Page 1 - Praktikum 2.ipynb - Colab

Transformasi Fourier 2D

Percobaan 1

!pip install opencv-python-headless numpy pillow
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!pip install opencv-python numpy matplotlib

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import cv2
import numpy as np
import matplotlib.pyplot as plt

# 1. Baca gambar grayscale (gunakan gambar kecil agar cepat, misalnya 64x64 atau 128x128)
img = cv2.imread("/content/content/grayscaleimage.jpeg", 0)
img = cv2.resize(img, (64, 64)) # resize agar komputasi tidak berat
M, N = img.shape

# 2. Hitung DFT 2D secara manual
F = np.zeros((M, N), dtype=complex)

for u in range(M):
for v in range(N):
sum_val = 0.0
for x in range(M):
for y in range(N):
e = np.exp(-2j * np.pi * ((u*x)/M + (v*y)/N))
sum_val += img[x, y] * e
F[u, v] = sum_val

# 3. Geser spektrum ke tengah
Fshift = np.fft.fftshift(F)

# 4. Magnitudo spektrum
magnitude_spectrum = 20 * np.log(np.abs(Fshift) + 1)

# 5. Rekonstruksi citra dengan inverse DFT
img_reconstructed = np.zeros((M, N), dtype=complex)

for x in range(M):
for y in range(N):
sum_val = 0.0
for u in range(M):
for v in range(N):
e = np.exp(2j * np.pi * ((u*x)/M + (v*y)/N))
sum_val += F[u, v] * e
img_reconstructed[x, y] = sum_val / (M * N)
# 6. Tampilkan hasil
plt.figure(figsize=(15,5))
plt.subplot(131), plt.imshow(img, cmap='gray'), plt.title("Gambar Asli")
plt.subplot(132), plt.imshow(magnitude_spectrum, cmap='gray'), plt.title("Spektrum Fourier (DFT 2D)")
plt.subplot(133), plt.imshow(img_reconstructed.real, cmap='gray'), plt.title("Hasil Rekonstruksi DFT")
plt.tight_layout()
plt.show()