrahieren
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block = np.zeros((8, 8))
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horizontal_pixel, vertical_pixel = min(8, width - i * 8), min(8, height - j * 8)
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block[0:vertical_pixel, 0:horizontal_pixel] = \
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img[j * 8: (j * 8) + vertical_pixel, i * 8: (i * 8) + horizontal_pixel]
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# In den Frequenzbereich tranformieren
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block_freq = dct(block)
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# Hochfrequente Anteile löschen
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values_to_delete = 8 * 8 * rate
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values_deleted = 0
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for m in range(0, 16):
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for n in range(0, m + 1):
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if values_deleted >= values_to_delete:
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break
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if 7 - m + n < 0 or 7 - n < 0:
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continue
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block_freq[7 - m + n, 7 - n] = 0.
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values_deleted += 1
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# Rücktransformation in den Bildbereich
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block = idct(block_freq)
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# Einfügen in Ursprungsbild
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img[j * 8: (j * 8) + vertical_pixel, i * 8: (i * 8) + horizontal_pixel] = \
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block[0:vertical_pixel, 0:horizontal_pixel]
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return img
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''' Bild laden '''
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img = cv2.imread("../../data/cameraman.png")
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img = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
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img = cv2.resize(img, (160, 160))
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img = (img.astype(np.float64) / 256)
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cv2.imshow("ORIGINAL", img)
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''' Funktion anwenden '''
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img = remove_dct(img, 0.8)
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''' Bild anzeigen '''
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cv2.imshow("IMG", img)
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cv2.waitKey(0)
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