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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Copula-based object detection"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('000000.png', '004325.png', '000000.png')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f\"{0:06d}.png\", f\"{4325:06d}.png\", \"000000.png\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>UQ methods</th>\n",
       "      <th colspan=\"4\" halign=\"left\">Ground truths</th>\n",
       "      <th colspan=\"4\" halign=\"left\">Preds</th>\n",
       "      <th colspan=\"5\" halign=\"left\">Bonferroni</th>\n",
       "      <th colspan=\"8\" halign=\"left\">Max additive</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>object's fields</th>\n",
       "      <th>x_min</th>\n",
       "      <th>y_min</th>\n",
       "      <th>x_max</th>\n",
       "      <th>y_max</th>\n",
       "      <th>x_min</th>\n",
       "      <th>y_min</th>\n",
       "      <th>x_max</th>\n",
       "      <th>y_max</th>\n",
       "      <th colspan=\"2\" halign=\"left\">x_min</th>\n",
       "      <th>...</th>\n",
       "      <th colspan=\"2\" halign=\"left\">y_max</th>\n",
       "      <th colspan=\"2\" halign=\"left\">x_min</th>\n",
       "      <th colspan=\"2\" halign=\"left\">y_min</th>\n",
       "      <th colspan=\"2\" halign=\"left\">x_max</th>\n",
       "      <th colspan=\"2\" halign=\"left\">y_max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>Bounds</th>\n",
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       "      <th>Exact value</th>\n",
       "      <th>Exact value</th>\n",
       "      <th>Exact value</th>\n",
       "      <th>Exact value</th>\n",
       "      <th>Exact value</th>\n",
       "      <th>Exact value</th>\n",
       "      <th>Exact value</th>\n",
       "      <th>Exact value</th>\n",
       "      <th>Lower bound</th>\n",
       "      <th>Upper bound</th>\n",
       "      <th>...</th>\n",
       "      <th>Lower bound</th>\n",
       "      <th>Upper bound</th>\n",
       "      <th>Lower bound</th>\n",
       "      <th>Upper bound</th>\n",
       "      <th>Lower bound</th>\n",
       "      <th>Upper bound</th>\n",
       "      <th>Lower bound</th>\n",
       "      <th>Upper bound</th>\n",
       "      <th>Lower bound</th>\n",
       "      <th>Upper bound</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>images</th>\n",
       "      <th>objects</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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       "      <th rowspan=\"2\" valign=\"top\">000000.png</th>\n",
       "      <th>object_0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>object_1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
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       "      <th rowspan=\"2\" valign=\"top\">000001.png</th>\n",
       "      <th>object_0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
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