Showcas_LK_1D.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial on how to use Directional DIC to measuere displacement from videos\n",
    "Unidirectional translation identification as introduced in:\n",
    "Masmeijer T., Habtour E., Zaletelj, K., & Slavič, J., (2024). **Directional DIC method with automatic feature selection**. *MSSP*.\n",
    "\"https://doi.org/10.1016/j.ymssp.2024.112080\".\n",
    "\n",
    "The implementation is based on the Lucas-Kanade method using least-squares iterative optimization with the Zero Normalized\n",
    "Cross Correlation optimization criterion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "sys.path.insert(0, os.path.realpath('__file__'))\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle\n",
    "import pyidi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the video"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = 'data/data_synthetic.cih'\n",
    "video = pyidi.VideoReader(filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Video info can easily be accessed (info might not be available depending on video file extension)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Date': '2016/08/31',\n",
       " 'Camera Type': 1,\n",
       " 'Record Rate(fps)': 1,\n",
       " 'Shutter Speed(s)': 1.0,\n",
       " 'Total Frame': 101,\n",
       " 'Original Total Frame': 101,\n",
       " 'Start Frame': 0,\n",
       " 'Image Width': 256,\n",
       " 'Image Height': 128,\n",
       " 'Color Type': 'Mono',\n",
       " 'Color Bit': 16,\n",
       " 'File Format': 'MRaw',\n",
       " 'EffectiveBit Depth': 12,\n",
       " 'EffectiveBit Side': 'Lower',\n",
       " 'Comment Text': 'Generated sequence.<br>Modify measurement info in<br>created .cih file if necessary.'}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "video.info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib qt\n",
    "import matplotlib.animation as animation\n",
    "\n",
    "def play_video(frame_range = None, interval=30, points = None, ij_counter = (0.65, 0.05)):\n",
    "    \n",
    "    \"\"\"\n",
    "    Plays the video from the given video object.\n",
    "    Args:\n",
    "        frame_range (range object): The range of frames to play.\n",
    "        interval (int): The interval between frames in milliseconds.\n",
    "        points (ndarray): Optional tracked points to plot on the video.\n",
    "        ij_counter (tuple): The position of the frame counter.\n",
    "    \"\"\"\n",
    "    if frame_range is None:\n",
    "        frame_range = range(0, video.info['Total Frame'])\n",
    "    fig, ax = plt.subplots()\n",
    "    im = ax.imshow(video.mraw[frame_range[0]], cmap='gray')\n",
    "    text = ax.text(ij_counter[0], ij_counter[1], '', transform=ax.transAxes, color='black', ha='right', va='bottom')\n",
    "\n",
    "    if points is not None:\n",
    "        pts = ax.plot(points[:,0,1], points[:,0,0], 'r.')\n",
    "\n",
    "    def update(i):\n",
    "        im.set_data(video.mraw[i])\n",
    "        text.set_text(f'Frame {i}')\n",
    "        if points is not None:\n",
    "            pts[0].set_data(points[:,i,1], points[:,i,0])\n",
    "        return im, text\n",
    "\n",
    "    ani = animation.FuncAnimation(fig, update, frames=frame_range, interval=interval)\n",
    "    plt.show()\n",
    "    return ani\n",
    "\n",
    "ani = play_video(range(1, video.info['Total Frame']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Lucas Kanade` method as a reference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "tol = 1e-8\n",
    "roi_size = (5,5)\n",
    "idi_lk = pyidi.LucasKanade(video)\n",
    "idi_lk.configure(reference_image = (0,100), resume_analysis = False, tol=tol, roi_size=roi_size)\n",
    "reference_image = idi_lk._set_reference_image(video, idi_lk.reference_image)\n",
    "\n",
    "# Select the highest gradient points\n",
    "Gi, Gj = np.gradient(reference_image)\n",
    "G = np.sqrt(Gi**2 + Gj**2)\n",
    "highest_points = np.argpartition(G.flatten(), -10)[-10:]\n",
    "arguments = np.unravel_index(highest_points, G.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the selected points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "points2d = np.array(arguments).T\n",
    "idi_lk.set_points(points2d)\n",
    "idi_lk.show_points()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compoute displacements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d7f71b09544c40c0ad2c24c9fda5bd76",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- Starting new analysis ---\n",
      " \n",
      "Computation start: 2024-12-03 12:48:06.666800\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computation duration: 00:00:2.35\n"
     ]
    }
   ],
   "source": [
    "displacementes_2d = idi_lk.get_displacements(processes=2, autosave=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Directional - Lucas Kanade` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "idi_dlk = pyidi.DirectionalLucasKanade(video)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the direction of motion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\git_repos\\pyidi\\pyidi\\methods\\_directional_lucas_kanade.py:110: UserWarning: The direction vector d must have a norm of 1. The input vector was normalized.\n",
      "  warnings.warn('The direction vector d must have a norm of 1. The input vector was normalized.')\n"
     ]
    }
   ],
   "source": [
    "tol = 1e-8\n",
    "roi_size = (5,5)\n",
    "\n",
    "dij = (0.5, 0.5) # set the direction of motion\n",
    "\n",
    "idi_dlk.configure(reference_image = (0,100), dij=dij, resume_analysis = False, tol=tol,roi_size=roi_size)\n",
    "\n",
    "reference_image = idi_dlk._set_reference_image(video, idi_dlk.reference_image)\n",
    "Gi, Gj = np.gradient(reference_image)\n",
    "G = np.sqrt(Gi**2 + Gj**2)\n",
    "highest_points = np.argpartition(G.flatten(), -10)[-10:]\n",
    "arguments = np.unravel_index(highest_points, G.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([0.70710678, 0.70710678])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "points1d = np.array(arguments).T\n",
    "idi_dlk.set_points(points1d)\n",
    "idi_dlk.show_points()\n",
    "idi_dlk.dij"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute displacements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "108dd84b40d544ef99ec16678805c50d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- Starting new analysis ---\n",
      " \n",
      "Computation start: 2024-12-03 12:49:22.648767\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computation duration: 00:00:2.27\n"
     ]
    }
   ],
   "source": [
    "displacements = idi_dlk.get_displacements(processes=2, autosave=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An existing analysis can also be loaded without computation and setting the arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "t_vec = np.arange(0, len(displacements[0])) * video.info['Record Rate(fps)']\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('Time (s)')\n",
    "ax.set_ylabel('Displacement (pixels)')\n",
    "for point in displacements:\n",
    "    ax.plot(t_vec, point[:,0]*dij[0] + point[:,1]*dij[1],'b', label=f'1D, d = {dij}')\n",
    "for point in displacementes_2d:\n",
    "    ax.plot(t_vec, point[:,0]*dij[0] + point[:,1]*dij[1], 'r', label=f'2D, d = {dij}')\n",
    "ax.plot(t_vec, displacementes_2d[0, :,0], 'r:', label = '2D - x', alpha=0.5)\n",
    "ax.plot(t_vec, displacementes_2d[0, :,1], 'r--', label = '2D - y', alpha=0.5)\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "by_label = dict(zip(labels, handles))\n",
    "ax.legend(by_label.values(), by_label.keys())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib qt\n",
    "td2d     = displacementes_2d +  points2d.reshape(len(points2d),1,2)\n",
    "td1d     = displacements +  points1d.reshape(len(points1d),1,2)\n",
    "combined_td = np.concatenate((td1d, td2d), axis=0)\n",
    "ani = play_video(range(1,video.N), points=combined_td)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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