main_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Verifying Stokes Law with AI & a novel Correction Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Importing external libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import deque\n",
    "from imutils.video import VideoStream\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import argparse\n",
    "import cv2\n",
    "import imutils\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Importing functions we made"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functions.discrete_differential import d_dt\n",
    "from functions.pixel_shift_perspective_correction import position_to_irl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Importing static variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils.static import ballLower, ballUpper, buffer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Declaring local variables and acquiring the video stream"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "frames_total = 0\n",
    "elements = []\n",
    "frame_shape = None\n",
    "pts = deque(maxlen=buffer)\n",
    "\n",
    "# Choosing the video file\n",
    "vs = cv2.VideoCapture(\"warehouse/media_store/kerosene_v1.mp4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Main tracking function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length of elements: 188\n",
      "Frames_shape: (711, 400, 3)\n"
     ]
    }
   ],
   "source": [
    "while True:\n",
    "    frame = vs.read()\n",
    "    frame = frame[1]\n",
    "    if frame is None:\n",
    "        break\n",
    "    frames_total += 1\n",
    "\n",
    "    frame = imutils.resize(frame, width=400)\n",
    "    if frames_total == 1:\n",
    "        frame_shape = frame.shape\n",
    "    blurred = cv2.GaussianBlur(frame, (11, 11), 0)\n",
    "    hsv = cv2.cvtColor(blurred, cv2.COLOR_BGR2HSV)\n",
    "\n",
    "    mask = cv2.inRange(hsv, ballLower, ballUpper)\n",
    "    mask = cv2.erode(mask, None, iterations=2)\n",
    "    mask = cv2.dilate(mask, None, iterations=2)\n",
    "\n",
    "    cnts = cv2.findContours(mask.copy(), cv2.RETR_EXTERNAL,\n",
    "        cv2.CHAIN_APPROX_SIMPLE)\n",
    "    cnts = imutils.grab_contours(cnts)\n",
    "    center = None\n",
    "\n",
    "    if len(cnts) > 0:\n",
    "        c = max(cnts, key=cv2.contourArea)\n",
    "        ((x, y), radius) = cv2.minEnclosingCircle(c)\n",
    "        # print vals upto 2 decimal places\n",
    "        # print(f\"x: {x:.2f},\\t y: {y:.2f},\\t radius: {radius:.2f}\", end = \"\\t\")\n",
    "        M = cv2.moments(c)\n",
    "        center = (int(M[\"m10\"] / M[\"m00\"]), int(M[\"m01\"] / M[\"m00\"]))\n",
    "        # print(f\"center: {center},\\t timestamp: {vs.get(cv2.CAP_PROP_POS_MSEC)}\")\n",
    "\n",
    "        # only proceed if the radius meets a minimum size\n",
    "        if radius > 10:\n",
    "            elements.append(\n",
    "                [\n",
    "                    vs.get(cv2.CAP_PROP_POS_MSEC),\n",
    "                    (x, y),\n",
    "                    center\n",
    "                ]\n",
    "            )\n",
    "            # draw the circle and centroid on the frame,\n",
    "            # then update the list of tracked points\n",
    "            cv2.circle(frame, (int(x), int(y)), int(radius),\n",
    "                (0, 255, 0), 2)\n",
    "            cv2.circle(frame, center, 5, (0, 0, 255), -1)\n",
    "\n",
    "    # update the points queue\n",
    "    pts.appendleft(center)\n",
    "\n",
    "    # loop over the set of tracked points\n",
    "    for i in range(1, len(pts)):\n",
    "        # if either of the tracked points are None, ignore\n",
    "        # them\n",
    "        if pts[i - 1] is None or pts[i] is None:\n",
    "            continue\n",
    "\n",
    "        # otherwise, compute the thickness of the line and\n",
    "        # draw the connecting lines\n",
    "        thickness = int(np.sqrt(buffer / float(i + 1)) * 2.5)\n",
    "        cv2.line(frame, pts[i - 1], pts[i], (0, 0, 255), thickness)\n",
    "\n",
    "    # show the frame to our screen\n",
    "    cv2.imshow(\"Frame\", frame)\n",
    "    key = cv2.waitKey(1) & 0xFF\n",
    "\n",
    "    # if the 'q' key is pressed, stop the loop\n",
    "    if key == ord(\"q\"):\n",
    "        break\n",
    "    # time.sleep(0.05)\n",
    "\n",
    "vs.release()\n",
    "cv2.destroyAllWindows()\n",
    "\n",
    "print(f\"Length of elements: {len(elements)}\\nFrames_shape: {frame_shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculating IRL velocities using pixel shift & accounting for perspective errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_axis_vals = [element[2][1] for element in elements]\n",
    "timestamps = [element[0] for element in elements]\n",
    "\n",
    "y_irl = [position_to_irl(y_axis_val, 0.45, 0, frame_shape[0], 0.3)[1] for y_axis_val in y_axis_vals]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Applying the discrete differential on the Y-axis values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "v_irl = d_dt(y_irl, timestamps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting various graphs to visualize the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Y-Axis values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ac254646d0>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([(float(i)-min(y_axis_vals))/(max(y_axis_vals)-min(y_axis_vals)) for i in y_axis_vals], color = \"r\")\n",
    "plt.plot([(float(i)-min(y_irl))/(max(y_irl)-min(y_irl)) for i in y_irl], color = \"g\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Velocity curve (discretely differentiated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ac2555c490>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(v_irl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting the graph along with the theoritical terminal velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ac255cc910>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(v_irl)\n",
    "plt.plot([25.541] * len(v_irl), color = \"green\", ls = \"-.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "8ed2725ebb182683c929bc36f7739f7a68f29a05c6786eaa06420c4995e1ae48"
  },
  "kernelspec": {
   "display_name": "Python 3.8.5 ('slf')",
   "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": "3.8.5"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}