Remove background for shadow 3D-PTV and detecting overlapping spheres

detect_overlapping_spheres.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from skimage import io, measure, morphology, feature\n",
    "from scipy import ndimage\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Load the image\n",
    "image = io.imread('./spheres_isolated.png')  # Replace with your image path\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from skimage import io, measure, morphology, feature\n",
    "from scipy import ndimage\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Load the image\n",
    "# image = io.imread('path_to_your_image.png')  # Replace with your image path\n",
    "\n",
    "def detect_spheres(binary_image):\n",
    "    # Label connected components\n",
    "    labeled_image = measure.label(binary_image)\n",
    "    properties = measure.regionprops(labeled_image)\n",
    "    \n",
    "    # Filter out small objects and objects touching the border\n",
    "    min_area = 100  # Adjust this value based on your image\n",
    "    height, width = binary_image.shape\n",
    "    filtered_props = [prop for prop in properties \n",
    "                      if prop.area >= min_area and \n",
    "                      0 < prop.centroid[0] < height-1 and \n",
    "                      0 < prop.centroid[1] < width-1]\n",
    "    \n",
    "    # Sort by area, largest first\n",
    "    filtered_props.sort(key=lambda x: x.area, reverse=True)\n",
    "    \n",
    "    # Take the four largest objects\n",
    "    largest_four = filtered_props[:4]\n",
    "    \n",
    "    # For the overlapping spheres, use distance transform to find peaks\n",
    "    mask = np.zeros_like(binary_image)\n",
    "    for prop in largest_four:\n",
    "        mask[prop.coords[:, 0], prop.coords[:, 1]] = 1\n",
    "    \n",
    "    distance = ndimage.distance_transform_edt(mask)\n",
    "    coordinates = feature.peak_local_max(distance, min_distance=10, num_peaks=4)\n",
    "    \n",
    "    return coordinates\n",
    "\n",
    "# Detect spheres\n",
    "centroids = detect_spheres(image)\n",
    "\n",
    "# Plot the results\n",
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "ax.imshow(image, cmap='gray')\n",
    "\n",
    "for centroid in centroids:\n",
    "    ax.plot(centroid[1], centroid[0], 'r.', markersize=15)\n",
    "\n",
    "ax.set_title('Detected Sphere Centroids')\n",
    "ax.axis('off')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Optional: Save the result\n",
    "plt.savefig('sphere_centroids_detected.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Function to detect non-overlapping spheres\n",
    "# def detect_non_overlapping(binary_image):\n",
    "#     labeled_image = measure.label(binary_image)\n",
    "#     properties = measure.regionprops(labeled_image)\n",
    "#     return [prop.centroid for prop in properties]\n",
    "\n",
    "# # Function to detect overlapping spheres\n",
    "# def detect_overlapping(binary_image):\n",
    "#     # Apply distance transform\n",
    "#     distance = ndimage.distance_transform_edt(binary_image)\n",
    "    \n",
    "#     # Find local maxima\n",
    "#     coordinates = feature.peak_local_max(distance, min_distance=10, exclude_border=True)\n",
    "    \n",
    "#     # If we found more than 4 peaks, keep only the 4 strongest\n",
    "#     if len(coordinates) > 4:\n",
    "#         peak_intensities = [distance[tuple(coord)] for coord in coordinates]\n",
    "#         sorted_indices = np.argsort(peak_intensities)[-4:]\n",
    "#         coordinates = coordinates[sorted_indices]\n",
    "    \n",
    "#     return coordinates\n",
    "\n",
    "# # Detect non-overlapping spheres\n",
    "# non_overlapping_centroids = detect_non_overlapping(image)\n",
    "\n",
    "# # If we found less than 4 spheres, use the overlapping detection method\n",
    "# if len(non_overlapping_centroids) < 4:\n",
    "#     centroids = detect_overlapping(image)\n",
    "# else:\n",
    "#     centroids = non_overlapping_centroids\n",
    "\n",
    "# # Plot the results\n",
    "# fig, ax = plt.subplots(figsize=(10, 10))\n",
    "# ax.imshow(image, cmap='gray')\n",
    "\n",
    "# for centroid in centroids:\n",
    "#     ax.plot(centroid[1], centroid[0], 'r.', markersize=15)\n",
    "\n",
    "# ax.set_title('Detected Sphere Centroids')\n",
    "# ax.axis('off')\n",
    "# plt.tight_layout()\n",
    "# plt.show()\n",
    "\n",
    "# # Optional: Save the result\n",
    "# plt.savefig('sphere_centroids_detected.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "# from skimage import io, measure, morphology, feature, segmentation\n",
    "# from scipy import ndimage\n",
    "# import matplotlib.pyplot as plt\n",
    "\n",
    "# # Load the image\n",
    "# # image = io.imread('path_to_your_image.png')  # Replace with your image path\n",
    "\n",
    "# def detect_spheres(binary_image):\n",
    "#     # Label connected components\n",
    "#     labeled_image = measure.label(binary_image)\n",
    "#     properties = measure.regionprops(labeled_image)\n",
    "    \n",
    "#     # Filter out small objects and objects touching the border\n",
    "#     min_area = 100  # Adjust this value based on your image\n",
    "#     height, width = binary_image.shape\n",
    "#     filtered_props = [prop for prop in properties \n",
    "#                       if prop.area >= min_area and \n",
    "#                       0 < prop.centroid[0] < height-1 and \n",
    "#                       0 < prop.centroid[1] < width-1]\n",
    "    \n",
    "#     # Sort by area, largest first\n",
    "#     filtered_props.sort(key=lambda x: x.area, reverse=True)\n",
    "    \n",
    "#     # Take the four largest objects\n",
    "#     largest_four = filtered_props[:4]\n",
    "    \n",
    "#     # Create a mask of the four largest objects\n",
    "#     mask = np.zeros_like(binary_image)\n",
    "#     for prop in largest_four:\n",
    "#         mask[prop.coords[:, 0], prop.coords[:, 1]] = 1\n",
    "    \n",
    "#     # Apply distance transform\n",
    "#     distance = ndimage.distance_transform_edt(mask)\n",
    "    \n",
    "#     # Use watershed to separate overlapping circles\n",
    "#     markers = np.zeros_like(mask, dtype=int)\n",
    "#     markers[distance < 3] = 1  # Background\n",
    "#     markers[distance > 30] = 2  # Foreground (adjust this threshold if needed)\n",
    "    \n",
    "#     # Find peaks for seeds\n",
    "#     peak_idx = feature.peak_local_max(distance, min_distance=20, num_peaks=4)\n",
    "#     for i, peak in enumerate(peak_idx, start=3):\n",
    "#         markers[tuple(peak)] = i\n",
    "    \n",
    "#     segments = segmentation.watershed(-distance, markers, mask=mask)\n",
    "    \n",
    "#     # Find centroids of the segmented regions\n",
    "#     centroids = []\n",
    "#     for i in range(3, 7):  # 3 to 6 are our four spheres\n",
    "#         coords = np.column_stack(np.where(segments == i))\n",
    "#         if len(coords) > 0:\n",
    "#             centroid = coords.mean(axis=0)\n",
    "#             centroids.append(centroid)\n",
    "    \n",
    "#     return np.array(centroids)\n",
    "\n",
    "# # Detect spheres\n",
    "# centroids = detect_spheres(image)\n",
    "\n",
    "# # Plot the results\n",
    "# fig, ax = plt.subplots(figsize=(10, 10))\n",
    "# ax.imshow(image, cmap='gray')\n",
    "\n",
    "# for centroid in centroids:\n",
    "#     ax.plot(centroid[1], centroid[0], 'r.', markersize=15)\n",
    "\n",
    "# ax.set_title('Detected Sphere Centroids')\n",
    "# ax.axis('off')\n",
    "# plt.tight_layout()\n",
    "# plt.show()\n",
    "\n",
    "# # Optional: Save the result\n",
    "# plt.savefig('sphere_centroids_detected.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "# from skimage import io, feature, draw\n",
    "# from scipy import ndimage\n",
    "# from skimage.transform import hough_circle, hough_circle_peaks\n",
    "# import matplotlib.pyplot as plt\n",
    "\n",
    "# # Load the image\n",
    "# # image = io.imread('path_to_your_image.png')  # Replace with your image path\n",
    "\n",
    "# def detect_spheres(binary_image):\n",
    "#     # Apply distance transform\n",
    "#     distance = ndimage.distance_transform_edt(binary_image)\n",
    "    \n",
    "#     # Use Hough circle transform to detect circles\n",
    "#     hough_radii = np.arange(20, 100, 2)  # Adjust this range based on your image\n",
    "#     hough_res = hough_circle(binary_image, hough_radii)\n",
    "    \n",
    "#     # Select the 4 most prominent circles\n",
    "#     accums, cx, cy, radii = hough_circle_peaks(hough_res, hough_radii,\n",
    "#                                                        total_num_peaks=4)\n",
    "    \n",
    "#     # Create a mask of the detected circles\n",
    "#     mask = np.zeros_like(binary_image, dtype=float)\n",
    "#     for center_y, center_x, radius in zip(cy, cx, radii):\n",
    "#         circy, circx = draw.circle_perimeter(int(center_y), int(center_x), int(radius))\n",
    "#         mask[circy, circx] = 1\n",
    "    \n",
    "#     # Combine the distance transform with the circle mask\n",
    "#     combined = distance * mask\n",
    "    \n",
    "#     # Find local maxima\n",
    "#     coordinates = feature.peak_local_max(combined, min_distance=20, num_peaks=4)\n",
    "    \n",
    "#     return coordinates\n",
    "\n",
    "# # Detect spheres\n",
    "# centroids = detect_spheres(image)\n",
    "\n",
    "# # Plot the results\n",
    "# fig, ax = plt.subplots(figsize=(10, 10))\n",
    "# ax.imshow(image, cmap='gray')\n",
    "\n",
    "# for centroid in centroids:\n",
    "#     ax.plot(centroid[1], centroid[0], 'r.', markersize=15)\n",
    "\n",
    "# ax.set_title('Detected Sphere Centroids')\n",
    "# ax.axis('off')\n",
    "# plt.tight_layout()\n",
    "# plt.show()\n",
    "\n",
    "# # Optional: Save the result\n",
    "# plt.savefig('sphere_centroids_detected.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "# from skimage import io, feature\n",
    "# from scipy import ndimage\n",
    "# import matplotlib.pyplot as plt\n",
    "\n",
    "# # Load the image\n",
    "# # image = io.imread('path_to_your_image.png')  # Replace with your image path\n",
    "\n",
    "# def detect_spheres(binary_image):\n",
    "#     # Apply distance transform\n",
    "#     distance = ndimage.distance_transform_edt(binary_image)\n",
    "    \n",
    "#     # Find local maxima\n",
    "#     coordinates = feature.peak_local_max(distance, min_distance=20, num_peaks=4, exclude_border=False)\n",
    "    \n",
    "#     return coordinates\n",
    "\n",
    "# # Detect spheres\n",
    "# centroids = detect_spheres(image)\n",
    "\n",
    "# # Plot the results\n",
    "# fig, ax = plt.subplots(figsize=(10, 10))\n",
    "# ax.imshow(image, cmap='gray')\n",
    "\n",
    "# for centroid in centroids:\n",
    "#     ax.plot(centroid[1], centroid[0], 'r.', markersize=15)\n",
    "\n",
    "# ax.set_title('Detected Sphere Centroids')\n",
    "# ax.axis('off')\n",
    "# plt.tight_layout()\n",
    "# plt.show()\n",
    "\n",
    "# # Optional: Save the result\n",
    "# plt.savefig('sphere_centroids_detected.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "# import matplotlib.pyplot as plt\n",
    "# from scipy import ndimage as ndi\n",
    "\n",
    "# from skimage.segmentation import watershed\n",
    "# from skimage.feature import peak_local_max\n",
    "\n",
    "\n",
    "# plt.imshow(image[10:400,500:800])\n",
    "# large_image = image.copy()\n",
    "# image = image.copy()[10:400,500:800]\n",
    "\n",
    "# # # Generate an initial image with two overlapping circles\n",
    "# # x, y = np.indices((80, 80))\n",
    "# # x1, y1, x2, y2 = 28, 28, 44, 52\n",
    "# # r1, r2 = 16, 20\n",
    "# # mask_circle1 = (x - x1) ** 2 + (y - y1) ** 2 < r1**2\n",
    "# # mask_circle2 = (x - x2) ** 2 + (y - y2) ** 2 < r2**2\n",
    "# # image = np.logical_or(mask_circle1, mask_circle2)\n",
    "\n",
    "# # Now we want to separate the two objects in image\n",
    "\n",
    "# # Generate the markers as local maxima of the distance to the background\n",
    "# distance = ndi.distance_transform_edt(image)\n",
    "# coords = peak_local_max(distance, footprint=np.ones((3, 3)), labels=image, min_distance=10)\n",
    "# mask = np.zeros(distance.shape, dtype=bool)\n",
    "# mask[tuple(coords.T)] = True\n",
    "# markers, _ = ndi.label(mask)\n",
    "# labels = watershed(-distance, markers, mask=image)\n",
    "\n",
    "# fig, axes = plt.subplots(ncols=3, figsize=(20, 20), sharex=True, sharey=True)\n",
    "# ax = axes.ravel()\n",
    "\n",
    "# ax[0].imshow(image, cmap=plt.cm.gray)\n",
    "# ax[0].set_title('Overlapping objects')\n",
    "# ax[1].imshow(-distance, cmap=plt.cm.gray)\n",
    "# ax[1].set_title('Distances')\n",
    "# ax[2].imshow(labels, cmap=plt.cm.nipy_spectral)\n",
    "# ax[2].set_title('Separated objects')\n",
    "\n",
    "# for a in ax:\n",
    "#     a.set_axis_off()\n",
    "\n",
    "# fig.tight_layout()\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "# from skimage import io, measure, morphology, feature\n",
    "# from skimage.draw import circle_perimeter\n",
    "# from scipy import optimize\n",
    "# import matplotlib.pyplot as plt\n",
    "\n",
    "# def fit_circle(x, y):\n",
    "#     def calc_R(xc, yc):\n",
    "#         return np.sqrt((x-xc)**2 + (y-yc)**2)\n",
    "    \n",
    "#     def f_2(c):\n",
    "#         Ri = calc_R(*c)\n",
    "#         return Ri - Ri.mean()\n",
    "    \n",
    "#     center_estimate = np.mean(x), np.mean(y)\n",
    "#     center, _ = optimize.leastsq(f_2, center_estimate)\n",
    "#     xc, yc = center\n",
    "#     Ri = calc_R(*center)\n",
    "#     R = Ri.mean()\n",
    "#     return xc, yc, R\n",
    "\n",
    "# def detect_spheres(binary_image):\n",
    "#     # Get contours\n",
    "#     contours = measure.find_contours(binary_image, 0.8)\n",
    "    \n",
    "#     centroids = []\n",
    "#     for contour in contours:\n",
    "#         # Get convex hull\n",
    "#         hull = morphology.convex_hull_image(np.zeros(binary_image.shape, dtype=bool) | measure.grid_points_in_poly(binary_image.shape, contour))\n",
    "#         hull_contour = measure.find_contours(hull, 0.8)[0]\n",
    "        \n",
    "#         # Calculate distances to hull\n",
    "#         distances = np.array([np.min(np.sum((contour - hp)**2, axis=1)) for hp in hull_contour])\n",
    "        \n",
    "#         # Find local maxima in distances\n",
    "#         peaks = feature.peak_local_max(distances, min_distance=20)\n",
    "        \n",
    "#         if len(peaks) > 1:  # Overlapping circles\n",
    "#             # Split contour at peaks and fit circles\n",
    "#             for i in range(len(peaks)):\n",
    "#                 start, end = peaks[i][0], peaks[(i+1)%len(peaks)][0]\n",
    "#                 segment = contour[start:end] if start < end else np.vstack((contour[start:], contour[:end]))\n",
    "#                 xc, yc, _ = fit_circle(segment[:, 1], segment[:, 0])\n",
    "#                 centroids.append((yc, xc))\n",
    "#         else:  # Single circle\n",
    "#             xc, yc, _ = fit_circle(contour[:, 1], contour[:, 0])\n",
    "#             centroids.append((yc, xc))\n",
    "    \n",
    "#     return np.array(centroids)\n",
    "\n",
    "# # Load the image\n",
    "# # image = io.imread('path_to_your_image.png')  # Replace with your image path\n",
    "\n",
    "\n",
    "# # Detect spheres\n",
    "# centroids = detect_spheres(image)\n",
    "\n",
    "# # Plot the results\n",
    "# fig, ax = plt.subplots(figsize=(10, 10))\n",
    "# ax.imshow(image, cmap='gray')\n",
    "\n",
    "# for centroid in centroids:\n",
    "#     ax.plot(centroid[1], centroid[0], 'r.', markersize=15)\n",
    "\n",
    "# ax.set_title('Detected Sphere Centroids')\n",
    "# ax.axis('off')\n",
    "# plt.tight_layout()\n",
    "# plt.show()\n",
    "\n",
    "# # Optional: Save the result\n",
    "# plt.savefig('sphere_centroids_detected.png', dpi=300, bbox_inches='tight')"
   ]
  }
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remove_background.ipynb