feat: dct script seemingly done

dct.py

+import argparse
+import numpy as np
+import numpy.typing as npt
+import matplotlib.pyplot as plt
+from PIL import Image
+
+Img = npt.NDArray[np.uint8]
+
+def load_img(path: str) -> Img:
+    img = Image.open(path).convert("L")
+
+    return np.array(img)
+
+
+def show_image(img: Img):
+    if len(img.shape) == 2:
+        plt.imshow(img, cmap="gray", vmin=0, vmax=255)
+    else:
+        plt.imshow(img)
+
+    plt.show()
+
+
+def sliding_window(img: Img, x_pos: int, y_pos: int, n: int):
+    sub_mat = np.zeros((n, n))
+
+    for i in range(x_pos, x_pos + n):
+        for j in range(y_pos, y_pos + n):
+            sub_mat[i - x_pos, j - y_pos] = img[i, j]
+
+    return sub_mat
+
+
+def cos_mat(n: int) -> Img:
+    mat = np.zeros((n, n))
+
+    for i in range(n):
+        for j in range(n):
+
+            if i == 0:
+                mat[i, j] = 1 / n
+            else:
+                mat[i, j] = np.sqrt(2 / n) *  np.cos((2 * j + 1) * i * np.pi \
+                    / (2 * n))
+
+    return mat
+
+
+def dct(padded_img: Img, kernel_size: int) -> Img:
+    c_mat = cos_mat(kernel_size)
+    c_t = np.transpose(c_mat)
+
+    final_img = np.zeros(padded_img.shape)
+
+    for i in range(0, padded_img.shape[0], kernel_size):
+        for j in range(0, padded_img.shape[1], kernel_size):
+            sub_mat = sliding_window(padded_img, i, j, kernel_size)
+            final_img[i:i+kernel_size, j:j+kernel_size] = c_mat @ sub_mat @ c_t
+
+    return final_img
+
+def idct(transformed_img: Img, kernel_size: int) -> Img:
+    c_mat = cos_mat(kernel_size)
+    c_t = np.transpose(c_mat)
+    
+    # Compute the inverse DCT matrix
+    inv_c_mat = np.linalg.inv(c_mat)
+    inv_c_t = np.transpose(inv_c_mat)
+    
+    final_img = np.zeros(transformed_img.shape)
+    
+    for i in range(0, transformed_img.shape[0], kernel_size):
+        for j in range(0, transformed_img.shape[1], kernel_size):
+            sub_mat = sliding_window(transformed_img, i, j, kernel_size)
+            final_img[i:i+kernel_size, j:j+kernel_size] = inv_c_mat @ sub_mat @ inv_c_t
+    
+    return final_img
+
+def quantized(kernel_size: int, quality: int) -> Img:
+    quant = np.zeros((kernel_size, kernel_size))
+
+    for i in range(0, quant.shape[0]):
+        for j in range(0, quant.shape[1]):
+            quant[i, j] = 1 + (i + j + 1) * quality
+
+    return quant
+
+
+def quantize_dct(dct_img: Img, kernel_size: int, quality: int) -> Img:
+    final_mat = dct_img.copy()
+    quant = quantized(kernel_size, quality)
+
+    for i in range(0, dct_img.shape[0], kernel_size):
+        for j in range(0, dct_img.shape[1], kernel_size):
+            final_mat[i:i+kernel_size, j:j+kernel_size] = np.round(dct_img[i:i+kernel_size, j:j+kernel_size] / quant)
+
+    return final_mat
+
+
+def pad_image(img: Img, kernel_size: int):
+    print(img.shape)
+    rows, cols = img.shape
+
+    pad_rows = (kernel_size - rows % kernel_size) % kernel_size
+    pad_cols = (kernel_size - cols % kernel_size) % kernel_size
+
+    return np.pad(img, ((0, pad_rows), (0, pad_cols)), mode='constant', constant_values=0)
+
+def plot_images(images, titles):
+    fig, axes = plt.subplots(1, 4, figsize=(12, 3))  # 1 row, 4 columns
+    for ax, img, title in zip(axes, images, titles):
+        ax.imshow(img, cmap='gray')
+        ax.set_title(title)
+        ax.axis('off')
+    plt.show()
+
+def main():
+    parser = argparse.ArgumentParser(prog='DCT converter')
+
+    _ = parser.add_argument('filepath')
+    args = parser.parse_args()
+
+    kernel_size = 8
+
+    img = load_img(args.filepath)
+    padded = pad_image(img, kernel_size)
+    print(f"og shape: {img.shape}")
+    print(f"new shape: {padded.shape}")
+
+    dct_img = dct(padded, kernel_size)
+    inv_dct = idct(dct_img, kernel_size)
+
+    q_dct = quantize_dct(dct_img, kernel_size, 2)
+    inv_q_dct = idct(q_dct, kernel_size)
+    
+    images = [dct_img, inv_dct, q_dct, inv_q_dct]
+    titles = ["DCT Image", "Inverse DCT", "Quantized DCT", "Inverse Quantized DCT"]
+    
+    plot_images(images, titles)
+
+
+
+if __name__ == "__main__":
+    main()