tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uXwa-vSiojGG"
   },
   "source": [
    "### Import Dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "5zlhFthZ_b8P"
   },
   "outputs": [],
   "source": [
    "from warnings import simplefilter\n",
    "simplefilter(action='ignore', category=FutureWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "iX1zGOsKyzyk"
   },
   "outputs": [],
   "source": [
    "# Importing functions from the modules in the qseg package\n",
    "from qseg.graph_utils import image_to_grid_graph, draw, draw_graph_cut_edges\n",
    "from qseg.dwave_utils import annealer_solver\n",
    "from qseg.utils import decode_binary_string\n",
    "\n",
    "# Additional necessary imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VH8MLDeqaY4o"
   },
   "source": [
    "### Create a sample Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 452
    },
    "id": "hTw9PaaBb4FP",
    "outputId": "79bdfd9a-8e33-4156-f03c-90ce9c12a708"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1bc48a1a2d0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "height,width = 3,3\n",
    "\n",
    "image = np.array([\n",
    "       [0.82,  0.1, 0.99],\n",
    "       [0.83,  0.2, 0.95],\n",
    "       [0.1,  0.05, 0.98]\n",
    "       ])\n",
    "plt.imshow(image, cmap=plt.cm.gray)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Sm4Gxf18t29p"
   },
   "source": [
    "### Convert Image to Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 499
    },
    "id": "32brLSSOlJ4_",
    "outputId": "ba2f3ca6-43fc-49c1-cf92-be0e30d6d7e0"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "normalized_nx_elist = image_to_grid_graph(image)  # We are using Guassian similarity metric as the edge weight metric\n",
    "G = nx.grid_2d_graph(image.shape[0], image.shape[1])\n",
    "G.add_weighted_edges_from(normalized_nx_elist)\n",
    "draw(G, image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bIlpQIJiuyHE"
   },
   "source": [
    "### Solve using D-Wave annealer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** This requires you to have an account in [D-Wave Ocean](https://cloud.dwavesys.com/), up on logging in, the D-Wave Leap dashboard is displayed, you can find the private token on the left column under **Solver API Token**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you do not wish to run the problem on the remote Quantum Annealer, you can also try out the Gurobi solver which runs locally on your machine. Scroll down for code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "caF70s_ylJz6",
    "outputId": "b81bdc68-4289-4e1b-c2e6-4d7eec8a7abd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'qpu_sampling_time': 182880.0,\n",
       " 'qpu_anneal_time_per_sample': 20.0,\n",
       " 'qpu_readout_time_per_sample': 50.86,\n",
       " 'qpu_access_time': 198804.76,\n",
       " 'qpu_access_overhead_time': 679.24,\n",
       " 'qpu_programming_time': 15924.76,\n",
       " 'qpu_delay_time_per_sample': 20.58,\n",
       " 'total_post_processing_time': 95.0,\n",
       " 'post_processing_overhead_time': 95.0,\n",
       " 'problem_formulation_time': 1.258246898651123,\n",
       " 'connection_time': 0.18280720710754395,\n",
       " 'embedding_time': 0.03640317916870117,\n",
       " 'response_time': 0.023007631301879883,\n",
       " 'sample_fetch_time': 0.001997709274291992,\n",
       " 'total_time': 4.44229531288147}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "samples_dataframe, execution_info_dict = annealer_solver(G, private_token = 'xxx-xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx')\n",
    "total_time = time.time()-start_time\n",
    "execution_info_dict['total_time'] = total_time\n",
    "execution_info_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "l0NvE4FuwxGD"
   },
   "source": [
    "### All samples received"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "id": "sO3Wb2nblJxH",
    "outputId": "3f55c683-1893-488e-ff48-8394d144efc8"
   },
   "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 th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>chain_break_fraction</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-4.0870</td>\n",
       "      <td>709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-4.0830</td>\n",
       "      <td>1288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.5878</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.5720</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.5098</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6  7  8  chain_break_fraction  energy  num_occurrences\n",
       "0  0  1  0  0  1  0  1  1  0                   0.0 -4.0870              709\n",
       "1  1  0  1  1  0  1  0  0  1                   0.0 -4.0830             1288\n",
       "2  1  1  0  1  1  0  1  1  0                   0.0 -2.5878                1\n",
       "3  0  0  1  0  0  1  0  0  1                   0.0 -2.5720                1\n",
       "4  0  1  1  0  1  1  1  1  0                   0.0 -1.5098                1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples_dataframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NxC1TdWRw4_P"
   },
   "source": [
    "### Decode binary solution string to a binary segmentation mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 452
    },
    "id": "4vXlBjxRlJrQ",
    "outputId": "423730b2-de6a-4e36-b1e3-514f4ec91b30"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1f6b6f54dd0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_binary_string = samples_dataframe.iloc[0][:-3]\n",
    "segmentation_mask = decode_binary_string(solution_binary_string, height, width)\n",
    "plt.imshow(segmentation_mask, cmap=plt.cm.gray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "WHHIPgatsr5_",
    "outputId": "ad4f0c95-40b2-4b39-c118-17735b944e5c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[((0, 0), (0, 1)),\n",
       " ((0, 1), (0, 2)),\n",
       " ((1, 0), (2, 0)),\n",
       " ((1, 0), (1, 1)),\n",
       " ((1, 1), (1, 2)),\n",
       " ((2, 1), (2, 2))]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cut_edges = [(u, v) for (u, v, d) in G.edges(data=True) if segmentation_mask[u]!=segmentation_mask[v]]\n",
    "cut_edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "cDxFlkh37da6"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 499
    },
    "id": "jZHV1xiI7THW",
    "outputId": "2fe4ba91-2b48-4f51-a9ea-ffb52195c1a8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_graph_cut_edges(G, image, cut_edges)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve using Gurobi Solver (Classical State-of-the-art)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gurobipy as gp\n",
    "from gurobipy import GRB\n",
    "from qiskit_optimization.applications import Maxcut # Used just for formulating the Maxcut problem as a QUBO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gurobi_qubo_solver(G):\n",
    "  w = -1 * nx.adjacency_matrix(G).todense()\n",
    "  max_cut = Maxcut(w)\n",
    "  qp = max_cut.to_quadratic_program()\n",
    "  linear = qp.objective.linear.coefficients.toarray(order=None, out=None)\n",
    "  quadratic = qp.objective.quadratic.coefficients.toarray(order=None, out=None)\n",
    "\n",
    "  linear = {int(idx):-round(value,2) for idx,value in enumerate(linear[0])}\n",
    "  quadratic = {(int(iy),int(ix)):-quadratic[iy, ix] for iy, ix in np.ndindex(quadratic.shape) if iy<ix and abs(quadratic[iy, ix])!=0}\n",
    "\n",
    "  qubo_matrix = np.zeros([len(linear),len(linear)])\n",
    "  for key,value in linear.items():\n",
    "    qubo_matrix[int(key),int(key)] = value\n",
    "  for key,value in quadratic.items():\n",
    "    qubo_matrix[int(key[0]),int(key[1])] = value/2\n",
    "    qubo_matrix[int(key[1]),int(key[0])] = value/2\n",
    "\n",
    "  n = qubo_matrix.shape[0]\n",
    "  model = gp.Model()\n",
    "  x = model.addVars(n, vtype=GRB.BINARY)\n",
    "  obj_expr = gp.quicksum(qubo_matrix[i, j] * x[i] * x[j] for i in range(n) for j in range(n))\n",
    "  model.setObjective(obj_expr)\n",
    "  model.setParam('OutputFlag', 0)\n",
    "  model.optimize()\n",
    "\n",
    "  if model.status == GRB.OPTIMAL:\n",
    "    solution = [int(x[i].X) for i in range(n)]\n",
    "    binary_string = ''.join(str(bit) for bit in solution)\n",
    "    return binary_string, model.objVal\n",
    "  else:\n",
    "    return None, None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "3ChO-ms37ncy"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2025-02-25\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "gurobi_qubo_solution, gurobi_qubo_value = gurobi_qubo_solver(G)\n",
    "total_time = time.time()-start_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1bc48d5a210>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbsAAAGiCAYAAAB+sGhNAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAdXElEQVR4nO3df2xV9f3H8dct0FvJuLcy6C8tIKKggC0ilOICNXZWJcwuS4boBAk/5lIWEaLSZZOJyxq/MjVx3dAs0kwkoENgQ4fD8itCBS00A2REkAGS3qJi75XqCtLP94/FOyttoeWee9t3n4/kJLunn3Pu57P28vT23tvjc845AQBgWFKiJwAAgNeIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8z2J36tQp3XvvvQoEAkpNTdXMmTN1+vTpNo8pKCiQz+drtj3wwANeTREA0E34vPrbmHfccYdqa2v1/PPP6+zZs5oxY4bGjBmjFStWtHpMQUGBrr32Wi1evDi6r3fv3goEAl5MEQDQTfT04qQHDhzQhg0b9O677+qmm26SJD333HO68847tWTJEmVlZbV6bO/evZWRkeHFtAAA3ZQnsauqqlJqamo0dJJUWFiopKQk7dy5Uz/84Q9bPfbll1/W8uXLlZGRocmTJ+tXv/qVevfu3er4xsZGNTY2Rm83NTXp1KlT+u53vyufzxebBQEA4sY5p88//1xZWVlKSorNq22exC4UCiktLa35HfXsqb59+yoUCrV63D333KOBAwcqKytL//znP/Xoo4/q4MGDeu2111o9pqysTI8//njM5g4A6ByOHz+uK6+8MibnalfsFi5cqCeffLLNMQcOHOjwZObMmRP93yNHjlRmZqZuvfVWHT58WFdffXWLx5SWlmr+/PnR2+FwWAMGDOjwHNC1hMPhRE8BcRQMBhM9BcRRnz59YnaudsVuwYIFuv/++9scM3jwYGVkZOjkyZPN9n/11Vc6depUu16Py8vLkyQdOnSo1dj5/X75/f6LPids4c1LgF2xfCmqXbHr37+/+vfvf8Fx+fn5qq+vV3V1tUaPHi1J2rRpk5qamqIBuxg1NTWSpMzMzPZMEwCAZjz5nN11112n22+/XbNnz9auXbu0fft2zZ07V3fffXf0nZgnTpzQsGHDtGvXLknS4cOH9cQTT6i6ulr//ve/9de//lXTpk3ThAkTdMMNN3gxTQBAN+HZh8pffvllDRs2TLfeeqvuvPNOfe9739MLL7wQ/frZs2d18OBBffHFF5Kk5ORkvfXWW7rttts0bNgwLViwQD/60Y/0t7/9zaspAgC6Cc8+VJ4okUiEF7G7EWM/vrgAPk7UvYTD4Zi9Ls/fxgQAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHmex668vFyDBg1SSkqK8vLytGvXrjbHv/rqqxo2bJhSUlI0cuRIvfHGG15PEQBgnKexW7VqlebPn69FixZp9+7dysnJUVFRkU6ePNni+B07dmjq1KmaOXOm9uzZo+LiYhUXF2vfvn1eThMAYJzPOee8OnleXp7GjBmj3//+95KkpqYmZWdn6+c//7kWLlx43vgpU6aooaFB69evj+4bN26ccnNztXTp0hbvo7GxUY2NjdHbkUhE2dnZMV4JOisPf3zRCfl8vkRPAXEUDocVCARici7PntmdOXNG1dXVKiws/N+dJSWpsLBQVVVVLR5TVVXVbLwkFRUVtTpeksrKyhQMBqMboQMAfJtnsfvkk0907tw5paenN9ufnp6uUCjU4jGhUKhd4yWptLRU4XA4uh0/fvzSJw8AMKVnoidwqfx+v/x+f6KnAQDoxDx7ZtevXz/16NFDdXV1zfbX1dUpIyOjxWMyMjLaNR4AgIvhWeySk5M1evRoVVZWRvc1NTWpsrJS+fn5LR6Tn5/fbLwkbdy4sdXxAABcFOehlStXOr/f7yoqKtz777/v5syZ41JTU10oFHLOOXffffe5hQsXRsdv377d9ezZ0y1ZssQdOHDALVq0yPXq1cvt3bv3ou8zHA47SWzdZEP3kuifN7b4buFwOGY/O56+ZjdlyhR9/PHHeuyxxxQKhZSbm6sNGzZE34Ry7NgxJSX978nl+PHjtWLFCv3yl7/UL37xC11zzTVau3atRowY4eU0AQDGefo5u0SIRCIKBoOJngbixNiPLy6Az9l1L13ic3YAAHQWxA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYJ7nsSsvL9egQYOUkpKivLw87dq1q9WxFRUV8vl8zbaUlBSvpwgAMM7T2K1atUrz58/XokWLtHv3buXk5KioqEgnT55s9ZhAIKDa2trodvToUS+nCADoBjyN3dNPP63Zs2drxowZuv7667V06VL17t1bL774YqvH+Hw+ZWRkRLf09HQvpwgA6AY8i92ZM2dUXV2twsLC/91ZUpIKCwtVVVXV6nGnT5/WwIEDlZ2drbvuukv79+9v834aGxsViUSabQAAfJNnsfvkk0907ty5856ZpaenKxQKtXjM0KFD9eKLL2rdunVavny5mpqaNH78eH300Uet3k9ZWZmCwWB0y87Ojuk6AABdX6d6N2Z+fr6mTZum3NxcTZw4Ua+99pr69++v559/vtVjSktLFQ6Ho9vx48fjOGMAQFfQ06sT9+vXTz169FBdXV2z/XV1dcrIyLioc/Tq1UujRo3SoUOHWh3j9/vl9/svaa4AANs8e2aXnJys0aNHq7KyMrqvqalJlZWVys/Pv6hznDt3Tnv37lVmZqZX0wQAdAOePbOTpPnz52v69Om66aabNHbsWD377LNqaGjQjBkzJEnTpk3TFVdcobKyMknS4sWLNW7cOA0ZMkT19fV66qmndPToUc2aNcvLaQIAjPM0dlOmTNHHH3+sxx57TKFQSLm5udqwYUP0TSvHjh1TUtL/nlx+9tlnmj17tkKhkC6//HKNHj1aO3bs0PXXX+/lNAEAxvmccy7Rk4ilSCSiYDCY6GkgToz9+OICfD5foqeAOAqHwwoEAjE5V6d6NyYAAF4gdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8T2O3bds2TZ48WVlZWfL5fFq7du0Fj9myZYtuvPFG+f1+DRkyRBUVFV5OEQDQDXgau4aGBuXk5Ki8vPyixh85ckSTJk3SLbfcopqaGs2bN0+zZs3Sm2++6eU0AQDG+ZxzLi535PNpzZo1Ki4ubnXMo48+qtdff1379u2L7rv77rtVX1+vDRs2tHhMY2OjGhsbo7cjkYiys7NjNm90bnH68UUn4fP5Ej0FxFE4HFYgEIjJuTrVa3ZVVVUqLCxstq+oqEhVVVWtHlNWVqZgMBjdCB0A4Ns6VexCoZDS09Ob7UtPT1ckEtGXX37Z4jGlpaUKh8PR7fjx4/GYKgCgC+mZ6AlcKr/fL7/fn+hpAAA6sU71zC4jI0N1dXXN9tXV1SkQCOiyyy5L0KwAAF1dp4pdfn6+Kisrm+3buHGj8vPzEzQjAIAFnsbu9OnTqqmpUU1NjaT/frSgpqZGx44dk/Tf19umTZsWHf/AAw/oww8/1COPPKJ//etf+sMf/qBXXnlFDz30kJfTBABY5zy0efNmJ+m8bfr06c4556ZPn+4mTpx43jG5ubkuOTnZDR482C1btqxd9xkOh1u8TzabG7qXRP+8scV3C4fDMfvZidvn7OIlEokoGAwmehqIE2M/vrgAPmfXvZj9nB0AAF4gdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA8zyN3bZt2zR58mRlZWXJ5/Np7dq1bY7fsmWLfD7feVsoFPJymgAA4zyNXUNDg3JyclReXt6u4w4ePKja2trolpaW5tEMAQDdQU8vT37HHXfojjvuaPdxaWlpSk1Njf2EAADdkqex66jc3Fw1NjZqxIgR+vWvf62bb7651bGNjY1qbGyM3o5EIpKkcDisQCDg+VwBAJ1fp3qDSmZmppYuXarVq1dr9erVys7OVkFBgXbv3t3qMWVlZQoGg9EtOzs7jjMGAHQFPueci8sd+Xxas2aNiouL23XcxIkTNWDAAL300kstfr2lZ3bZ2dk8swMM8vl8iZ4C4iiW/453yl9jftPYsWP19ttvt/p1v98vv98fxxkBALqaTvVrzJbU1NQoMzMz0dMAAHRhnj6zO336tA4dOhS9feTIEdXU1Khv374aMGCASktLdeLECf35z3+WJD377LO66qqrNHz4cP3nP//Rn/70J23atEn/+Mc/vJwmAMA4T2P33nvv6ZZbbonenj9/viRp+vTpqqioUG1trY4dOxb9+pkzZ7RgwQKdOHFCvXv31g033KC33nqr2TkAAGivuL1BJV4ikYiCwSBvUAEM4g0q3Uss/x3v9K/ZAQBwqYgdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMI/YAQDMI3YAAPOIHQDAPGIHADCP2AEAzCN2AADziB0AwDxiBwAwj9gBAMwjdgAA84gdAMA8YgcAMM/T2JWVlWnMmDHq06eP0tLSVFxcrIMHD17wuFdffVXDhg1TSkqKRo4cqTfeeMPLaQIAjPM0dlu3blVJSYneeecdbdy4UWfPntVtt92mhoaGVo/ZsWOHpk6dqpkzZ2rPnj0qLi5WcXGx9u3b5+VUAQCG+ZxzLl539vHHHystLU1bt27VhAkTWhwzZcoUNTQ0aP369dF948aNU25urpYuXXrB+4hEIgoGgwqHwwoEAjGbO4DE8/l8iZ4C4iiW/47H9TW7cDgsSerbt2+rY6qqqlRYWNhsX1FRkaqqqloc39jYqEgk0mwDAOCb4ha7pqYmzZs3TzfffLNGjBjR6rhQKKT09PRm+9LT0xUKhVocX1ZWpmAwGN2ys7NjOm8AQNcXt9iVlJRo3759WrlyZUzPW1paqnA4HN2OHz8e0/MDALq+nvG4k7lz52r9+vXatm2brrzyyjbHZmRkqK6urtm+uro6ZWRktDje7/fL7/fHbK4AAHs8fWbnnNPcuXO1Zs0abdq0SVddddUFj8nPz1dlZWWzfRs3blR+fr5X0wQAGOfpM7uSkhKtWLFC69atU58+faKvuwWDQV122WWSpGnTpumKK65QWVmZJOnBBx/UxIkT9bvf/U6TJk3SypUr9d577+mFF17wcqoAAMM8fWb3xz/+UeFwWAUFBcrMzIxuq1atio45duyYamtro7fHjx+vFStW6IUXXlBOTo7+8pe/aO3atW2+qQUAgLbE9XN28cDn7AC7+Jxd99JlP2cHAEAiEDsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgHrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADmETsAgHnEDgBgnqexKysr05gxY9SnTx+lpaWpuLhYBw8ebPOYiooK+Xy+ZltKSoqX0wQAGOdp7LZu3aqSkhK988472rhxo86ePavbbrtNDQ0NbR4XCARUW1sb3Y4ePerlNAEAxvX08uQbNmxodruiokJpaWmqrq7WhAkTWj3O5/MpIyPjou6jsbFRjY2N0dvhcFiSFIlEOjBjAEBn4ZyL2bk8jd23fR2ivn37tjnu9OnTGjhwoJqamnTjjTfqt7/9rYYPH97i2LKyMj3++OPn7c/Ozr70CQMAEubTTz9VMBiMybl8LpbpbENTU5N+8IMfqL6+Xm+//Xar46qqqvTBBx/ohhtuUDgc1pIlS7Rt2zbt379fV1555Xnjv/3Mrr6+XgMHDtSxY8di9n9SVxCJRJSdna3jx48rEAgkejpx0R3XLLHu7rTu7rhm6b9PjAYMGKDPPvtMqampMTln3J7ZlZSUaN++fW2GTpLy8/OVn58fvT1+/Hhdd911ev755/XEE0+cN97v98vv95+3PxgMdqsfjq8FAoFut+7uuGaJdXcn3XHNkpSUFLu3lcQldnPnztX69eu1bdu2Fp+dtaVXr14aNWqUDh065NHsAADWefpuTOec5s6dqzVr1mjTpk266qqr2n2Oc+fOae/evcrMzPRghgCA7sDTZ3YlJSVasWKF1q1bpz59+igUCkn6768YL7vsMknStGnTdMUVV6isrEyStHjxYo0bN05DhgxRfX29nnrqKR09elSzZs26qPv0+/1atGhRi7/atKw7rrs7rlli3d1p3d1xzZI36/b0DSo+n6/F/cuWLdP9998vSSooKNCgQYNUUVEhSXrooYf02muvKRQK6fLLL9fo0aP1m9/8RqNGjfJqmgAA4+L2bkwAABKFv40JADCP2AEAzCN2AADziB0AwDwTsTt16pTuvfdeBQIBpaamaubMmTp9+nSbxxQUFJx3KaEHHnggTjPumPLycg0aNEgpKSnKy8vTrl272hz/6quvatiwYUpJSdHIkSP1xhtvxGmmsdOeNVu5PNS2bds0efJkZWVlyefzae3atRc8ZsuWLbrxxhvl9/s1ZMiQ6Lubu4r2rnnLli3nfa99Pl/0401dQUcugSZ1/cd1oi79ZiJ29957r/bv36+NGzdG/1LLnDlzLnjc7Nmzm11K6P/+7//iMNuOWbVqlebPn69FixZp9+7dysnJUVFRkU6ePNni+B07dmjq1KmaOXOm9uzZo+LiYhUXF2vfvn1xnnnHtXfNko3LQzU0NCgnJ0fl5eUXNf7IkSOaNGmSbrnlFtXU1GjevHmaNWuW3nzzTY9nGjvtXfPXDh482Oz7nZaW5tEMY68jl0Cz8LhO2KXfXBf3/vvvO0nu3Xffje77+9//7nw+nztx4kSrx02cONE9+OCDcZhhbIwdO9aVlJREb587d85lZWW5srKyFsf/+Mc/dpMmTWq2Ly8vz/30pz/1dJ6x1N41L1u2zAWDwTjNLj4kuTVr1rQ55pFHHnHDhw9vtm/KlCmuqKjIw5l552LWvHnzZifJffbZZ3GZUzycPHnSSXJbt25tdYyFx/W3Xcy6Y/HY7vLP7KqqqpSamqqbbropuq+wsFBJSUnauXNnm8e+/PLL6tevn0aMGKHS0lJ98cUXXk+3Q86cOaPq6moVFhZG9yUlJamwsFBVVVUtHlNVVdVsvCQVFRW1Or6z6ciapf9dHio7O1t33XWX9u/fH4/pJlRX/15fitzcXGVmZur73/++tm/fnujpXJKLuQSaxe91ey/91tHHdpePXSgUOu9XFz179lTfvn3b/P39Pffco+XLl2vz5s0qLS3VSy+9pJ/85CdeT7dDPvnkE507d07p6enN9qenp7e6xlAo1K7xnU1H1jx06FC9+OKLWrdunZYvX66mpiaNHz9eH330UTymnDCtfa8jkYi+/PLLBM3KW5mZmVq6dKlWr16t1atXKzs7WwUFBdq9e3eip9YhTU1Nmjdvnm6++WaNGDGi1XFd/XH9bRe77lg8tuN68db2WLhwoZ588sk2xxw4cKDD5//ma3ojR45UZmambr31Vh0+fFhXX311h8+LxGnv5aHQdQ0dOlRDhw6N3h4/frwOHz6sZ555Ri+99FICZ9YxF3sJNGu8uvRbSzpt7BYsWBD9+5mtGTx4sDIyMs57w8JXX32lU6dOKSMj46LvLy8vT5J06NChThe7fv36qUePHqqrq2u2v66urtU1ZmRktGt8Z9ORNX9bd7k8VGvf60AgEP2D693B2LFju2Qs2nMJtK7+uP6meF/6rdP+GrN///4aNmxYm1tycrLy8/NVX1+v6urq6LGbNm1SU1NTNGAXo6amRpI65aWEkpOTNXr0aFVWVkb3NTU1qbKystl/7XxTfn5+s/GStHHjxlbHdzYdWfO3dZfLQ3X173Ws1NTUdKnvtevAJdAsfK87su5v69Bj+5Le3tJJ3H777W7UqFFu586d7u2333bXXHONmzp1avTrH330kRs6dKjbuXOnc865Q4cOucWLF7v33nvPHTlyxK1bt84NHjzYTZgwIVFLuKCVK1c6v9/vKioq3Pvvv+/mzJnjUlNTXSgUcs45d99997mFCxdGx2/fvt317NnTLVmyxB04cMAtWrTI9erVy+3duzdRS2i39q758ccfd2+++aY7fPiwq66udnfffbdLSUlx+/fvT9QSOuTzzz93e/bscXv27HGS3NNPP+327Nnjjh496pxzbuHChe6+++6Ljv/www9d79693cMPP+wOHDjgysvLXY8ePdyGDRsStYR2a++an3nmGbd27Vr3wQcfuL1797oHH3zQJSUlubfeeitRS2i3n/3sZy4YDLotW7a42tra6PbFF19Ex1h8XHdk3bF4bJuI3aeffuqmTp3qvvOd77hAIOBmzJjhPv/88+jXjxw54iS5zZs3O+ecO3bsmJswYYLr27ev8/v9bsiQIe7hhx924XA4QSu4OM8995wbMGCAS05OdmPHjnXvvPNO9GsTJ05006dPbzb+lVdecddee61LTk52w4cPd6+//nqcZ3zp2rPmefPmRcemp6e7O++80+3evTsBs740X7+t/tvb12udPn26mzhx4nnH5ObmuuTkZDd48GC3bNmyuM/7UrR3zU8++aS7+uqrXUpKiuvbt68rKChwmzZtSszkO6il9Upq9r2z+LjuyLpj8djmEj8AAPM67Wt2AADECrEDAJhH7AAA5hE7AIB5xA4AYB6xAwCYR+wAAOYROwCAecQOAGAesQMAmEfsAADm/T9/CV2O6ZyyygAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "segmentation_mask = decode_binary_string(gurobi_qubo_solution, height, width)\n",
    "plt.imshow(segmentation_mask, cmap=plt.cm.gray)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NOTE**: *Gurobi is an off-the-shelf solver, it is not open source and licensed. The free version allows to run problems upto size 200 only, which is the number of nodes in our case. However, if you are a student or part of an educational institute, you can obtain an academic license for non commercial use for free.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [
    "15HtXN2NoVb1",
    "vy44j3zSoYuw",
    "752InhCl1Hag",
    "uXwa-vSiojGG",
    "CNYU7X0LoquZ",
    "TTtjsUSK3xi6"
   ],
   "provenance": []
  },
  "kernelspec": {
   "display_name": "venv",
   "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": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}