bump_detect.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import cv2\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from tqdm import tqdm_notebook\n",
    "import av\n",
    "from av.video.stream import VideoStream\n",
    "import numpy as np\n",
    "import tqdm\n",
    "from sklearn.model_selection import cross_val_score\n",
    "import os\n",
    "import catboost\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_stats_for_file(array_file):\n",
    "    array_file = np.array(array_file)\n",
    "\n",
    "    minim_mean = array_file.mean() - array_file.min()\n",
    "    maxim_mean = array_file.max() - array_file.mean()\n",
    "    std = array_file.std()\n",
    "\n",
    "    diff = np.diff(array_file , n = 1)\n",
    "    min_max_1 = diff.max() - diff.min()\n",
    "    std_diff_1 = diff.std()\n",
    "\n",
    "    diff = np.diff(array_file , n = 2)\n",
    "    min_max_2 = diff.max() - diff.min()\n",
    "    std_diff_2 = diff.std()\n",
    "\n",
    "    diff = np.diff(array_file , n = 3)\n",
    "    min_max_3 = diff.max() - diff.min()\n",
    "    std_diff_3 = diff.std()\n",
    "\n",
    "    return [minim_mean , maxim_mean , std, min_max_1 , std_diff_1 , min_max_2 , std_diff_2 ,min_max_3 , std_diff_3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def print_image(frame):\n",
    "    r = 1000.0 / frame.shape[1]\n",
    "    dim = (1000, int(frame.shape[0] * r))\n",
    "    resized = cv2.resize(frame, dim, interpolation = cv2.INTER_AREA)\n",
    "\n",
    "    cv2.imshow('frame',resized)\n",
    "    k = cv2.waitKey(30) & 0xff\n",
    "    if k == ord('q'):\n",
    "        return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "path = 'trainset/'\n",
    "files = [video for video in os.listdir(path) if \".avi\" in video and \"._\" not in video]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "real_answ = pd.DataFrame.from_csv(\"train.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9a714e003dc44f7696e570dcbfa35e9a"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File: akn.078.031.left.avi\n",
      "\n"
     ]
    }
   ],
   "source": [
    "all_diff_norm = []\n",
    "all_diff_x = []\n",
    "all_diff_y = []\n",
    "for file in tqdm_notebook(files[3:4]):\n",
    "    input_container = av.open(path + file)\n",
    "    input_packets = input_container.demux()\n",
    "    point_file = file[:-8]+'txt'\n",
    "    y,x = open(path+point_file, 'r').readline().split(' ')\n",
    "    x,y = int(x), int(y)\n",
    "    diff_dist = []\n",
    "    diff_x = []\n",
    "    diff_y = []\n",
    "    num = 0\n",
    "    for packet in input_packets:\n",
    "        frames = packet.decode()\n",
    "        for raw_frame in frames:\n",
    "            num+=1\n",
    "            if (num<10):\n",
    "                continue\n",
    "            frame = raw_frame.to_rgb().to_nd_array()\n",
    "            frame =  cv2.cvtColor(frame, cv2.COLOR_RGB2BGR)\n",
    "            frame = frame[x - 100 : x + 200 , y - 100 : y + 100]\n",
    "            if (num % 300) == 0:\n",
    "                all_diff_norm.append(diff_dist)\n",
    "                all_diff_x.append(diff_x)\n",
    "                all_diff_y.append(diff_y)\n",
    "            if (num % 10) == 0:\n",
    "                # params for ShiTomasi corner detection\n",
    "                feature_params = dict( maxCorners = 100,\n",
    "                                    qualityLevel = 0.3,\n",
    "                                    minDistance = 7,\n",
    "                                    blockSize = 7 )\n",
    "\n",
    "                # Parameters for lucas kanade optical flow\n",
    "                lk_params = dict( winSize  = (10,10),\n",
    "                               maxLevel = 2,\n",
    "                               criteria = (cv2.TERM_CRITERIA_EPS | cv2.TERM_CRITERIA_COUNT, 10, 0.03))\n",
    "\n",
    "                # Create some random colors\n",
    "                color = np.random.randint(0,255,(100,3))\n",
    "                # Take first frame and find corners in it\n",
    "                old_frame = frame\n",
    "                old_gray = cv2.cvtColor(old_frame, cv2.COLOR_BGR2GRAY)\n",
    "                p0 = cv2.goodFeaturesToTrack(old_gray, mask = None, **feature_params)\n",
    "\n",
    "                # Create a mask image for drawing purposes\n",
    "                mask = np.zeros_like(old_frame)\n",
    "\n",
    "            else:\n",
    "                try:\n",
    "                    frame_gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)\n",
    "                    # calculate optical flow\n",
    "                    p1, st, err = cv2.calcOpticalFlowPyrLK(old_gray, frame_gray, p0, None, **lk_params)\n",
    "                    # Select good points\n",
    "                    good_new = p1[st==1]\n",
    "                    good_old = p0[st==1]\n",
    "\n",
    "                    diff_dist.append(np.mean(np.linalg.norm(good_new-good_old, axis = 1)))\n",
    "                    diff_x.append(np.mean(good_new[:, 0] - good_old[:, 0]))\n",
    "                    diff_y.append(np.mean(good_new[:, 1] - good_old[:, 1]))\n",
    "\n",
    "                    # draw the tracks\n",
    "                    for i,(new,old) in enumerate(zip(good_new,good_old)):\n",
    "                        a,b = new.ravel()\n",
    "                        c,d = old.ravel()\n",
    "                        mask = cv2.line(mask, (a,b),(c,d), color[i].tolist(), 2)\n",
    "                        frame = cv2.circle(frame,(a,b),5,color[i].tolist(),-1)\n",
    "                    img = cv2.add(frame,mask)\n",
    "                    #print_image(img)\n",
    "                    # Now update the previous frame and previous points\n",
    "                    old_gray = frame_gray.copy()\n",
    "                    p0 = good_new.reshape(-1,1,2)\n",
    "                except Exception:\n",
    "                        print(\"Some error\")\n",
    "                        pass\n",
    "    print (\"File:\", file)\n",
    "np.save(\"all_diff_norm\",all_diff_norm)\n",
    "np.save(\"all_diff_x\",all_diff_x)\n",
    "np.save(\"all_diff_y\",all_diff_y)\n",
    "    #cv2.destroyAllWindows()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12068b160>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lOHwDhZIHdTL6YYTlToDppTQ9o2vP5evJw9fjszp9eO56sw6pRV+bKoSe0XQx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\nzTElubgta0wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1228f99b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(diff_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x121e40438>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GwHUK7/nik/j599/T9u/UDwbQY2nNYuy6b3rv948mizCOEcYyeUoFSrbMQa83rnGc4H/8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\n42A3M8uMg93MLDMOdjOzzDjYzcwy8y82Gk/QuDd4fwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120697668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(diff_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_diff_norm = np.load('all_diff_norm.npy')\n",
    "all_diff_x = np.load('all_diff_x.npy')\n",
    "all_diff_y = np.load('all_diff_y.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>file_name</th>\n",
       "      <th>bridge</th>\n",
       "      <th>city_entry</th>\n",
       "      <th>city_exit</th>\n",
       "      <th>road_bump</th>\n",
       "      <th>screen_wipers</th>\n",
       "      <th>zebra</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>akn.022.008.left.avi</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>akn.031.029.left.avi</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>akn.031.037.left.avi</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>akn.078.031.left.avi</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>akn.082.013.left.avi</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              file_name  bridge  city_entry  city_exit  road_bump  \\\n",
       "0  akn.022.008.left.avi       0           0          0          1   \n",
       "1  akn.031.029.left.avi       0           0          0          1   \n",
       "2  akn.031.037.left.avi       0           0          0          1   \n",
       "3  akn.078.031.left.avi       0           0          1          0   \n",
       "4  akn.082.013.left.avi       0           0          1          0   \n",
       "\n",
       "   screen_wipers  zebra  \n",
       "0              0      0  \n",
       "1              0      1  \n",
       "2              1      1  \n",
       "3              0      0  \n",
       "4              0      0  "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real_answ.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#best rand_seed = 77612067520192\n",
    "def train_cat_boost(graphs_chan_1, graphs_chan_2, graphs_chan_3, class_name = 'bridge'):\n",
    "    model = catboost.CatBoostClassifier(random_seed=77612067520192)\n",
    "    for_xgb_train = []\n",
    "    for i in range(len(graphs_chan_1)):\n",
    "        for_xgb_train.append(np.hstack((get_stats_for_file(graphs_chan_1[i]), get_stats_for_file(graphs_chan_3[i]))))\n",
    "    for_xgb_train = np.array(for_xgb_train)\n",
    "    data = pd.DataFrame(for_xgb_train)\n",
    "    data[\"res\"] = real_answ[class_name]\n",
    "    a = cross_val_score(model, data.drop(\"res\", axis=1), data[\"res\"].values, cv = 2, scoring='roc_auc')\n",
    "    print( a.mean(), a.std())\n",
    "    model.fit(data.drop([\"res\"] , axis=1) , data[\"res\"].values)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.865824503906 0.0294457663644\n"
     ]
    }
   ],
   "source": [
    "model = train_cat_boost(all_diff_norm, all_diff_x, all_diff_y, class_name = 'road_bump')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model.save_model(\"model_road_bump\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "path = 'validationset/'\n",
    "files = [video for video in os.listdir(path) if \".avi\" in video and \"._\" not in video]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ea96cb14ab9e4aee97080025d7c28246"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File: akn.031.008.left.avi\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/envs/open_cv/lib/python3.5/site-packages/numpy/core/fromnumeric.py:2909: RuntimeWarning: Mean of empty slice.\n",
      "  out=out, **kwargs)\n",
      "/anaconda/envs/open_cv/lib/python3.5/site-packages/numpy/core/_methods.py:80: RuntimeWarning: invalid value encountered in true_divide\n",
      "  ret = ret.dtype.type(ret / rcount)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.031.041.left.avi\n",
      "File: akn.048.067.left.avi\n",
      "File: akn.078.047.left.avi\n",
      "File: akn.079.064.left.avi\n",
      "File: akn.081.021.left.avi\n",
      "File: akn.081.054.left.avi\n",
      "File: akn.082.001.left.avi\n",
      "File: akn.084.020.left.avi\n",
      "File: akn.090.121.left.avi\n",
      "File: akn.112.004.left.avi\n",
      "File: akn.113.142.left.avi\n",
      "File: akn.131.019.left.avi\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.132.075.left.avi\n",
      "File: akn.136.038.left.avi\n",
      "File: akn.136.059.left.avi\n",
      "File: akn.136.213.left.avi\n",
      "File: akn.136.274.left.avi\n",
      "File: akn.139.044.left.avi\n",
      "Some error\n",
      "Some error\n",
      "File: akn.145.038.left.avi\n",
      "File: akn.145.141.left.avi\n",
      "File: akn.151.155.left.avi\n",
      "File: akn.152.144.left.avi\n",
      "File: akn.160.015.left.avi\n",
      "File: akn.160.030.left.avi\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.160.215.left.avi\n",
      "File: akn.160.227.left.avi\n",
      "File: akn.160.230.left.avi\n",
      "Some error\n",
      "Some error\n",
      "File: akn.160.370.left.avi\n",
      "File: akn.160.379.left.avi\n",
      "File: akn.165.068.left.avi\n",
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      "File: akn.178.106.left.avi\n",
      "File: akn.178.218.left.avi\n",
      "File: akn.179.103.left.avi\n",
      "File: akn.182.002.left.avi\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
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      "Some error\n",
      "Some error\n",
      "File: akn.182.004.left.avi\n",
      "File: akn.182.062.left.avi\n",
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      "File: akn.184.109.left.avi\n",
      "File: akn.184.110.left.avi\n",
      "File: akn.184.150.left.avi\n",
      "Some error\n",
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      "File: akn.185.062.left.avi\n",
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      "Some error\n",
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      "Some error\n",
      "Some error\n",
      "File: akn.185.171.left.avi\n",
      "File: akn.186.054.left.avi\n",
      "File: akn.186.063.left.avi\n",
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      "File: akn.187.029.left.avi\n",
      "File: akn.187.170.left.avi\n",
      "File: akn.189.245.left.avi\n",
      "Some error\n",
      "Some error\n",
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      "File: akn.189.249.left.avi\n",
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      "File: akn.220.010.left.avi\n",
      "File: akn.220.031.left.avi\n",
      "File: akn.222.004.left.avi\n",
      "Some error\n",
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      "File: akn.223.010.left.avi\n",
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      "File: akn.241.044.left.avi\n",
      "File: akn.241.109.left.avi\n",
      "File: akn.241.130.left.avi\n",
      "Some error\n",
      "Some error\n",
      "File: akn.241.131.left.avi\n",
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      "File: akn.244.272.left.avi\n",
      "File: akn.245.047.left.avi\n",
      "File: akn.246.009.left.avi\n",
      "Some error\n",
      "Some error\n",
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      "File: akn.246.061.left.avi\n",
      "File: akn.249.032.left.avi\n",
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      "File: akn.263.023.left.avi\n",
      "File: akn.266.392.left.avi\n",
      "File: akn.267.150.left.avi\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.268.054.left.avi\n",
      "File: akn.268.082.left.avi\n",
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      "File: akn.269.097.left.avi\n",
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      "File: akn.275.080.left.avi\n",
      "File: akn.276.214.left.avi\n",
      "File: akn.276.240.left.avi\n",
      "Some error\n",
      "File: akn.276.246.left.avi\n",
      "File: akn.277.119.left.avi\n",
      "File: akn.278.125.left.avi\n",
      "File: akn.279.014.left.avi\n",
      "File: akn.279.020.left.avi\n",
      "File: akn.279.027.left.avi\n",
      "File: akn.279.032.left.avi\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.279.044.left.avi\n",
      "File: akn.279.235.left.avi\n",
      "File: akn.282.018.left.avi\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
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      "Some error\n",
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      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.282.069.left.avi\n",
      "File: akn.283.210.left.avi\n",
      "File: akn.289.007.left.avi\n",
      "Some error\n",
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      "File: akn.289.046.left.avi\n",
      "Some error\n",
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      "Some error\n",
      "Some error\n",
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      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.289.047.left.avi\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.289.055.left.avi\n",
      "File: akn.289.063.left.avi\n",
      "File: akn.289.068.left.avi\n",
      "File: akn.289.109.left.avi\n",
      "File: akn.292.002.left.avi\n",
      "File: akn.295.193.left.avi\n",
      "File: akn.308.095.left.avi\n",
      "Some error\n",
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      "File: akn.343.101.left.avi\n",
      "Some error\n",
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      "File: akn.344.029.left.avi\n",
      "Some error\n",
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      "File: akn.344.046.left.avi\n",
      "Some error\n",
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      "File: akn.344.074.left.avi\n",
      "Some error\n",
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      "File: akn.344.090.left.avi\n",
      "Some error\n",
      "File: akn.345.037.left.avi\n",
      "Some error\n",
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      "File: akn.345.074.left.avi\n",
      "File: akn.345.215.left.avi\n",
      "Some error\n",
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      "Some error\n",
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      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "Some error\n",
      "File: akn.346.244.left.avi\n",
      "File: akn.389.020.left.avi\n",
      "File: akn.389.270.left.avi\n",
      "File: akn.390.126.left.avi\n",
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      "File: akn.394.005.left.avi\n",
      "File: akn.394.111.left.avi\n",
      "File: akn.394.115.left.avi\n",
      "File: akn.394.163.left.avi\n",
      "File: akn.394.210.left.avi\n",
      "File: akn.394.216.left.avi\n",
      "File: akn.398.102.left.avi\n",
      "File: akn.419.006.left.avi\n",
      "File: akn.419.022.left.avi\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File: akn.421.450.left.avi\n",
      "File: akn.425.139.left.avi\n",
      "File: akn.430.048.left.avi\n",
      "\n",
      "CPU times: user 18min 18s, sys: 4min 13s, total: 22min 32s\n",
      "Wall time: 15min 53s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "all_diff_norm = []\n",
    "all_diff_x = []\n",
    "all_diff_y = []\n",
    "for file in tqdm_notebook(files):\n",
    "    input_container = av.open(path + file)\n",
    "    input_packets = input_container.demux()\n",
    "    point_file = file[:-8]+'txt'\n",
    "    y,x = open(path+point_file, 'r').readline().split(' ')\n",
    "    x,y = int(x), int(y)\n",
    "    diff_dist = []\n",
    "    diff_x = []\n",
    "    diff_y = []\n",
    "    num = 0\n",
    "    for packet in input_packets:\n",
    "        frames = packet.decode()\n",
    "        for raw_frame in frames:\n",
    "            num+=1\n",
    "            if (num<10):\n",
    "                continue\n",
    "            frame = raw_frame.to_rgb().to_nd_array()\n",
    "            frame =  cv2.cvtColor(frame, cv2.COLOR_RGB2BGR)\n",
    "            frame = frame[x - 100 : x + 200 , y - 100 : y + 100]\n",
    "        \n",
    "            if (num % 10) == 0:\n",
    "                # params for ShiTomasi corner detection\n",
    "                feature_params = dict( maxCorners = 100,\n",
    "                                    qualityLevel = 0.3,\n",
    "                                    minDistance = 7,\n",
    "                                    blockSize = 7 )\n",
    "\n",
    "                # Parameters for lucas kanade optical flow\n",
    "                lk_params = dict( winSize  = (10,10),\n",
    "                               maxLevel = 2,\n",
    "                               criteria = (cv2.TERM_CRITERIA_EPS | cv2.TERM_CRITERIA_COUNT, 10, 0.03))\n",
    "\n",
    "                # Create some random colors\n",
    "                color = np.random.randint(0,255,(100,3))\n",
    "                # Take first frame and find corners in it\n",
    "                old_frame = frame\n",
    "                old_gray = cv2.cvtColor(old_frame, cv2.COLOR_BGR2GRAY)\n",
    "                p0 = cv2.goodFeaturesToTrack(old_gray, mask = None, **feature_params)\n",
    "\n",
    "                # Create a mask image for drawing purposes\n",
    "                mask = np.zeros_like(old_frame)\n",
    "\n",
    "            else:\n",
    "                try:\n",
    "                    frame_gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)\n",
    "                    # calculate optical flow\n",
    "                    p1, st, err = cv2.calcOpticalFlowPyrLK(old_gray, frame_gray, p0, None, **lk_params)\n",
    "                    # Select good points\n",
    "                    good_new = p1[st==1]\n",
    "                    good_old = p0[st==1]\n",
    "\n",
    "                    diff_dist.append(np.mean(np.linalg.norm(good_new-good_old, axis = 1)))\n",
    "                    diff_x.append(np.mean(good_new[:, 0] - good_old[:, 0]))\n",
    "                    diff_y.append(np.mean(good_new[:, 1] - good_old[:, 1]))\n",
    "\n",
    "                    # draw the tracks\n",
    "                    for i,(new,old) in enumerate(zip(good_new,good_old)):\n",
    "                        a,b = new.ravel()\n",
    "                        c,d = old.ravel()\n",
    "                        mask = cv2.line(mask, (a,b),(c,d), color[i].tolist(), 2)\n",
    "                        frame = cv2.circle(frame,(a,b),5,color[i].tolist(),-1)\n",
    "                    img = cv2.add(frame,mask)\n",
    "                    #print_image(img)\n",
    "                    # Now update the previous frame and previous points\n",
    "                    old_gray = frame_gray.copy()\n",
    "                    p0 = good_new.reshape(-1,1,2)\n",
    "                except Exception:\n",
    "                        print(\"Some error\")\n",
    "                        pass\n",
    "    all_diff_norm.append(diff_dist)\n",
    "    all_diff_x.append(diff_x)\n",
    "    all_diff_y.append(diff_y)\n",
    "    print (\"File:\", file)\n",
    "np.save(\"all_diff_norm_val\",all_diff_norm)\n",
    "np.save(\"all_diff_x_val\",all_diff_x)\n",
    "np.save(\"all_diff_y_val\",all_diff_y)\n",
    "    #cv2.destroyAllWindows()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_diff_norm = np.load('all_diff_norm_val.npy')\n",
    "all_diff_x = np.load('all_diff_x_val.npy')\n",
    "all_diff_y = np.load('all_diff_y_val.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = catboost.CatBoostClassifier().load_model(\"model_road_bump\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_binary(class_name):\n",
    "    if (class_name == 'bridge'):\n",
    "        return '100000'\n",
    "    elif (class_name == 'city_entry'):\n",
    "        return '010000'\n",
    "    elif (class_name == 'city_exit'):\n",
    "        return '001000'\n",
    "    elif (class_name == 'road_bump'):\n",
    "        return '000100'\n",
    "    elif (class_name == 'screen_wipers'):\n",
    "        return '000010'\n",
    "    elif (class_name == 'zebra'):\n",
    "        return '000001'\n",
    "    else:\n",
    "        print(\"Error\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#92\n",
    "def test_model(graphs_chan_1, graphs_chan_2, graphs_chan_3, class_name = 'road_bump', model=model):\n",
    "    binary_class = get_binary(class_name)\n",
    "    for_xgb_test = []\n",
    "    for i in range(len(all_diff_norm)):\n",
    "        for_xgb_test.append(np.hstack((get_stats_for_file(graphs_chan_1[i]), get_stats_for_file(graphs_chan_3[i]))))\n",
    "    sub = pd.DataFrame(files)\n",
    "    sub.columns = [\"file_name\"]\n",
    "    sub['road_bump'] = model.predict_proba(for_xgb_test)[:,1]\n",
    "\n",
    "    for i in sub.values:\n",
    "        if (i[1]>=0.82):\n",
    "            sub.loc[sub.file_name == i[0], \"road_bump\"] = '000100'\n",
    "        else:\n",
    "            sub.loc[sub.file_name == i[0], \"road_bump\"] = '000000'\n",
    "\n",
    "    sub.to_csv('4.txt' , sep = ' ' , header=None , index=None)\n",
    "    print (sub[sub['road_bump'] == binary_class].shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19\n"
     ]
    }
   ],
   "source": [
    "sub = test_model(all_diff_norm_val, all_diff_x_val, all_diff_y_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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