Initial commit with project files

3_Signalorientierte_Bildverarbeitung/ü1/l_b.py

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