Added Smoothing methods

Face Mesh - Video.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 38,
    "id": "ddaddef7",
    "metadata": {},
    "outputs": [],
@@ -17,6 +17,14 @@
     "from varname import nameof\n",
     "import matplotlib.pyplot as plt\n",
     "\n",
+    "# single exponential smoothing\n",
+    "from statsmodels.tsa.holtwinters import SimpleExpSmoothing\n",
+    "\n",
+    "from scipy.signal import savgol_filter\n",
+    "\n",
+    "from statsmodels.nonparametric.kernel_regression import KernelReg\n",
+    "\n",
+    "\n",
     "mp_face_mesh = mp.solutions.face_mesh\n",
     "face_mesh = mp_face_mesh.FaceMesh(min_detection_confidence=0.5, min_tracking_confidence=0.5)\n",
     "\n",
@@ -244,7 +252,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "afaa8cf4",
+   "id": "76fa937f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -262,7 +270,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "a8563fbf",
+   "id": "c253af13",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -288,7 +296,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "281362d2",
+   "id": "39c681f9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -310,7 +318,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "3f5e2e86",
+   "id": "67d7552f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -336,7 +344,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "dbcdcd78",
+   "id": "c02d4191",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -361,10 +369,135 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "id": "3b2327ad",
+   "execution_count": 40,
+   "id": "60e94db4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def smoothing(list_considered):\n",
+    "        \n",
+    "    count = 0\n",
+    "    frame_count, yaw, pitch, roll = [], [], [], []\n",
+    "    \n",
+    "    for record in list_considered:\n",
+    "        count += 1\n",
+    "        frame_count.append(count)\n",
+    "        yaw.append(record[0])\n",
+    "        pitch.append(record[1])\n",
+    "        roll.append(record[2])\n",
+    "      \n",
+    "    \n",
+    "    single_exponential_smoothing(yaw, frame_count)\n",
+    "    \n",
+    "    savgol_filtering_smoothing(yaw, frame_count)\n",
+    "    \n",
+    "    kernel_regression_smoothing(yaw, frame_count)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "9b26ec2e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def single_exponential_smoothing(list_considered, frame_count):   \n",
+    "    # create class\n",
+    "    model = SimpleExpSmoothing(list_considered)\n",
+    "   \n",
+    "    # fit model\n",
+    "    model_fit = model.fit()\n",
+    "     \n",
+    "    # make prediction\n",
+    "    yhat = model_fit.predict()\n",
+    "    \n",
+    "    print(yhat)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "id": "1c147f94",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "def savgol_filtering_smoothing(list_considered, frame_count):\n",
+    "    x = frame_count\n",
+    "    y = list_considered\n",
+    "    \n",
+    "    #filter size = 15 to consider half a second\n",
+    "    yhat = savgol_filter(y, 15, 3)\n",
+    "\n",
+    "    plt.plot(x, y, color='green')\n",
+    "    plt.plot(x, yhat, color='red')\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "id": "4e99b996",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def kernel_regression_smoothing(list_considered, frame_count):\n",
+    "    x = frame_count\n",
+    "    y = list_considered\n",
+    "    \n",
+    "    kr = KernelReg(y,x,'c')\n",
+    "    plt.plot(x, y, '+')\n",
+    "    y_pred, y_std = kr.fit(y)\n",
+    "\n",
+    "    plt.plot(x, y_pred)\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "id": "dbec1b8c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "End of video input\n",
+      "[-10.65248915]\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[INFO] FINISHED PROCESSING\n"
+     ]
+    }
+   ],
    "source": [
     "#video details\n",
     "VIDEO_STREAM = 'test_videos/me/dark_far_right.mp4'\n",
@@ -372,7 +505,7 @@
     "output_folder = 'result_analysis/me/' + video_name\n",
     "\n",
     "#to save details of rotational angles\n",
-    "raw_rot_angle_records, smoothed_rot_angle_records, diff_rot_angle_records = [], [], []\n",
+    "raw_rot_angle_records, diff_rot_angle_records, single_exponential_smoothed_rot_angle_records = [], [], []\n",
     "\n",
     "#processing\n",
     "get_rotational_angles()\n",
@@ -382,20 +515,7 @@
     "if not (os.path.isdir(output_folder)):\n",
     "    os.makedirs(output_folder, mode = 0o777, exist_ok = False)\n",
     "    \n",
-    "write_to_csv_rot_angles(raw_rot_angle_records, output_folder + '/' + video_name + '_raw_rotational_angles.csv')\n",
-    "\n",
-    "find_diff_rot_angles(raw_rot_angle_records)\n",
-    "write_to_csv_rot_angles(diff_rot_angle_records, output_folder + '/' + video_name + '_diff_rotational_angles.csv')\n",
-    "\n",
-    "    #plotting and saving graphs\n",
-    "output_folder_graphs = output_folder + '/graphs'\n",
-    "         #check if specified path for graphs exists, if not create it\n",
-    "if not (os.path.isdir(output_folder_graphs)):\n",
-    "    os.makedirs(output_folder_graphs, mode = 0o777, exist_ok = False)\n",
-    "    \n",
-    "\n",
-    "plot_rot_angles(output_folder_graphs, \"Raw\", raw_rot_angle_records)    \n",
-    "plot_rot_angles(output_folder_graphs, \"Differences in\", diff_rot_angle_records)   \n",
+    "smoothing(raw_rot_angle_records)\n",
     "    \n",
     "print('[INFO] FINISHED PROCESSING')"
    ]