[Question 1] Import libraries
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Question 1.ipynb
151
Question 1.ipynb
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@ -113,7 +113,7 @@
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{
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"data": {
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"data": {
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"text/plain": [
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"text/plain": [
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"<matplotlib.image.AxesImage at 0x1f7c0c56340>"
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"<matplotlib.image.AxesImage at 0x1a0a1a77340>"
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]
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]
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},
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"execution_count": 6,
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"execution_count": 6,
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"metadata": {},
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"metadata": {},
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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"from scipy import ndimage"
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"from scipy import ndimage\n",
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"from scipy.ndimage import convolve"
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]
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]
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{
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@ -539,30 +540,68 @@
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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"def compute_gradient_magnitude(gr_im, kx, ky):\n",
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"def compute_gradient_magnitude(gr_im, kx, ky):\n",
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" # Ensure the image is a float64 for computation\n",
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" \"\"\"\n",
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" gr_im_float64 = gr_im.astype(np.float64)\n",
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" Compute gradient magnitude of a grey image with given kernels.\n",
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"\n",
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"\n",
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" # Compute gradients in x and y direction\n",
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" Parameters:\n",
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" grad_x = cv2.filter2D(gr_im_float64, -1, kx.astype(np.float64))\n",
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" - gr_im: 2D numpy array, input grey image.\n",
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" grad_y = cv2.filter2D(gr_im_float64, -1, ky.astype(np.float64))\n",
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" - kx: 2D numpy array, horizontal kernel.\n",
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" - ky: 2D numpy array, vertical kernel.\n",
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"\n",
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"\n",
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" # Compute gradient magnitude\n",
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" Returns:\n",
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" magnitude = np.sqrt(grad_x**2 + grad_y**2)\n",
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" - grad_mag: 2D numpy array, gradient magnitude.\n",
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" \"\"\"\n",
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" # Validate input gr_im\n",
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" if not isinstance(gr_im, np.ndarray) or gr_im.dtype != np.uint8 or gr_im.ndim != 2:\n",
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" raise ValueError(\"gr_im must be a 2-dimensional numpy array of data type uint8\")\n",
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" # Convert inputs to float64 for computation\n",
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" gr_im = gr_im.astype(np.float64)\n",
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" kx = kx.astype(np.float64)\n",
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" ky = ky.astype(np.float64)\n",
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" \n",
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" \n",
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" return magnitude\n",
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" # Compute horizontal and vertical gradients using convolution\n",
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" grad_x = convolve2d(gr_im, kx, mode='same', boundary='symm')\n",
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" grad_y = convolve2d(gr_im, ky, mode='same', boundary='symm')\n",
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" \n",
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" # Compute gradient magnitude\n",
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" grad_mag = np.sqrt(grad_x**2 + grad_y**2)\n",
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" \n",
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" print(\"Gradient Magnitude Array:\")\n",
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" print(grad_mag)\n",
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" \n",
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" return grad_mag.astype(np.float64)\n",
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"\n",
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"\n",
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"def compute_gradient_direction(gr_im, kx, ky):\n",
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"def compute_gradient_direction(gr_im, kx, ky):\n",
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" # Ensure the image is a float64 for computation\n",
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" \"\"\"\n",
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" gr_im_float64 = gr_im.astype(np.float64)\n",
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" Compute gradient direction of a grey image with given kernels.\n",
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" \n",
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" # Compute gradients in x and y direction\n",
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" grad_x = cv2.filter2D(gr_im_float64, -1, kx.astype(np.float64))\n",
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" grad_y = cv2.filter2D(gr_im_float64, -1, ky.astype(np.float64))\n",
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"\n",
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"\n",
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" # Compute gradient direction\n",
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" Parameters:\n",
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" direction = np.arctan2(grad_y, grad_x)\n",
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" - gr_im: 2D numpy array, input grey image.\n",
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" - kx: 2D numpy array, horizontal kernel.\n",
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" - ky: 2D numpy array, vertical kernel.\n",
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"\n",
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" Returns:\n",
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" - grad_dir: 2D numpy array, gradient direction.\n",
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" \"\"\"\n",
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" # Validate input gr_im\n",
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" if not isinstance(gr_im, np.ndarray) or gr_im.dtype != np.uint8 or gr_im.ndim != 2:\n",
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" raise ValueError(\"gr_im must be a 2-dimensional numpy array of data type uint8\")\n",
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" # Convert inputs to float64 for computation\n",
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" gr_im = gr_im.astype(np.float64)\n",
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" kx = kx.astype(np.float64)\n",
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" ky = ky.astype(np.float64)\n",
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" \n",
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" \n",
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" return direction"
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" # Compute horizontal and vertical gradients using convolution\n",
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" grad_x = convolve2d(gr_im, kx, mode='same', boundary='symm')\n",
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" grad_y = convolve2d(gr_im, ky, mode='same', boundary='symm')\n",
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" \n",
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" # Compute gradient direction\n",
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" grad_dir = np.arctan2(grad_y, grad_x)\n",
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" \n",
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" print(\"Gradient Direction Array:\")\n",
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" print(grad_dir)\n",
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" \n",
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" return grad_dir.astype(np.float64)\n"
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]
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]
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},
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},
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{
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{
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@ -582,15 +621,38 @@
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"execution_count": 23,
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"execution_count": 23,
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"id": "63663950",
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"id": "63663950",
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"metadata": {},
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Gradient Magnitude Array:\n",
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"[[0. 0. 0. ... 0. 0. 0.]\n",
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" [0. 0. 0. ... 0. 0. 0.]\n",
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" [0. 0. 0. ... 0. 0. 0.]\n",
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" ...\n",
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" [0. 0. 0. ... 0. 0. 0.]\n",
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" [0. 0. 0. ... 0. 0. 0.]\n",
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" [0. 0. 0. ... 0. 0. 0.]]\n",
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"Gradient Direction Array:\n",
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"[[0. 0. 0. ... 0. 0. 0.]\n",
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" [0. 0. 0. ... 0. 0. 0.]\n",
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" [0. 0. 0. ... 0. 0. 0.]\n",
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" ...\n",
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" [0. 0. 0. ... 0. 0. 0.]\n",
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" [0. 0. 0. ... 0. 0. 0.]\n",
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" [0. 0. 0. ... 0. 0. 0.]]\n"
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]
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}
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],
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"source": [
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"source": [
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"# For convolution\n",
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"# For convolution\n",
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"# magnitude = compute_gradient_magnitude(gr_im, kx_conv, ky_conv)\n",
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"magnitude = compute_gradient_magnitude(gr_im, kx_conv, ky_conv)\n",
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"# direction = compute_gradient_direction(gr_im, kx_conv, ky_conv)\n",
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"direction = compute_gradient_direction(gr_im, kx_conv, ky_conv)\n",
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"\n",
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"\n",
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"# For Cross-Correlation\n",
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"# For Cross-Correlation\n",
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"magnitude = compute_gradient_magnitude(gr_im, kx_cross, ky_cross)\n",
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"# magnitude = compute_gradient_magnitude(gr_im, kx_cross, ky_cross)\n",
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"direction = compute_gradient_direction(gr_im, kx_cross, ky_cross)"
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"# direction = compute_gradient_direction(gr_im, kx_cross, ky_cross)"
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]
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]
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},
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},
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{
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{
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@ -628,25 +690,46 @@
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}
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}
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],
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],
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"source": [
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"source": [
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"assert np.allclose(m1_magnitude, magnitude), np.allclose(m1_direction, direction)\n",
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"all_pass = 0\n",
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"print (\"PASS: Method 1\")\n",
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"\n",
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"\n",
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"assert np.allclose(m2_magnitude, magnitude), np.allclose(m2_direction, direction)\n",
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"try:\n",
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"print (\"PASS: Method 2\")\n",
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" assert np.allclose(m1_magnitude, magnitude), np.allclose(m1_direction, direction)\n",
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" print (\"PASS: Method 1\")\n",
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" all_pass = all_pass + 1\n",
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"except AssertionError as e:\n",
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" print(\"Fail: Method 1\", e)\n",
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"\n",
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"\n",
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"assert np.allclose(m3_magnitude, magnitude), np.allclose(m3_direction, direction)\n",
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"try:\n",
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"print (\"PASS: Method 3\")\n",
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" assert np.allclose(m2_magnitude, magnitude), np.allclose(m2_direction, direction)\n",
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" print (\"PASS: Method 2\")\n",
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" all_pass = all_pass + 1\n",
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"except AssertionError as e:\n",
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" print(\"Fail: Method 2\", e)\n",
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"\n",
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"\n",
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"assert np.allclose(m4_magnitude, magnitude), np.allclose(m4_direction, direction)\n",
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"try:\n",
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"print (\"PASS: Method 4\")\n",
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" assert np.allclose(m3_magnitude, magnitude), np.allclose(m3_direction, direction)\n",
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" print (\"PASS: Method 3\")\n",
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" all_pass = all_pass + 1\n",
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"except AssertionError as e:\n",
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" print(\"Fail: Method 1\", e)\n",
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"\n",
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"\n",
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"print (\"ALL PASS\")"
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"try:\n",
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" assert np.allclose(m4_magnitude, magnitude), np.allclose(m4_direction, direction)\n",
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" print (\"PASS: Method 4\")\n",
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" all_pass = all_pass + 1\n",
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"except AssertionError as e:\n",
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" print(\"Fail: Method 1\", e)\n",
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"\n",
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"if all_pass == 4:\n",
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" print (\"ALL PASS\")\n",
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"else:\n",
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" print(f\"{all_pass} Passed, {4 - all_pass} Failed\")"
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]
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]
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},
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},
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": null,
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"execution_count": null,
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"id": "fb616c86",
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"id": "cc4a6cdb",
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"metadata": {},
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"metadata": {},
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"outputs": [],
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"outputs": [],
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"source": []
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"source": []
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