Ball_radar.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f1179478-766f-48d1-9666-5f7deec0bd5a",
   "metadata": {},
   "source": [
    "# Plotting ball on radar view"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "829856a4-45a9-42e0-8f0e-20f0f682505c",
   "metadata": {},
   "source": [
    "Warning : I am not a top python programmer so improvements are probably possible on the code bellow\n",
    "\n",
    "The method relies mainly on ML and signal processing. This what I like to do : mixing Computer Vision with all kinds of different techniques trying to guess which one is interesting at different steps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6ff5013-8158-4f92-9acb-c59bf34065c6",
   "metadata": {},
   "source": [
    "## Ball detection and coordinate transformation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe48a7d4-2044-4104-9733-1585d34c5953",
   "metadata": {},
   "source": [
    "This can be done by assembling various components of the main programm\n",
    "https://github.com/roboflow/sports/blob/main/examples/soccer/main.py\n",
    "\n",
    "Then this script is just given for information\n",
    "\n",
    "As one of the main problem is to detect when the ball is in the air, we need the whole time history of detections. This is the reason why all detections are stored in an array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c5e6da75-4fcd-4cc5-bf15-65452450dd39",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mrun_ball_radar\u001b[39m(source_video_path: \u001b[38;5;28mstr\u001b[39m, device: \u001b[38;5;28mstr\u001b[39m) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m np\u001b[38;5;241m.\u001b[39mndarray:\n\u001b[1;32m      2\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m    Run ball detection on a video and locate it on radar view.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03m    If sevral detections in one frame, all are kepts\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;124;03m        np.ndarray: each line (frame_index, x_coordiante, y_ coordinate)\u001b[39;00m\n\u001b[1;32m     12\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[1;32m     13\u001b[0m     ball_detection_model \u001b[38;5;241m=\u001b[39m YOLO(BALL_DETECTION_MODEL_PATH)\u001b[38;5;241m.\u001b[39mto(device\u001b[38;5;241m=\u001b[39mdevice)\n",
      "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
     ]
    }
   ],
   "source": [
    "def run_ball_radar(source_video_path: str, device: str) -> np.ndarray:\n",
    "    \"\"\"\n",
    "    Run ball detection on a video and locate it on radar view.\n",
    "    If sevral detections in one frame, all are kepts\n",
    "\n",
    "    Args:\n",
    "        source_video_path (str): Path to the source video.\n",
    "        device (str): Device to run the model on (e.g., 'cpu', 'cuda').\n",
    "\n",
    "    Retruns:\n",
    "        np.ndarray: each line (frame_index, x_coordiante, y_ coordinate)\n",
    "    \"\"\"\n",
    "    ball_detection_model = YOLO(BALL_DETECTION_MODEL_PATH).to(device=device)\n",
    "    pitch_detection_model = YOLO(PITCH_DETECTION_MODEL_PATH).to(device=device)\n",
    "    frame_generator = sv.get_video_frames_generator(source_path=source_video_path)\n",
    "    ball_tracker = BallTracker(buffer_size=20)\n",
    "    ball_annotator = BallAnnotator(radius=6, buffer_size=10)\n",
    "\n",
    "    def callback(image_slice: np.ndarray) -> sv.Detections:\n",
    "        result = ball_detection_model(image_slice, imgsz=640, verbose=False)[0]\n",
    "        return sv.Detections.from_ultralytics(result)\n",
    "\n",
    "    slicer = sv.InferenceSlicer(\n",
    "        callback=callback,\n",
    "        overlap_filter_strategy=sv.OverlapFilter.NONE,\n",
    "        slice_wh=(640, 640),\n",
    "    )\n",
    "    i_frame = 0\n",
    "    t0 = time.time()\n",
    "    ball_xy = []\n",
    "    for frame in frame_generator:\n",
    "        detections = slicer(frame).with_nms(threshold=0.1)\n",
    "        detections = ball_tracker.update(detections)\n",
    "        \n",
    "        result = pitch_detection_model(frame, verbose=False)[0]\n",
    "        keypoints = sv.KeyPoints.from_ultralytics(result)\n",
    "        \n",
    "        mask = (keypoints.xy[0][:, 0] > 1) & (keypoints.xy[0][:, 1] > 1)\n",
    "        transformer = ViewTransformer(\n",
    "            source=keypoints.xy[0][mask].astype(np.float32),\n",
    "            target=np.array(CONFIG.vertices)[mask].astype(np.float32)\n",
    "        )\n",
    "        xy = detections.get_anchors_coordinates(anchor=sv.Position.BOTTOM_CENTER)\n",
    "        transformed_xy = transformer.transform_points(points=xy)\n",
    "        \n",
    "        frame_xy = np.vstack((np.repeat(i_frame,len(transformed_xy)) , transformed_xy.T)).T\n",
    "        \n",
    "        if len(ball_xy) > 0:\n",
    "            ball_xy = np.vstack((ball_xy, frame_xy))\n",
    "        else: ball_xy = frame_xy.copy()\n",
    "\n",
    "        i_frame += 1\n",
    "        \n",
    "        if i_frame % 50 == 0: \n",
    "            print(i_frame, f\"{time.time() - t0:.2f}\")\n",
    "        \n",
    "    return ball_xy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f1fd707-7666-4592-8fcd-b60b94fd1766",
   "metadata": {},
   "source": [
    "## Post processing of ball trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1c917a2c-79a6-4dc0-a5d9-06a2cc4448dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy import interpolate\n",
    "from scipy.signal import find_peaks\n",
    "\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "from sklearn.neighbors import kneighbors_graph, KDTree\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import RANSACRegressor\n",
    "\n",
    "from scipy.linalg import expm\n",
    "from filterpy.kalman import KalmanFilter\n",
    "from filterpy.common import Q_discrete_white_noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e79b3523-6921-4ed8-bb8d-c1a1e106003d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.0000000e+00, 1.4858859e+03, 3.0527632e+03],\n",
       "       [1.0000000e+00, 1.4867784e+03, 3.0535281e+03],\n",
       "       [2.0000000e+00, 1.4742407e+03, 3.0858040e+03],\n",
       "       [3.0000000e+00, 1.4631831e+03, 3.1161887e+03],\n",
       "       [4.0000000e+00, 1.4362982e+03, 3.1695132e+03]], dtype=float32)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "source_video_path = 'data/2e57b9_0.mp4'\n",
    "\n",
    "ball_xy = np.load(source_video_path[:-4] + '_ball.npy')\n",
    "ball_xy[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc289f38-1b6c-4e55-9fb8-65a8e96f2f3e",
   "metadata": {},
   "source": [
    "We now have an array where each line is a ball detection, first the index of the frame for this detection and x and y coordiantes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6a0513f6-f082-42ee-982e-4ddbf70d9c09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-207.76468200683598, 10269.522555541993, -7729.348376464844, 97.5864135742188)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_frame = ball_xy[:,0].max() + 1\n",
    "plt.scatter (ball_xy[:,1], -ball_xy[:,2], c=ball_xy[:,0], \n",
    "                   norm = plt.Normalize(vmin=0, vmax=n_frame), cmap=\"nipy_spectral\", s=0.5)\n",
    "plt.axis('equal')\n",
    "plt.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7426f47-fd24-4b0e-adcb-8fa61bf2edf9",
   "metadata": {},
   "source": [
    "Color changes according time.\n",
    "\n",
    "To obtain a plat that has the same orientation as the radar view sign of y coordinate has to be changed"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fba116ac-9db4-48e6-a3bf-16749cab7445",
   "metadata": {},
   "source": [
    "#### About the selection of the video"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c7c18ff-5c9e-4135-b0ab-f2111b1bf70f",
   "metadata": {},
   "source": [
    "I took this video as ball is often in the air and a good test to solve this problem\n",
    "It happens that we have some frame with no detection but no frame with several detection.\n",
    "\n",
    "I believe desttroy information is never a good idea so I keep all detections even when they are several one in the same frame. In this case the detection that is clother to ball trajectory will be the better one. To make this selection I would recommand to build a graph and select the shortest path.\n",
    "\n",
    "If you wish to see how tell me in which video this is needed ;)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "730e8542-1f18-4826-970c-f542cb6c719f",
   "metadata": {},
   "source": [
    "## Detection of... false detections"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fe1afce-3437-4c31-ab68-5f77cd94bcd1",
   "metadata": {},
   "source": [
    "False detections will be ouliers in the ball trajectory. As we can see, they appears as isolated points in the plot above.\n",
    "\n",
    "This isolation in not only true in space (what we see on the plot), it is also true in time. Then to detect outliers we will keep frame indexes.\n",
    "\n",
    "To detect points that are isolated we will use agglomerative clustering with 'single' leakage i.e. a cluster will be broken as soon as one detection is too far away.\n",
    "An important point to use a clustering technique is choice of hyperparameter. And for that nothing is better tnat data themselves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1c26adcc-2cf4-40e1-b13d-6148e529b58b",
   "metadata": {},
   "outputs": [],
   "source": [
    "fs = 25\n",
    "Xraw = ball_xy.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "627c62c3-48b7-4b4a-b0d2-d383004a8a63",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "X = scaler.fit_transform(Xraw)\n",
    "X[:,0] *= 2\n",
    "tree = KDTree(X)\n",
    "dist, ind = tree.query(X, k=max(fs//3, 10))\n",
    "thresh = 2*np.quantile(dist[:,-1], 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eff16160-0859-42ff-9cee-c4463e63f654",
   "metadata": {},
   "source": [
    "First we normalize the data and then give more weight to the time dimension (intuition is that the ball can travel fast in space but not in time !)\n",
    "\n",
    "And then determine what an abnormal distance can be using the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2dd3618a-48c8-4545-b39f-e0eaa5a2534e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>AgglomerativeClustering(connectivity=&lt;687x687 sparse matrix of type &#x27;&lt;class &#x27;numpy.float64&#x27;&gt;&#x27;\n",
       "\twith 3435 stored elements in Compressed Sparse Row format&gt;,\n",
       "                        distance_threshold=0.15649464662108045,\n",
       "                        linkage=&#x27;single&#x27;, n_clusters=None)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;AgglomerativeClustering<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.cluster.AgglomerativeClustering.html\">?<span>Documentation for AgglomerativeClustering</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>AgglomerativeClustering(connectivity=&lt;687x687 sparse matrix of type &#x27;&lt;class &#x27;numpy.float64&#x27;&gt;&#x27;\n",
       "\twith 3435 stored elements in Compressed Sparse Row format&gt;,\n",
       "                        distance_threshold=0.15649464662108045,\n",
       "                        linkage=&#x27;single&#x27;, n_clusters=None)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "AgglomerativeClustering(connectivity=<687x687 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 3435 stored elements in Compressed Sparse Row format>,\n",
       "                        distance_threshold=0.15649464662108045,\n",
       "                        linkage='single', n_clusters=None)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_graph = kneighbors_graph(X[:,0].reshape(-1,1), 5, include_self=False)\n",
    "clustering = AgglomerativeClustering(n_clusters=None, linkage='single', \n",
    "                                     connectivity=knn_graph, distance_threshold=thresh)\n",
    "clustering.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "178de225-2805-4078-95bf-7e43b4db0d92",
   "metadata": {},
   "source": [
    "Then we underline a point should be considered in its neighbouring or local connectivity and apply the clustering "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0fff4d2c-6e89-4fee-ade9-0ffd9ee97d00",
   "metadata": {},
   "outputs": [],
   "source": [
    "labs, n_in_labs = np.unique(clustering.labels_, return_counts=True)\n",
    "outs = np.array([])\n",
    "for lab, n_in in zip(labs, n_in_labs):\n",
    "    if n_in < 3:\n",
    "        outs = np.append(outs, np.where(clustering.labels_== lab)[0])\n",
    "outs = np.sort(outs).astype(np.int16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70fe9100-6862-4cda-9515-38f5695109db",
   "metadata": {},
   "source": [
    "\"isolation\" criteria is a cluster with two detections or less"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "85042d90-1aa7-4ba5-94e1-b2f3b8910c36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(ball_xy[:,1], -ball_xy[:,2], s=0.5)\n",
    "plt.plot(ball_xy[outs,1], -ball_xy[outs,2],'r.')\n",
    "plt.legend(['detections','outliers'])\n",
    "plt.axis('equal')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "249848f6-a4d4-46f1-a452-688fe0ef29dc",
   "metadata": {},
   "source": [
    "Not so bad !\n",
    "\n",
    "If we consider the outlier in the vicinity of the end of the trajectory, it is a good example of a point that is not far in space but far in time.\n",
    "\n",
    "Note : I also considered DBScan, Local Outlier Factor but results were not convincing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "262b42bf-4947-42bb-a0f7-f6591584d7dd",
   "metadata": {},
   "source": [
    "## Kalman smoothing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d9e6d2f-3598-43bc-baec-c6cde21114cf",
   "metadata": {},
   "source": [
    "We can see in the last plot taht somme points seems to be out of the main trajectory and some erratic moves occur. In order too imrove that while keeping as mauch as physical meaning Kalman smoothing is a good tool.\n",
    "To learn more about Kalman smoothin unsing filterpy I strongly recommand https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python it's realy fantastic.\n",
    "\n",
    "Kalman smoothing uses the same basis as Kalman filtering and levrage the knowledge of \"future\" detections\n",
    "\n",
    "To apply Kalman smoothing we need to have a detection at every time stamp.\n",
    "\n",
    "Let's first delete the otliers and the interpolate missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "92beca8a-19c8-4280-b3e6-c3edd8ee32f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "ball_xy_val = np.delete(ball_xy, outs, axis=0)\n",
    "f = interpolate.interp1d(ball_xy_val[:,0], ball_xy_val[:,1:], axis=0, fill_value='extrapolate')\n",
    "frames = np.arange(ball_xy[-1,0]+1)\n",
    "ball_int = f(frames)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50a2ef89-e6ba-453a-9a73-bc3126054281",
   "metadata": {},
   "source": [
    "Let's examine what we have so far"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9cc9f031-0f76-4336-8676-d1a4a1c15e62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'y')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "ax1.plot(frames, ball_int[:,0])\n",
    "ax1.set_title('x')\n",
    "ax2.plot(frames, ball_int[:,1])\n",
    "ax2.set_title('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c229f2b-6d6b-414d-80c3-e853708fb2ae",
   "metadata": {},
   "source": [
    "We can see that depending on time, noise can show very different amplitudes and this is a limitation of Kalman smoothing as it optimizes a mean squared error. A way to get rid of big errors would be to apply an \"aggressive\" smoothing. But that would also lead to loss of meaningful signal especially when the ball changes direction suddenly like in the first half of this video. Let's try a way to arrange that.\n",
    "\n",
    "To understand the meaning of different element in Kalman filter and how to tune parameters please refer to  https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a3a067ed-ff33-42a1-9a09-75bbe0619774",
   "metadata": {},
   "outputs": [],
   "source": [
    "dim_x = 4\n",
    "A = np.zeros((dim_x,dim_x))\n",
    "for i in range(dim_x-1): A[i, i+1] = 1\n",
    "dt = 1\n",
    "\n",
    "f = KalmanFilter (dim_x=dim_x, dim_z=1)\n",
    "f.F = expm(A * dt )\n",
    "\n",
    "f.H = np.zeros((1,dim_x))\n",
    "f.H[0,0] = 1\n",
    "f.P *= 10. \n",
    "f.R = 100**2 \n",
    "\n",
    "varQ = 10\n",
    "f.Q = Q_discrete_white_noise(dim=dim_x, dt=dt, var=varQ**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4d7ef01b-04f3-4a08-8230-bb4ae37804ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7ebd3c4eaab0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = ball_int[:,1].copy()\n",
    "\n",
    "f.x = np.zeros((dim_x,1))\n",
    "f.x[0,0] = zs[0]\n",
    "mu, cov, _, _ = f.batch_filter(zs)\n",
    "xs, Ps, Ks,_ = f.rts_smoother(mu, cov)\n",
    "\n",
    "traj = xs.squeeze()[:,0]\n",
    "deltas = traj - zs\n",
    "\n",
    "plt.scatter(frames, deltas, s=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c0e88bbc-bc93-4a7a-b8e1-369ef581a092",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(deltas, bins=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b155c27a-2831-4be8-a871-cdc2077660ae",
   "metadata": {},
   "source": [
    "These two plots show the same thing : distribution of error in \"mainly\" gaussian\" and we have a few outliers.\n",
    "\n",
    "There are some rigourous methods to tackle this problem but I suggest one which is easy to imlement : outliers are detected when a large error occurs and are replaced by the Kalman smoothing estimate.\n",
    "\n",
    "Once again to define \"big\" error data statistics are used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a2ad6edc-5638-44e0-aaa1-0abca71899d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[20.0102473  29.81891568]\n",
      "[16.37388877 25.37679908]\n",
      "[15.97592599 24.29219762]\n",
      "[15.86781636 23.99508458]\n",
      "[15.75506673 23.66873935]\n"
     ]
    }
   ],
   "source": [
    "ball_int_save = ball_int.copy()\n",
    "for i_loop in range(5):\n",
    "    for i in range(2):\n",
    "    \n",
    "        zs = ball_int[:,i].copy()\n",
    "        #f.x = np.array([[zs[0], 0, 0]]).T\n",
    "        f.x = np.zeros((dim_x,1))\n",
    "        f.x[0,0] = zs[0]\n",
    "        mu, cov, _, _ = f.batch_filter(zs)\n",
    "        xs, Ps, Ks,_ = f.rts_smoother(mu, cov)\n",
    "        if i==0:\n",
    "            traj = xs.squeeze()[:,0].copy()\n",
    "            d_ball = xs.squeeze()[:,1].copy()\n",
    "            d2_ball = xs.squeeze()[:,2].copy()\n",
    "        else:\n",
    "            traj = np.vstack((traj, xs.squeeze()[:,0])).T\n",
    "            d_ball = np.vstack((d_ball, xs.squeeze()[:,1])).T\n",
    "            d2_ball = np.vstack((d2_ball, xs.squeeze()[:,2])).T\n",
    "            \n",
    "    deltas = np.abs(traj - ball_int)\n",
    "    thresholds = 5 * np.median(deltas,axis=0)\n",
    "    print(thresholds)\n",
    "    for i in range(2):\n",
    "        ball_int[:,i] = np.where(deltas[:,i] < thresholds[i], ball_int[:,i], traj[:,i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b06cc0d6-d23d-4e01-8c08-40ed887a5334",
   "metadata": {},
   "source": [
    "We can see that after the third iteration valeus of threshlod do not vary anymore. That could be a better termination criteria.\n",
    "\n",
    "Let's plot the error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0c344359-665b-428c-8797-ab1cc858e7e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(traj[:,1] - zs, bins=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40b02f74-c984-46f8-90d8-0e7f3029a4e3",
   "metadata": {},
   "source": [
    "Ok, that is not a pure gaussian but not uggly and outliers are not here any more\n",
    "\n",
    "And on the top of that for free we have an estimate of first and second derivatives\n",
    "\n",
    "Let's have a look at our ball trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d225560b-51d5-400f-bdaf-e5afc4a99813",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1012.7509613984148,\n",
       " 10171.221318917207,\n",
       " -7322.791885084262,\n",
       " -65.50570533424161)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter (traj[:,0], -traj[:,1], c=frames, \n",
    "                   norm = plt.Normalize(vmin=0, vmax=n_frame), cmap=\"nipy_spectral\", s=0.5)\n",
    "plt.axis('equal')\n",
    "plt.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecb6ddf9-3735-462c-9908-9cdc1eedd7a2",
   "metadata": {},
   "source": [
    "## Detection of linear segment"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ddcf818-80ac-4fbc-87be-da24b78c812e",
   "metadata": {},
   "source": [
    "When the ball is moving on the ground it's movment is rectilinear and uniform. Then portions of the trajectory should be linear.\n",
    "To detect them I tried sevral tricks including Hough transform but it seems that RANSAC works best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "57de87b4-dd64-4d25-bc1a-db951e5428fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7ebd3c6f5190>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg = RANSACRegressor(random_state=1, residual_threshold = 50)\n",
    "reg.fit(traj[500:,1].reshape(-1,1), traj[500:,0])\n",
    "\n",
    "plt.scatter(traj[:,0], -traj[:,1],s=0.5)\n",
    "plt.scatter(traj[500:,0][reg.inlier_mask_], -traj[500:,1][reg.inlier_mask_], s=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c47bbe2-d4dc-474c-a3a6-5efa2d0084ce",
   "metadata": {},
   "source": [
    "This exemple (excluding the 500 first frames) is here to show that there is a risk the linear segment includes detections that come too soon or too late.\n",
    "\n",
    "To avoid this situation we eliminate the part of the segment that is isolated. To do that we again use Agglomerative clustering\n",
    "\n",
    "In addition to that it seems RANSAC is not so efficient when the slope is too big so we fit a regressor with both axes as reference. And once points have been attached to a linear segment they are deleted. Wrapping all that together gives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "96a1a354-314a-4a4b-aa6f-5d9067485a4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_ins=[]\n",
    "\n",
    "traj_reg = traj.copy()\n",
    "reg_frames = frames.copy()\n",
    "ins = []\n",
    "long_seg = True\n",
    "i = 0\n",
    "while long_seg:\n",
    "\n",
    "    reg1 = RANSACRegressor(random_state=i, residual_threshold = 50 )\n",
    "    reg1.fit(traj_reg[:,0].reshape(-1,1), traj_reg[:,1])\n",
    "    frames_in_reg_1 = reg_frames[reg1.inlier_mask_]\n",
    "\n",
    "    clustering1 = AgglomerativeClustering(n_clusters=None, linkage='single', \n",
    "                                         distance_threshold=15)\n",
    "    clustering1.fit(frames_in_reg_1.reshape(-1,1))\n",
    "    labs1, n_in_labs1 = np.unique(clustering1.labels_, return_counts=True)\n",
    "    \n",
    "    reg2 = RANSACRegressor(random_state=i, residual_threshold = 50 )\n",
    "    reg2.fit(traj_reg[:,1].reshape(-1,1), traj_reg[:,0])\n",
    "    frames_in_reg_2 = reg_frames[reg2.inlier_mask_]\n",
    "\n",
    "    clustering2 = AgglomerativeClustering(n_clusters=None, linkage='single', \n",
    "                                         distance_threshold=15)\n",
    "    clustering2.fit(frames_in_reg_2.reshape(-1,1))\n",
    "    labs2, n_in_labs2 = np.unique(clustering2.labels_, return_counts=True)\n",
    "    \n",
    "    n_max = max(n_in_labs1.max(), n_in_labs2.max())\n",
    "    long_seg = n_max > 25\n",
    "    \n",
    "    if long_seg:\n",
    "        \n",
    "        if n_in_labs1.max() > n_in_labs2.max():\n",
    "            new_ins = frames_in_reg_1[clustering1.labels_== np.argmax(n_in_labs1)].astype(np.int16)\n",
    "        else:\n",
    "            new_ins = frames_in_reg_2[clustering2.labels_== np.argmax(n_in_labs2)].astype(np.int16)\n",
    "    \n",
    "        ins.append(new_ins)\n",
    "        indexes = np.searchsorted(reg_frames, new_ins)\n",
    "        reg_frames = np.delete(reg_frames, indexes)\n",
    "        traj_reg = np.delete(traj_reg, indexes, axis=0)\n",
    "        i += 1\n",
    "    else:\n",
    "        all_ins = np.hstack(ins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "04b5e2a6-a133-4b22-b1c4-280af3d647ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(traj[:,0], -traj[:,1], s=0.2)\n",
    "plt.scatter(traj[all_ins,0], -traj[all_ins,1], s=0.5)\n",
    "plt.axis('equal')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc02ac02-1167-4669-ae23-8b882ec0ccf3",
   "metadata": {},
   "source": [
    "On top of that we know that eack begining and ending of a linear segment is a vertice. So unless the ball experience a sudden change, the segment that joins verticies will also be included in the trajectory."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e34ba6a-c2c0-4ce1-8645-6a5283b56297",
   "metadata": {},
   "source": [
    "## Peaks of acceleration"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6fb9167-bb55-47e3-94dd-44b5b32851a7",
   "metadata": {},
   "source": [
    "So now we need to detect the points where ball rebunds on the ground (and keep the same direction) or a player (and direction changes).\n",
    "\n",
    "When such rebunds occur, we have peaks in the acceleration of the ball. And remember, Kalman smoothing gave us an estimation of acceleration ! Calculation of curvature seems to be too noisy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3221b366-63d3-42c2-a531-c445e8758f4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "acc = np.linalg.norm(d2_ball, axis=1)\n",
    "peaks, properties = find_peaks(acc, distance= int(0.8*fs), prominence=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4790c13a-ed2a-458b-8056-924110356a7e",
   "metadata": {},
   "source": [
    "The peaks are interesting when the ball is in the air, that will last for a while. This is the reason we eliminate peaks that too clothe from each other or from a linear segment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5fb327c2-7195-402d-8cd7-9894d015f31b",
   "metadata": {},
   "outputs": [],
   "source": [
    "debs = np.sort(np.array([seg[0] for seg in ins]))\n",
    "ends = np.sort(np.array([seg[-1] for seg in ins]))\n",
    "\n",
    "peaks_in = []\n",
    "for end, deb in zip(ends[:-1], debs[1:]):\n",
    "    in_between = np.logical_and(peaks >= end + 8, peaks <= deb - 8)\n",
    "    peaks_in.append(peaks[in_between])\n",
    "new_pts = np.hstack(peaks_in)\n",
    "\n",
    "vertices = np.hstack((debs, ends, new_pts, [0, frames[-1]]))\n",
    "vertices = np.sort(np.unique(vertices)).astype(np.int16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b702fd33-de5e-4611-ad2b-382e97b6a749",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(traj[:,0], -traj[:,1], s=0.2)\n",
    "plt.scatter(traj[all_ins,0], -traj[all_ins,1], s=0.5)\n",
    "plt.plot(traj[vertices,0], -traj[vertices,1], 'r.')\n",
    "plt.axis('equal')\n",
    "plt.axis('off')\n",
    "plt.legend(['detections','linear segments', 'vertices'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02dce484-ef23-4001-9183-80e5045d9bc8",
   "metadata": {},
   "source": [
    "## Final estimation of ball trajectory in radar view"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9e4a68e-b3fd-4f72-b3a8-2cece9bb14aa",
   "metadata": {},
   "source": [
    "Next we assume that when the ball rolls on ground and when it has a ballistic movement, the projection on the ground will be rectilinear with uniform speed.\n",
    "\n",
    "We can see some imperfections :\n",
    "- during the second linear segment there is a vertical control of the ball by one player which is not detected and this will lead to a false speed of the ball\n",
    "- before third linear segment some rebunds are not detected and this will not cause error with the rectilinear assumption"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e81bf1eb-b74a-4cd4-801e-8dd3aae03b58",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = interpolate.interp1d(vertices, traj[vertices], axis=0, fill_value='extrapolate')\n",
    "ball_radar = f(frames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b8b31de6-7fd3-4397-a2e7-9087682bf24b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RzRsLn/LeAJ1GzR4CD8RpAmqXUkuiRNS2ptMGR9S9kW3WwZadBuvaOZwu8DCsDBARUbc4pg38Tb9h/MEnEGItAAJioZm1hhUCD8EwQETUDeypOc9ktuDdz9fhvoKXYbQVwpowGjr/UGD4AoYCieM0ARFRNyhxmWFrjAY97r9tJt4Lfx6/+IxGfrmFZzv0EKwMkBO+yyHqHP7NXMjxmEwMOQshbTEiA/TQjX+e1QEJY2WAnPBdDlHnGA16zBuVyCDQhOMx+b44Crk13vDK2cmNiSSOYYCccOUAEblKakoscpLmoEIfwY2JJI7TBERE1GNW7czGmUO7cRu+Q29DLU9uJFFeYg+AiIjkKzUlFmtqh2KzMBR3XlyKIACoKrZXB9hDIBmcJiAichGT2YJVO7NhMlvEHopkGA16+Oq8sC+3DKtPBuGYWQfhRBp7CCSGYYCIyEXYgNsyRy8SBOBz3IAKfQRQlstAICHsGVA4Losich3+PbXNZLZgzS85iKg4hFk5z0FTkQdcPAbwDeHGRCJjZUDh+E6GyHW4zLBtjimDLaUx+GfvpcCA6fYvcGMi0bGBUOEcSwi5lJCI3MHxWjO43yVYdaQ/ZsUUsalQAjhNQEREbud0avSipcCBjUBADDDzUwYCEbAyQEREbpeaEouq2npUWepROvheBJ3aA5Q3bEzEHgK3Y88AERG5XfMlhxuSlsDSb6r9i+whcDuGAQXhGmgi9+HfW/uaLjn8tjACn0Q+C4x9Fug1+nwPAbkFw4CCcOUAkfvw7619jtUXc0YmYGSiEeP6hWPV8UBYdIHAiXTuQ+BGbCBUEK6BJnIf/r11nqOp8LqgPEz64yn41+RDFRjHpkI3YBggIiJJcASoKks9SrP/g0fLFsO/5hxOhwxHREQk9Fc9wFDQQxgGiIhIUhyhYFZMEQq3rUBVaSEGWvYiO2ICQm7/lJWWHsAwQEREkmUyW5CethUp2e+irLoexwc8jNFjJnAKxsUYBoiISPIsa++E9vA/IQTYtzL+tjACyXGB8NV5MRS4AFcTyBiXNhGRXOivegDqwFhoKvIw2fQxnrW8gYiKQ1yx4SIMAzLGpU1E0sBg7gIxQ+yrCgZMh06jRu+CrZiV8xxuDDtnX5LIx7dbuB2xjPEkRETS4AjmADBvVKLIo/FgMUOA6R/Z9x4oOgZNeS6m136DVUf68/HtJvYMEBH1MO450APysuznMQBQOuIJrM0LbXzjw8e68xgGiIjIM22454KzHTqdDZFVgg7jNAEREXmm4QuAZmc7nDX4XgChnB7tJFYGiIjIc+Vl2c9wWFUMnEwHLp0GTP+IUzOdxMoAERF5rqZNhTvQeLbD9ccD2VTYCVxaKBNcukREihYzBPANaTzb4ayYIoxMNHK6oIMYBmSCewoQSR9Dew8bvsDeTFiei6BfXsW8oqXQ5O/jY94BDAMykZoSyxRMJHEM7T2sycZEAIADG6FePxdnDu3mY94ONhASEbkJm9rcKC8LWDcXQlkujkdcx7MdtoNhgIiI5KmVjYkYCi7EaQIiIpKnJk2FnC5oGysDREQkX02mC06HDEdERCT0Vz1gDwrUiJUBD8SOZCKiDmpoKlQNnI74YB/ojnyDY9++xtfPZhgGPBA7komIOsGxMdHYZ3E6eBiqSguRnrZV7FFJCsOAB+IyQiLPxwqfCGKGICIiEgMtWZh67Cn7FAIBYM8AEZEoeHY9kbCHoEUMA0REIuCeAyLKy8Kxb19DVWkhBlqyoA6MbTwFslIxDBARkeKYzBZs2fo9bjj6FAIs56AaON3eV6BQ7BkgIiLFMRr0qDAOwhtBz+B0yPDGsx0qFcMAEREpUmpKLIKShqJS7Q/hRBqwbq5iAwHDgISx25iIqOcYDXr46rzwpWYyKvQRQHmuffviDfcoLhQwDEgY9xMgIupZjurA5j5LYek31X7hwY1AxkpRx+VuXmIPgFrn2EeA+wkQEfUMR3VgsykK27zuw4qrBQQB53sIFLLCgJUBCTMa9Jg3KpHLjohkjNOB4ktNiYXeS42SylpM/6YaFWp/4ES6onoIGAaIiETE6UDxGQ16LJsxGKXVdThdXIU/HxuGEq8wWMty8d+/34/CV/og/1+rxR5mj+I+A0REIuLmQ9KxePMhrN6dA5tNwBDtSdyl+QEpwu8IRxnqVF6oVAfAMvp5RF5zp9hDdTmGASIiItiD2fs7s/Fbbil6h/vDR6dBn/zvMOn06/CGBRCAM6owVN+3F0kR/mIP16UYBiSC7w6IiKSp9PgeWDbch8DqU/jQdiNWa2/Guj+PkFUgYM+ARHDekIhImoKShiEiOgF61GOIOhuWOitmfvALjp+rEHtoLsOlhRLBZYRERNKmApAcFwj9GQ0sdVZMf383+kb4Y8lNAz2+SsBpAiIiovbs+wJIWwKMeRrHoyZh5ge/oLSyDmq1CgE+Xh4/bcBpAiIiieCeAxL2+1dA2Wng96+QFOGPdX8egct7BcNHp0ZlTR1e3HRQ7BF2C8MAEZFEsHfIcyRF+GPdvJGYMjgGarUaCUY/sYfULewZICKSCPYOSdjAGUDRMfvHJnx0GvhoNfDRaUQamGuwMiAClgKJqCXcglzCmkwTNOWr1SDIVwdfLcMAdRJLgURE8jB5cDQuMvpi8uBosYfSLZwmEAFLgUREHqaVaYLtRwpgE+wfuZqAOoWlQCIiD5O9HajIs39sYDJbUGWpR3JcoMe/ufP4MFB6fA+OvXczSo/vEXsoREQkV4njAP8Y+8cG6zNzsS+3DL46L49/c+fRYaD0+B7UfXE7Lj73Iwq3rRB7OERE3cYGY4nK3g6U59k3HsrLAgCM6xcOtcr+0dN5dBgo2fQ8jNZzKFcHI2z8I2IPh4io29hgLFHDFwABMUB5LpCxEoBzv4Cn89gwYDJbUF5TDwAoC+iDoKRhIo+odUz6RNRRqSmxGJlo9Pg5aNmJGQKMeRoIiAUSx8mqXwDw4DCQnrYVAoAD+ssRNOllsYfTJiZ9IuooNhhLWJO9Btb8koNNv50FAFn8rjx2aeH1BR/Cx/IrquNGwU/CVQGASwmJiGRHaPbRw3lkGCg9vgfq3L1QAagoK4HUd4R2JH0iIvJgDXsNVPS5CSgDJg+OwpwRCWKPyiU8cprg7I/LYRDKAQChqjKRR0NERIrQME1QsucfsllS6OCRYeCX8FkQoAIAeJX9F0j7H5FHRETkWmw8li6jn1Y2SwodPDIMnPW7BKuQev6CnUuBbx8Sb0BERC7GxmMJGjgDCIxDht842SwpdPDIMOCr02Ct763Y4H/7+d6NrE8kUyFgoiei7uISQwn6/SsIZaeRmP+9bJYUOnhkGJgzIgEXh/lhrd8tSPObeD4Q7FwqiUDARE9E3cUlhtJ1rsL+Rk9OvxuPDANGgx7LZgyGQe+F9/wfwHqDvUIgAPZAsO8LUcfHRE9EJEMDZ6BcH4ntXtfIZkmhg0eGAcA5ELxrm44TqosANPx+vlkgaiBgoicikqHfv0KAJR+3+NhPjCenqWCPDQPA+UAwNTkan4Q9hnKV/VzSgmCD7dsHG08mQURE5AoqAIIAbPrtLNb8kiP2cFzGo8MAYA8Ej0zoi4fnzMKbEUtR17CPkspWi/rPpjEQEJFHY0OyhDSsJjgadp39cxlNFXh8GHAwGvS4/7aZ+DjoEVgFFSAAmpoS2D6d4pZAwD9YIuoJbEiWkIZNh6627MRFRl9MHhwt9ohcRjZhALAHgpn3PI6lugfsgU0AVLXlsH02vccDAf9giagnsCFZekyVtdxnQOqMBj1m37MQ76tmnA8ENcXAP//So9+Xf7BE1BPYkCwhDdMEuuSZ3IHQEyRF+GPCfSvwWN19jYFAKDzUo3sQ8A+WiEjmGqYJarK+xH9NVdj02xmxR+QysgwDgD0Q7DZcizfrp5+/UCKbEhERdQZ7kqRFkNnpiwEZhwEAeHf2ZXjXNh0r6qfbqwMABBduSsQ/UCJyB/YkSUTDNEHoyNsweXAUAPnsNSDrMHB5LyM+vD0F71in44gQdz7FuWhTIv6BEpE7sCdJIhqmCfz/+Bq+Oi/syy2Tzeu/rMMAAIzrH4mP5qRgYd08FAsGe4VAsKHunw/gHxu/7laq4x8oEbkDe5KkZ1y/cFk1Eco+DAD2QBB9yXDcUfckauEFCICXUIfU3+7BhtWvdzkQ8A+UiHpMXhaw4Z7GZdGlx/fg2Hs3o/T4HpEHpmAN0wQYOAPbjxTIanmhIsIAACyZNghjx0zAt/FPwqZSAypAi3rcYVqBFZ+uxYptRzscCtgrQKRwzQ7ULV7W3c8zVgIHN9o/AijctgIXn9uCwm0r3PADUosapglq961FlaVeVqcxVkwYcGxbPOPux6GZuhKqhh9di3o8Vvg0ft29A2t253TovtgrQCRxrj4wt3OgbvGy7n4+fAFw6TT7RwCRQ25ApXcEIofc4MIHiroiv9yCfbll8NV5yaYyrJgw4CR5NjB1JVQq+48fiAq8KKzEN/vP4Pi5inZvzl4BIhfqiXfZrj4wt3OgbvGy7n4eMwSY/pH9Y14W/He/Bv+ac8jP+o5VSbFw0yEZSp4NTFkJVcOnSTiFKWWf4emvf2/3puwVIEXxxHfZrj4wt3Wgdmh+WXc/b/r4r5sLlOWiwjsCn+MGViXF0jhNsE5W/QKAksMAYA8Eo55qDAQPazZgUsmnrV6dvQIkOZ098HblNp74LtvVB+bWDtTukLESQnkuSnXheEG3EDvKY5ASH+T+cVCjyAC97KrDyg4DADDmSWDUU42f3lbzJSr2fNbiVdkrQJ3m7nfV7X3eldt44rtsGamIHYUidRher52ObwojkFtajXs/y+zQlCa5WMM0geWS6e1f18MwDADAmCeRjXgAgAqA4Yf7W9y2mL0CMtPdA3FHruPud9Xtfd6V28jpXbanycuCkLYYIdYCXO99EJEB3lAJQJWlHou/Pyz26JSnYZqgZM8/ZPfG0EvsAUhF7Q1vo3jTbQhRme0bE+1cClXwRfapBNinCNZn5iI1JZa9Au6Sl2U/6A1f0NhE5dLPHQdWwH5w6uznQPvXaXqA7YmPjgOrQ3ufd/U2JIrabS/Dv+YsKrVGDEx9Gpsik/H+zmwcOlOOZyZeIvbwFMvop5VdAyHDQIP+V4zBe3+8iVuOPoAAVbU9EHyzwN5PkDy7cYoAAOaNShR1rJLQ0wdqoPsH654+UHfkOp098PJATU3kl1sQBxWK/fsiPmkYAOCZG/qLPCoFGzgDKDqGDL9xsFXZGwiTIvzFHpVLMAw0MXPKjXjkrWK8bnm5oUJgA759EAjri9SUSwHAM6YIWjqwSu1ddUfedUvtXXVX3mUTdVHp8T2w2WzICRyG4Ikvij0cAhqnCa4OTsPxxEmecTzoIPYMNGE06PH0Pbfg7ibbFgu2Wtg+m470tK2umyLwxKVa7m4qAzhXTYpW/v2LiC/NgEajRlBDVYDEJ8BesZHblDErA80kRfjjhL4Pnqy9F69r34cGAlQ1xbh83zNYH9Af85LKuv+u293l76b/l8q7ar6jJmpV6fE9CKk4ChXsy9hIIgbOQEXeIfyAK4HMXFlNGTMMtGDFzMG4e009UAcs174HlQqItJ61l4S2LO18E5nYTWUtXcaDNZFkFW5bgYvrSlDhHYWA8c+LPRxy+P0r+NfkYwTS4NvvIbFH41IMAy0Y1z8Sg2IC8HXe1YirL8B8r83YFzcHIw1617zr5rtqImpD5JAbUJm2D6oxz3BaS4IEQV7NgwCgEgRBEHsQUnT8XAWuf+vfqLcJ8NGqseuJsbKaHyIiaSo9vgfq9XPhX3MOqoHTGfSlZN8XsO5YjPToe5E8ab6sjglsIGxFUoQ/Vt02BCF+Wrw7+zJZ/dKJSKLysqBePxd+Nfmo8I5wrkCS+LK3Q11xBvElv4g9EpfjNEEbxvWPRFb/SLGHQUQKYdn1Dgw151Chj4SQ+imnCKQmcRwqju3CjroBsmsgZGWAiEgidgnJMGnC8Guv+7icUIoaGgj/hJ9ltccAwMoAEZE05GVh9JkPobIW4irVPrFHQy2otdqghX25p05mU8esDBARScGORdCU50LtFwb9VQ+IPRpqwb+9x6BIE45/e48ReyguxzBARCQBtVYbBAC1Yf3ZKyBRwyt3INRagOGVO8QeissxDBARiS0vC/nlFvymT8Em491ij4ZaYaqshQABpspasYficgwDRERi27EIccW/INhPh9FjJog9GmpF8LBbYPaOQvCwW8QeissxDBARiazWagNgb0zjnibSpT+8Af41+dAf3iD2UFyOYYCISEycIvAY+eUWCBCQX24ReyguxzBARCSWvCxg3VzEFWfANyiMUwQSx2kCIiJyudptL0MoOwWbXxh637iQUwQSx2kCIiJyOXu5WYU8fSKXE3oAThMQEZFr5WUhMkCP0yEjEDDxRbFHQx0QMPFFZEf8SZa/L4YBIiIx7FgEXU464oN9eB4CD2GNTMaO/othjUwWeyguxzBARORueVmw5h+AAKFxWSFJX3raVgzc8xjS07aKPRSX44mKiIjcLWMlVJWFKNJE4F/GuzFd7PFQh0yq2ght1U7UVQUBmCz2cFyKYYCIyN0Sx0H4bwZ+i76Xywk9SHXKfJwqrkZYynzIbd0HpwmIiNwpLwtIWwJNRR7GaX/nckIPsjYvFIv0f8XavFCxh+JyDANERO7SsMkQynKBgFhg+AKxR0SdMCumCM9a3sCsmCKxh+JynCYgInKXjJUQynNR4R0B2+SPEMS9BTyKT+b7SDy3FXWZPoDMVoCwMkBE5C6J41Chj8AXvrfJstQsd5t9pyHDdxQ2+04Teygux8oAEZE7NPQK+Necw9jAAwhJiRV7RNRJo8dMwPqA/kiV4e+OlQEiInfYsQgoOw0Vz0PgsYwGPeYllcG45S/2cCcjDANERG4iADilT4Qp8FKxh0JdYDJbcOzb1yAc2AhkrBR7OC7FMEBE1NMa3kWeDhmBj7W3YH1mrsgDoq5Yn5mLz3EDjodPkN1KEPYMEBH1tB2LgOwdiEwYjeheI2U556wEqSmxWI+RCEmZCchsmoeVASKinpSXBZw7AECATqPGvFGJ7BfwYKHlh2D4bj57BoiIqBMyVgKVRUBgPDD2WbFHQ92wPjMXUYf/Bu3hb9gzQEREnZA4Dlb/aGyPuoeNgx4uNSUWZy+5C3WXTJFdzwDDABFRT2nYW0BVngefU+lsHCTJYgMhEVFPaHIeAiEgBmd738XGQQ+3PjMXAw//DdqqnYCXBpj+kdhDchmGASKinpCxEijPAwJjoZn5KabzPAQeLzUlFunld6GuKgh6mU0TqARBEMQeBBGR7Oz7AkhbAox5GkieLfZoiNrEngEiIldr6BUQynJx7JdvYDJbxB4RuYDJbMGGTZtgWXsnlxYSEbXFZLZg1c7sxgNg08+bf022Gs5DUKkLxue4gY2DMiHnpYXsGSCibjOZLVifmWvfoS0zF7uzTQCAeaMSnT4H0Ph/x3VTU2JhNOid7kMum/Loogdxx0EZkXPPAMMAEXVJawHAceBr7aPj/62FhqraevjqvBqvvz4zF+P6hWP7kQLPCAqO8nHiWOjGPot5MYnijodcqiigP8xjJkAv9edhJzEMEFGXtBYAjAY95o06fwBs/rnj/62FhSpL/QWVhIwTJtgEOAUFyYaChvMQIHEswBUEsuJ4zoeWH8L02m/sGw/J5HfMMEBEHda0GtBWAOiI1kKDyWyBb8P3cHBUBqos9dj5RyEyTpiwbMZg6QWChvMQCBBwuqQafmaL9MZIXeZ4Tk7Kfw84+o39QpnsNcClhUTUYat2ZmN3tgkjE42dPvi7gslswWNf7YfZUg+D3kt6gWDDPcCBjSjXh2N54DOI7j9SlMeJelhelr2BUEaVAYYBImpT02oAANGb/CQbCPKy7FMEAEpHPIG1eaHSns6gTpNjk6sDlxYSUZsc86TrM3MbS/livhAaDXosmzEYBr0Xaups0lm25+gVABCUNEz0x4lcz/G3kJ621V4FktFeA+wZIKI2tbQaQGyOQLC+WW+BaBp6BQAWWuVMzj0DrAwQUYscGwQBkOS7XKNB37hEUfRNjDJWApVFQGA8MPZZccdCPaLpFIH+qgeAS6fJ6jTGDANE1KKm0wNSJZkxJo4DAmJQMXIhVh0PFD+ckMs5PddihtgrAjJpHgQ4TUBErZDi9EBzkhhjw3kIUJ6L/KzvsFvfFwC4ikBmnJ5rXE1ARHLmid3Soo+5YTkhAmJQOvkjriJQgg33AAc32qcK2DNARHIjmbJ7J4g+5oYpAox5mqsIZMzpJFvDF8iuZ4DTBETUSBJl904SdcxNpgiQvR1Inu3+MZBbOJ9LY4hsKgIOrAwQkeRXDrSl6bbGbj89csOpiuEbJqt3iXSh1JRYjEw0nu8ZkNk+AwwDRCR+qd0FxPwZasP6cxWBkmSstPcMZKwUeyQuw2kCIvLI6YHm3P4zNDlV8aagO51Ox0zy4zRN4KgCyagaxNUERESdlZcFrJtr7xUYMB2m6/7X41ZhUOeIvmqlhzEMECmY3F7g3PbzfDbNfh4Cv3Dgli9ls9acOkFmew2wZ4BIweTQK9BUT/882w/lY8grW1FU2dAbEDlAFgcC6hin5YUy6xtgzwCRgsmhV6Cpnv55Hl63DwmWYziSX4GrEsfaT1W8M1s2lRVqm5z7BjhNQKQwcpsacKfLX9mCZbWLcI3mN6gTx2FV/OvYnW3CyEQjGwcVQM5/O5wmIFIYuU0NtMSpnOvC+xykzsElqlONlzmtPSfZc+xpYTToZbfXAKcJiBRGblMDLXHeLc4179jX7M7BLOsmhKrLUecXA/3YZ502PCKFcfQMALLYjZBhgEhhlHAAc3XgMZktyDxVgkLbIAzAEfwedQ+uZ+Og4jhNE8isZ4DTBEQK0ROlc6lyKue6wPrMXFxk+QMPqNYhAkW4qDRDUY8n2cl5io2VASKF6InSuVJMDDkL7+JFCBWKUKQJh2HUg3w8Fcip4rRlKacJiMjzKKFXoDlXdX/X7HoX0dZC5KtC8W7Is4gvjlLk46l0TlNsMpsm4NJCIpKtVTuzu730z2S24P/++b9IOfk+vvC7DXuDr8eyGYNlt7SMOkauywtZGSAi2XLFu/f0tK245uT7CLEW4or6vZg48RFZHQSocxzTQ6HlhzC99hvZbEfMMEAkc3J9J9MRrlg5Mdn0MbTWczB7GfGpMBFxv55GqEGvyMeTzgfLSfnvAUe/sV/IngEikjo2unU9EJnMFlSWWxAHFQp8e+M/5otQcroU3jr7S6dSH08lawyYeQ8AXhrZ9AwwDBDJHBvduh6I0tO2ondVLRAyAluMd6G6xIr4EF8kRfgr+vEk2KcGZFARcOA+A0Qy5+o1956oq9sGX1/wIQbU/AqjnxY7zTGoswo4VVKl+MdT6Rx7TJQe3yObLYkZBohkipvinNelQJSXBZw7CBUAU2Udeof7w0utQl29jY+pwjkqTYXbVsjmNMYMA0QyJefd0rqjwyEpYyV864pR4R2FgIkvwkengUoFnKuo5WOqcI5KU9j4R4BLp8mib4A9A0QyxV6BlnWofyAvC7UVRcgPHo6AiS8iKGkYcPQQ9F4axAZ58zFVuPOrVBKBpGFiD8clWBkgkin2CrSsQ/0DOxZBm5OOksparM0LhclswW+5pQCAQXFBfEzJTkanMWYYICJFabr3QIvTBXlZsOYfACAg0McLqSmxeH9nNvafLoUgCPDVatw/aJIky653YPt9Iyy73hF7KN3GMEAkM2wc7JhWeyoyVkJVWYgiTQQyE++H0aDHrznFqLUK8NN7Yc7IBFHGS9Kz2XcaMnxHYbPvNLGH0m0MA0Qyw8bBjnFMF4zrF+4cnhLHweofja+D5mDw0NEAAJ2XGmqVCnEhPpwioEajx0zA78OWYfSYCWIPpdsYBohkpqtr6pXGMV2w/UjB+fCUlwWkLYGm4gwGVGdi+5ECAMDiqQNxde9QLJ46UORRk5QYyw5iXtFSGMsOij2UbmMYIJIZVzcONp126Oz/PUFqSiyS4wJRZalH5Y8vQig7hUqvYOQkzWkMVEkR/lh951AkRfiLPFqSlIyVstlngEsLiWTClSckanpfTZfiAejU/x23dxxURT1hUl6W/UU7cRyQvb3xo3H4AsTX5CHq8N9wpr4AiQAOC/GoMA7ilAC1bfgCWOqt2KybgtFmi0c/XxgGiGSiuyckai0AtLRfQUf/31qQaBoSuv0C2spB/oKPVcXAyXTg1B6gIu/8RwCT6q3QVu1EddzVOFodj+PRsznNQu2LGYJPIp/F7mwTijJzPfrEVSpBEASxB0FE3deVykBLAcDRb+CKg3XT+wfQ+e/lONA7dnhr6aDvOMj7x9gP7q197DUa8A258PZN71sm56YnN8nLgmXXO9jsOw2jx0zw6MoAwwCRh+tsCOjpANCZMc+KKULhthXYUTcAY7UH0HvElJYP9Jc2LN06uLHjB/mWDvo80JMrbbjH/py8dJrHn8GQYYDIw63amd14QO9ImbLp9XssAHSidC+cSEeFPhz+lgLY/KOhKj8DISAaGvOZ8wf6tioDPMiTWJpWrjz8OcgwQOThOlIZaK1c36UA0NqBvukBu4ul++11A+FzKh3V8aMxTvu7LF5kSd5c2bgrJoYBIg/W0ReiTlUP2ntX39qBvmkpv9foLpXuXRpaiNxgw6ZNiDr8N5y95C5MnzxZ7OF0GcMAkQdr7yDvOLhODDmLml3vImz8Iwjy0XbtYO/mRrzOTn8QicGy9k5oD3+DukumQD9rtdjD6TKGASIP1rQRL2j/h0DiOFiObsUuIRlXqfZhl5AMn1PpiPWuQXzpnrYb8TrakOem0j2rBOQRZNI3wDBA5MFKj+9B4bYVuMinBrpT/wL8Y2Ary4NJEwqjtQhCgL0hrz7hGuj8Q9tuxJNwQx6rBCRZDANEJLbD785E76JtOKHti17eFdgbcgMu0Z3DfzRDcJVqH/R9J0j2AN8ZjirBuH7h2H6kgBUCko4N90A4sBHHwycg5PZPPfZ5yR0IiTzY3ujZOFlUCaO1EokVR6GvzUR+UBjG3Xg1EPOQ/UrJs8UdpAs4zrfgqBAAXdtlkcjlhi/A8QIzPscNiPbgXQhZGSDyYCazBWt25yDCfAiTq/+JElMB4kr2QDVgmr0aIIPyZVPsIyApksPyQoYBIjlpOn/pOKOaDHZHawn7CEgS2DNARJLWfL8AD3+xak4O78ZIBmTSM8AwQCR3jv3Te40+v7UvQwGRa+Rl4di3r9l7BvqP9NgqFRsIieTOsZywqtgeChyXyaC0CXT/1M1E3RIzBCG3f4roJr0snoiVASKlkGk/AZsKSUyOvT7Cxj+CoKRhYg+nyxgGiJRIpv0EbCokdzv19p8QV7wbVbpQ+M39ymP/jhgGiJRMZv0E7B8gd6v9ZCq0OWkAAFXiOOD2jSKPqGvUYg+AiEQ0fIHz+Qp2LLIHhLwsccfVRY7NiQB7lcBktog8IpK7qquegkVjsH9ScVbcwXQDwwCRksUMsfcMjH3WORRkrLQHAg8NBo6mwvWZuWIPhWRubV4o6m0NBfYyz32+cTUBEZ0PBXlZQEaIc5Mh4HFNho5mQk/u7ibpM5ktqLLUw0sFwMMn3NkzQEQtk0GTIXsIqKeYzBY89tV+WOptWGm6G0E1uUBwL+ChfWIPrUs4TUBELXNUC7K3e2w/AacLqKe8ue0P/JJdhJpaKwJs5fYLq0ziDqobOE1ARG1rvmlRVbHHrDzgdAH1lG2HzqGmXsCZ0mqoYbVfaLOKO6huYGWAiNrWVpOhxHF1AfUUx/x6haUOVk3DFJS11qMqZ00xDBBRxzQPBcMXeMyKA04XkKuN7x8BjVqFqlobvg5bAGh0gK0O+GGh2EPrEjYQElHXecimRWwkJFczmS0YuzwdZdX1CPT2wl7dPVDXlgP6AOCp02IPr9NYGSCirvOQTYs4XUCuZjToMXlQNLzUKlTX1sNS77n9AgAbCImoO5rvTyDxJkOe4ZBc6ZHxfbDjaAHOltagBP7wQSXgaxR7WF3CMEBE3ddaKAAktWERVxeQKxkNeoT4aXG2tAYBtgr7hR66vJDTBETkOhJvMuR0AbmaTqMGVIBVsHn0JoSsDBCR6zlCAXC+yVBCUwecLiBXSYkPwW+55Si2BSBAU81pAiKiFklw0yJOF5CrzB+diB8P5iOgshIAYCvLhTovS/TA21lcWkhE7uE410FVMXAy3T6NIHI/AZcckiscP1eByvfGYJBwDFABqsRxwO0bxR5Wp7BngIjco3k/QeI40XsJuBkRuUJShD9yEm5GrcpebK82l4g8os5jGCAi92p+AqSMlaI1GaamxGJkopHTBdR1eVnAZ9MwqfADaFEPCEDWOSuOn6sQe2SdwmkCIhKHY9pg+AL7Rw/YyZCoUV6WfZOtcwcAcwEAAfW+4cioisLrlhnQJ6Rg3byRYo+yw9hASETiaLriQOQmQ/YOUIe1EALgFwFEDoB5xBNYuM6MfEsNkq02sUfaKQwDRCQ+kTct4lJD6pC8LGDdXKDsNJqGgNIRT2D1iSBkppdAAKD3UiMlPkTs0XYKpwmISHocUwiJ4+y9BT1cIWBlgNrkVA0oBPzCnEPAqRKcLq4GAMQG++DyhGDMGZHgUc8lhgEiki7HhkWO3QwdPQY9FAwYCshJS1MCgfHAzE9hCrwUj321HycK7fsLeGoIcOA0ARFJl6OXoGmTYQ/2E3C6gAC02hdQG9Yfm4x3Y7BXbyz+aj/MlnqPDwEOrAwQkWdww6ZFrAwoXAshwOoXgdPaXtgR/WfsKI+BTbD3BNTU2eCtVWPZjMGyeK64NAxYrVbU1dW56u6IOkyr1UKj0Yg9DHIHN/cTkEI0aw50hICPdbfiX+Y4VNTUwd9bi4vD/PDMxEuw/UiBrEKjS8KAIAjIz89HaWmpC4ZE1DVBQUGIjIyESqUSeyjkDj3UT8DqgMK00BxYG9YfS2umY0e5fTOq2GAf9I8OgK9O4/HTAa1xSc+AIwiEh4fD19eXL8bkVoIgoKqqCgUFBQCAqKgokUdEbtFD/QTsG1AARwBwyN4BQIA1IA5rE17B98VRsMCG2GC1LPoBOqLbYcBqtTYGAaPRM0/dSJ7Px8cHAFBQUIDw8HBOGShBD21axDMaytgFPQFAbcJo5AUOg0oF7I6fj49OBMNqq8bFYX6y6QfoiG6HAUePgK+vb7cHQ9QdjudgXV0dw4DSuHDTIqNBj9SUWE4VyEkbqwOW1kzHjrpYaNQqTDZEYfIgACooohrQlMuWFnJqgMTG5yBdEAocZ0bsZIWAUwUy0cbWwaUjnsAj/1bBjHpFTQe0hvsMEJH8OEKBo8kQ6FSTIacKZKCFrYNrw/pjfcBcnPPvD5wEaupKYNB7KWo6oDUMA82MHj0aycnJePPNN8UeipP09HSMGTMGJSUlCAoKEns4RJ6hi02GRoPe5RUBk9mCNbtzUFVnbbzMV6fB5EHRslumJqoLVgeEO1UCThyvhEZ9FpMHRWF03zA+7g0YBrrhk08+wcMPP+zyJZUtBZKRI0fi7NmzCAwMdOn3IpK1tpoMgXb7CVyxzNARAhz711fUnN+LJchXh99yy1BTZ0PGCRPfoXZHK1sHl07+CGvzQlF1sh41dSWy2THQ1RgGPIROp0NkZKTYwyDyXF3oJ+hu74DJbLlg//r+0RGNX3dUBhZ/fxiWehvW7M6Br96L71Y7o43mwPUBc/F9ugCbUIgrLgpmJaANarEHIKbKykrMmTMHBoMBUVFRWL58udPXa2trsXDhQsTExMDPzw/Dhg1Deno6AHvZ/s4770RZWRlUKhVUKhVefPHFdm/n8PPPP2PUqFHw9fVFcHAwrrvuOpSUlOCOO+7Azp078dZbbzXeb05ODtLT06FSqZyqEBs2bMCll14KvV6PhISEC8afkJCAJUuW4K677oK/vz/i4+PxwQcfOP18999/P6KiouDt7Y2EhAQsXbrUZY8vkSQ5QkH2dnuFYMcieyjIy7rgqqkpsRiZaOxy78D6zFzU1NkQG+yDqZdF4+3Zl+GZG/o3/ntkfF8kRfhj2YzBGNUnDFAB6UcL8dhX+2EyW7r7k8pbXhbw2TTgi5vt+wSYzwF+4ahNGIMN/Zbjf2NexUcngnG6uBp6LzXmjEzAvFGJDAKtUHRl4PHHH0daWhq+/vprREZG4umnn0ZmZiaSk5MBAHfeeSdycnLw5ZdfIjo6Gl9//TWuv/56/P777xg5ciTefPNNPP/88zh69CgAwGAwtHu73r17Y9++fRg3bhzuuusuvP322/Dy8kJaWhqsViveeust/PHHHxgwYABefvllAEBYWBhycnKcxp6ZmYmZM2fixRdfxKxZs7B7924sWLAARqMRd9xxR+P1li9fjldeeQVPP/001q9fj/vuuw/XXHMN+vXrh7fffhvffvst1q1bh/j4eJw+fRqnT5/u8cedSBJamjZo1mTYnWWGJrMFVZZ6DO3Vfkna0aNgMlvwW24ZqwTtaWHr4Dx9IlRjnsHzv+pgybfhiouAyYOiFLlMsCu6vR1xTU0NTp48iV69esHb29tV4+pxZrMZRqMRa9aswaxZswAAxcXFiI2NxZ///Gc88MAD6N27N3JzcxEdHd14u2uvvRZDhw7FkiVLWuwZyM7Obvd2t9xyC06dOoVdu3a1OLaWegaaNxDeeuutKCwsxNatWxuvs3DhQnz33Xc4ePAgAHtl4Oqrr8Znn30GwL5TX2RkJF566SXMnz8fDz74IA4ePIiffvpJFsvyPPW5SCJznOugaZNhr9GNTYarjgdid7YJIxONHZoqcPQZVNXWY9/psg7fzlW3l7U2tg4+quktyxMIuYukKgPu3BM8OzsbtbW1GDFiRONlISEh6Nu3LwAgKysLgiCgT58+TrezWCxt7rTYkdvt27cPM2bM6Nb4Dx8+jClTpjhdduWVV+LNN9+E1Wpt3HRn0KBBjV9XqVSIjIxs3Lb3jjvuwPjx49G3b19cf/31mDRpEiZMmNCtcRF5nHaaDFOv+19UWepRVVsPk9nS6mtT84N4cmxgl6YYmlYJIOS0+30VoVlfgAABFd5RKLv+Izz/qw5m1MPgpZblCYTcRVJhwJ0bfbRXELHZbNBoNMjMzLxgNzvHdEBXb+fYOrc7BEG44N18Sz+TVqt1+lylUsFmswEAhgwZgpMnT+KHH37ATz/9hJkzZ+Laa6/F+vXruz0+Io/UQpOhcctfEK+bgm8LI+Cry231tcnx+tU0BHTngGQ06OGr90L60UL8llumzHe6rZxS+KA1Dmv95+LMrzrU1Nmc9gpIivAXe9QeSVJhwJ0bfSQlJUGr1SIjIwPx8fEAgJKSEvzxxx8YNWoULrvsMlitVhQUFODqq69u8T50Oh2sVqvTZR253aBBg7B9+3a89NJLHb7f5vr373/BNMPu3bvRp0+fTm3FGxAQgFmzZmHWrFlITU3F9ddfj+LiYoSEhHT4Pohkp9mmRZPji9C/Soe9ptkwmZ0P8o6KwLh+4QDg0nelqSmxyDhhgqXehvWZrQcR2WklBOTpE7Er9s/YVBQFby0rAa4kqTDQExt9tMZgMODuu+/G448/DqPRiIiICDzzzDNQq+0LLPr06YNbb70Vc+bMwfLly3HZZZehqKgIO3bswMCBAzFx4kQkJCTAbDZj+/btGDx4MHx9fTt0u6eeegoDBw7EggULMH/+fOh0OqSlpWHGjBkIDQ1FQkIC9uzZg5ycHBgMhhYPzI8++iiuuOIKvPLKK5g1axZ++eUXvPvuu1i5cmWHH4MVK1YgKioKycnJUKvV+OqrrxAZGclNjYgcGqYNdFXF6Fv0E0qq6rAFwGVnvsDe6NkYeuW1jcsCAddXNI0GPZbNGGzfrEgp0wUtNAee1vbCx7pbka3tgysMwRhtPN9YyUqAa0gqDLjb66+/DrPZjBtvvBH+/v549NFHUVZW1vj11atXY9GiRXj00UeRl5cHo9GIESNGYOLEiQDsGwHNnz8fs2bNgslkwgsvvIAXX3yx3dv16dMHW7duxdNPP42hQ4fCx8cHw4YNw+zZswEAjz32GObOnYv+/fujuroaJ0+evGDsQ4YMwbp16/D888/jlVdeQVRUFF5++WWnlQTtMRgMePXVV3Hs2DFoNBpcccUV+P777xsDEZHiNZk2qNMF4qzvNFz238/Qu2gLehXtwOkjSYgOWIAzfv16rKLpmC7YnW1qc5rC4zVrDrT6hTdWAj46EQxrrYCLw+xLBGUfiESg2NUEJD98LpI7lB7fA99/3AitrQYAUKkzQm9MgNY3CBj7bKdPmdwRx89VYPH3h/HMxEvk9064pSmBgDgs8n0CRzW9ccVFwfbrcYlgj1J0ZYCIqLOCkoYBN74JbHsBsNXBUF0MnLU3PiP/ABAUD3gHuDQYbD9SAJtg/yibMNBOX8CRoih4e7ES4C4MA0REnZU82/7PcUCrKQfKTtkPapXn7NfJ2wt4aYFrX7JftxvG9QtHxglTY5OiR2snBGwpjUGyIdCpL4B6HsMAEVFXxQwBbm/YvfCCYNAQCjY9BPzfx92qFsimMtDKzoFNQ8BIhgBRMAwQEblC82Dw/ULg3O9AfQ2Q93/2y7s4jeDxlYE2mgMZAqSBYYCIyNVihgD3/tT2NEIngsGm/WfwX1MVNu0/g0cm9HXTD+ECrewcuDlxKUOAxDAMEBH1lDanEZoEgzN7gejLWg8FqmYfpa6FEFCpM6LItzdW629DkKE/Q4DEMAwQEblDS8HgzF6gutj+L3t7q9WCyYOi8WtOCapqrdLeeKi9EJA4FNE8E6MkMQwQEbmbIxh0cBphf9CdyC0x4OCZMvx2uhSD4oIa78pXp5HG+vsmzYEMAZ6Hmw6RbPC5SB6tpWAA+8uzzcsXqwx/waqyoQAAdZPpAn9vLWKDfXB5QrA4oaBJNUAwF6BSF+IUAnwZAjwCw4ALfPLJJ3j44YdRWloq9lA6LCcnB7169cLevXuRnJws9nBcgs9Fko2mwaBhRYJNo0e+T29Uqw3YGftnnPW7BABw+Gw5ThdXAwAuDvNz39kNnUKAvZpRro/CG0HPMAR4IE4TeAhXH7zj4uJw9uxZhIaGdn9wkGe4IBJN0/6CfV8A3/0V6roqRJsPAAAS/3uycQqhdPQTWH0iGpmnSmC21OOxr/b3bCBooS+gVB2C/2ovxqG+9yPaOIghwAMxDDRRW1sLnU7n0d+7o/ej0WgQGRnZ7e/XE+rq6qDVasUeBpE0JM8Gwvq22lsQlH8AjwTFo1ZrwNL66ThgSeyZQNBKCCg29MHfdLfijF8/LJvgpqoEuZyiT083evRo3H///fjrX/+K0NBQjB8/Hm+88QYGDhwIPz8/xMXFYcGCBTCbzU63++STTxAfHw9fX1/cdNNNMJlMTl/Pzs7GlClTEBERAYPBgCuuuAI//fST03USEhKwaNEi3HHHHQgMDMS9997b5lh79eoFALjsssugUqkwevRoAMAdd9yBqVOnYunSpYiOjkafPn0AAJ9//jkuv/xy+Pv7IzIyErfccgsKCgoa7y8nJwcqlQr79u1rvOzQoUOYOHEiDAYDIiIicPvtt6OoqKjx6zabDa+++iqSkpKg1+sRHx+PxYsXtzk+m82Gl19+GbGxsdDr9UhOTsaPP/54wTjWrVuH0aNHw9vbGx988AECAgKwfv16p8dg06ZN8PPzQ0VFRZuPFZHsOCoF9/4EzP4SSBwLxFwBGCKAygIg7/+gy0nDs6XP49mS56DN3481u3Nc9/0bmgOF7O0QzOdQrArCzxiMBbbH8bz/S4gfeKX7pieoRyg6DADAp59+Ci8vL/z8889YtWoV1Go13n77bRw4cACffvopduzYgYULFzZef8+ePbjrrruwYMEC7Nu3D2PGjMGiRYuc7tNsNmPixIn46aefsHfvXlx33XWYPHkyTp065XS9119/HQMGDEBmZiaee+65Nsf5n//8BwDw008/4ezZs9i4cWPj17Zv347Dhw9j27Zt2Lx5MwB7heCVV17B/v378c9//hMnT55s8/TGZ8+exahRo5CcnIxff/0VP/74I86dO4eZM2c2Xuepp57Cq6++iueeew6HDh3CP/7xD0RERLQ5vrfeegvLly/HsmXL8Ntvv+G6667DjTfeiGPHjjl9/yeeeAIPPvggDh8+jJtuugk333wzVq9e7XSd1atXIzU1Ff7+HrwdK1F3tRQMfEIAAJqaYgyy/IollkW44f/movaTqfYDeVflZQGfTQO+uBlC2WmYEIRdtsG40/Io5tQ8gaOaJLx046WYNyqRQcDTCd1UXV0tHDp0SKiuru7uXbndqFGjhOTk5Davs27dOsFoNDZ+Pnv2bOH66693us6sWbOEwMDANu+nf//+wjvvvNP4+UUXXSRMnTq1w2M9efKkAEDYu3ev0+Vz584VIiIiBIvF0ubt//Of/wgAhIqKihbv77nnnhMmTJjgdJvTp08LAISjR48K5eXlgl6vFz788MNOjS86OlpYvHix02VXXHGFsGDBAqfbvfnmm07X2bNnj6DRaIS8vDxBEAShsLBQ0Gq1Qnp6eqs/oyc/F4m6JTdTENbcJAgfjBPqX+stWF8IEGwN/4TXegvCB+PsX8/N7Nz9vd5bEF4IFGwvBAinnrtYmPr020KfpzcLIxb/JMx4/2fhWH55j/5Y5D7S6hnIywIyVgLDF/TIOcFbcvnllzt9npaWhiVLluDQoUMoLy9HfX09ampqUFlZCT8/v8Z3rk2NGDHCqfRdWVmJl156CZs3b8aZM2dQX1+P6urqCyoDzb93Vw0cOPCCPoG9e/fixRdfxL59+1BcXAybzQYAOHXqFPr373/BfWRmZiItLQ0Gg+GCr2VnZ6O0tBQWiwXjxo3r8LjKy8tx5swZXHnllU6XX3nlldi/f7/TZc0fi6FDh+LSSy/FmjVr8OSTT+Kzzz5DfHw8rrnmmg5/fyLFaNJwqMnLwvG1T6KyvBhxahOCK8819hfUn/g38n37YNtFf0VZ8IALlyK20BdQogrG7/VxWFY/E4dwMe66qhfmsxIgO9IKAxkrgYMN5e/pH7nlW/r5+TX+/7///S8mTpyI+fPn45VXXkFISAh27dqFu+++G3V1dQAAoQMrMR9//HFs2bIFy5YtQ1JSEnx8fJCamora2tpWv7erfgbAHkYmTJiACRMm4PPPP0dYWBhOnTqF66677oIxONhsNkyePBmvvvrqBV+LiorCiRMnujw+lcp5D1VBEC64rKXH4p577sG7776LJ598EqtXr8add955we2IqJmYIdg08B2s/vkkLq45hr96rUOgugZ9kQO9UIvYygOYdOivOKeKQHaGL6qmLkJciO+FOwdqjThojcdSy3Tss14MABgQ7Y9nbrjwzQR5PmmFgeELnD+62a+//or6+nosX74carW9nWLdunVO1+nfvz8yMjKcLmv++b///W/ccccdjRUEs9mMnJycbo3N8c7farW2e90jR46gqKgI//M//4O4uDgA9p+tLUOGDMGGDRuQkJAAL68Lnxa9e/eGj48Ptm/fjnvuuadD4wsICEB0dDR27drl9I5+9+7dGDp0aLs/x2233YaFCxfi7bffxsGDBzF37tx2b0NEwJwRCfhm7xn8brkY99qeQnJ0EG7x2Y2xp1dCLdQjzFqKMKEUghUo3nArKrw0MNTbG6HNXkac0PTC/+JmHNIkQqUHBvh6wVfnhSVTB4r8k1FPkVYYiBnitopASxITE1FfX4933nkHkydPxs8//4z333/f6ToPPvggRo4ciddeew1Tp07F1q1bnaYIACApKQkbN27E5MmToVKp8NxzzzWW6bsqPDwcPj4++PHHHxEbGwtvb28EBga2eN34+HjodDq88847mD9/Pg4cOIBXXnmlzfv/y1/+gg8//BCzZ8/G448/jtDQUBw/fhxffvklPvzwQ3h7e+OJJ57AwoULodPpcOWVV6KwsBAHDx7E3Xff3er4Hn/8cbzwwgtITExEcnIyVq9ejX379uHvf/97uz9zcHAwpk2bhscffxwTJkxAbGxslx47IqUxGvT4aO7leOHbg+gfHdBQ1h8J4LHGqYBqcwkqC04iRCgB6oFCBOEYErDSejNydf0QG+yD6WLtakju192mA09u2ho1apTw0EMPOV32xhtvCFFRUYKPj49w3XXXCWvWrBEACCUlJY3X+fjjj4XY2FjBx8dHmDx5srBs2TKnBsKTJ08KY8aMEXx8fIS4uDjh3XffveB7XXTRRcKKFSs6Nd4PP/xQiIuLE9RqtTBq1ChBEOwNhFOmTLnguv/4xz+EhIQEQa/XCyNGjBC+/fZbpwa/lhr+/vjjD+Gmm24SgoKCBB8fH6Ffv37Cww8/LNhsNkEQBMFqtQqLFi0SLrroIkGr1Qrx8fHCkiVL2hyf1WoVXnrpJSEmJkbQarXC4MGDhR9++MHpsWo+jqa2b98uABDWrVvX7uPjyc9FIjGUHMsQTrwxQTi+fILw8dr1wqLNB4VFmw8Kb2w9IhRV1Ig9PHIjbkesUEePHkW/fv1w7NgxJCUliT2cVv3973/HQw89hDNnzrS7mRKfi0REXSOtaQJyi+LiYqxfvx4BAQGNPQVSU1VVhZMnT2Lp0qWYN2+eaDtDEhEpgeI3HZKKJUuWwGAwtPjvT3/6k0u/1913341Vq1bhvffeg14vzbnA1157DcnJyYiIiMBTTz0l9nCIiGSN0wQSUVxcjOLi4ha/5uPjg5iYGDePyPPwuUhE1DWcJpCIkJAQhISEiD0MIiJSIJdNE3SzwEDUbXwOEhF1TbfDgONUs1VVVd0eDFF3OJ6DPP0xEVHndHuaQKPRICgoqPH0uL6+vtwyltxKEARUVVWhoKAAQUFB0Gg0Yg+JiMijdLuBELC/GOfn56O0tNQFQyLqmqCgIERGRjKMEhF1kkvCgIPVam08oQ+RO2m1WlYEiIi6yKVhgIiIiDwPNx0iIiJSOIYBIiIihWMYICIiUjiGASIiIoVjGCAiIlI4hgEiIiKFYxggIiJSOIYBIiIihWMYICIiUjiGASIiIoVjGCAiIlI4hgEiIiKFYxggIiJSOIYBIiIihft/uAXMH70bK1QAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(traj[:,0], -traj[:,1], s=0.2)\n",
    "plt.scatter(ball_radar[:,0], -ball_radar[:,1], s=0.5)\n",
    "plt.axis('equal')\n",
    "plt.axis('off')\n",
    "plt.legend(['detections','radar_trajectory'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a52e612c-c8f6-4e44-862f-47df9402f8ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'y')"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "ax1.plot(frames, traj[:,0])\n",
    "ax1.plot(frames, ball_radar[:,0])\n",
    "ax1.set_title('x')\n",
    "ax2.plot(frames, traj[:,1])\n",
    "ax2.plot(frames, ball_radar[:,1])\n",
    "ax2.set_title('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39ac4450-74d5-43cb-bcaf-9f3288de9488",
   "metadata": {},
   "source": [
    "In these plots, just after frame 200, we can see the error induce when missing the detection of the vertical control by one player"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "5b014db4-0ebb-4348-b2ff-34ec9e2c958d",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save(source_video_path[:-4] + '_ball_radar.npy', ball_radar)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6d9eee6-d274-4864-a71c-692f826d6f02",
   "metadata": {},
   "source": [
    "The result has been included in a video available here https://drive.google.com/file/d/1FJvpVmD1kMLt1hgrkiUTy1bgqHvTp-e8/view?usp=sharing\n",
    "\n",
    "I hope this will be useful for you.\n",
    "\n",
    "I am a teacher at ENSTA Paris (Fance) and an independant consultant, if you have similar problems and think I can help : eric.fenaux@gmail.com"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "420cc6bb-fd09-4d7c-935c-50fa114a1f66",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}