05b_quality_assurance/jaccard_index_versus_accuracy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "86c146e0-c557-43f5-b372-4899c856f299",
   "metadata": {},
   "source": [
    "# Jaccard-Index versus Accuracy\n",
    "\n",
    "Depending on the use-case some metrics are sub-optimal for determining segmentation quality. We demonstrate this by comparing segmentation results on differently cropped images.\n",
    "\n",
    "See also:\n",
    "* [Maier-Hein, Reinke et al. (Arxiv 2023). Metrics reloaded: Pitfalls and recommendations for image analysis validation\n",
    "](https://arxiv.org/abs/2206.01653)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "abb6988a-077c-474a-9255-8d23b5aeb48c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from skimage.data import human_mitosis\n",
    "from the_segmentation_game import metrics\n",
    "import napari_segment_blobs_and_things_with_membranes as nsbatwm\n",
    "import stackview"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "425d990b-d660-4676-b076-261255eefd71",
   "metadata": {},
   "source": [
    "We use the `human_mitosis` example dataset from scikit-image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2ff66847-93cf-4551-befe-2f0da40f21e2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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\"></img>\n",
       "</td>\n",
       "<td style=\"text-align: center; vertical-align: top;\">\n",
       "\n",
       "<table>\n",
       "<tr><td>shape</td><td>(70,&nbsp;70)</td></tr>\n",
       "<tr><td>dtype</td><td>uint8</td></tr>\n",
       "<tr><td>size</td><td>4.8 kB</td></tr>\n",
       "<tr><td>min</td><td>8</td></tr><tr><td>max</td><td>79</td></tr>\n",
       "</table>\n",
       "<img src=\"data:image/png;base64,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\"></img>\n",
       "</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "StackViewNDArray([[10, 11,  9, ..., 11, 11, 10],\n",
       "                  [10, 10, 11, ..., 12, 12, 11],\n",
       "                  [ 9,  9, 10, ..., 12, 11, 11],\n",
       "                  ...,\n",
       "                  [10,  9,  9, ..., 11, 12, 11],\n",
       "                  [10, 10, 10, ..., 13, 12, 12],\n",
       "                  [10, 10, 10, ..., 13, 13, 13]], dtype=uint8)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image = human_mitosis()[95:165, 384:454]\n",
    "\n",
    "stackview.insight(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a499359-ffed-449a-9311-fa51f2a474f8",
   "metadata": {},
   "source": [
    "Let's assume this is a reference annotation performed by an expert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8682b2a0-c471-415c-a08b-a33ae0c272a4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tr>\n",
       "<td>\n",
       "<img src=\"data:image/png;base64,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\"></img>\n",
       "</td>\n",
       "<td style=\"text-align: center; vertical-align: top;\">\n",
       "<b><a href=\"https://www.napari-hub.org/plugins/napari-segment-blobs-and-things-with-membranes\" target=\"_blank\">nsbatwm made </a>image</b><br/>\n",
       "<table>\n",
       "<tr><td>shape</td><td>(70,&nbsp;70)</td></tr>\n",
       "<tr><td>dtype</td><td>int32</td></tr>\n",
       "<tr><td>size</td><td>19.1 kB</td></tr>\n",
       "<tr><td>min</td><td>0</td></tr><tr><td>max</td><td>3</td></tr>\n",
       "</table>\n",
       "\n",
       "</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "StackViewNDArray([[0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  ...,\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reference_labels = nsbatwm.voronoi_otsu_labeling(image)\n",
    "reference_labels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d037de8-23a1-4e5d-90c3-b2fec0fcff3f",
   "metadata": {},
   "source": [
    "Furthermore, this create a segmentation result we would like to determine the quality of."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "08a19089-92ea-4920-aa44-b019faf6ae5b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tr>\n",
       "<td>\n",
       "<img 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\"></img>\n",
       "</td>\n",
       "<td style=\"text-align: center; vertical-align: top;\">\n",
       "<b><a href=\"https://www.napari-hub.org/plugins/napari-segment-blobs-and-things-with-membranes\" target=\"_blank\">nsbatwm made </a>image</b><br/>\n",
       "<table>\n",
       "<tr><td>shape</td><td>(70,&nbsp;70)</td></tr>\n",
       "<tr><td>dtype</td><td>int32</td></tr>\n",
       "<tr><td>size</td><td>19.1 kB</td></tr>\n",
       "<tr><td>min</td><td>0</td></tr><tr><td>max</td><td>3</td></tr>\n",
       "</table>\n",
       "\n",
       "</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "StackViewNDArray([[0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  ...,\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_labels = nsbatwm.gauss_otsu_labeling(image, outline_sigma=3)\n",
    "\n",
    "test_labels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53229a19-b2bb-4910-9f9d-682387975ce3",
   "metadata": {},
   "source": [
    "## Quality measurement\n",
    "There are plenty of quality metrics for measuring how well the two label images fit to each other. In the following we use [accuracy and jaccard index as implemented in The Segmentation Game](https://github.com/haesleinhuepf/the-segmentation-game#metrics), a napari-plugin for measuring quality metrics of segmentation results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9a3ff87a-4653-417f-9f60-1d0a551f58cc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9744898"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.roc_accuracy_binary(reference_labels, test_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e990bce5-d0e9-483a-a90c-78b7d43cc549",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7274754206261056"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.jaccard_index_sparse(reference_labels, test_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98f221fb-113e-4efa-9ffc-4fd349a4bcf3",
   "metadata": {},
   "source": [
    "We will now apply the same metrics to the label image again, but crop the label image by removing some of the zero-value pixels in the top and left of the label image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a824e910-e224-4ae6-ba45-bf4ded55b895",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.95"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.roc_accuracy_binary(reference_labels[20:,20:], test_labels[20:,20:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "02d9bee7-834d-4675-8344-31cafbec1dde",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7274754206261056"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.jaccard_index_sparse(reference_labels[20:,20:], test_labels[20:,20:])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a252ee6f-809f-47a0-beb9-221ad23605ce",
   "metadata": {},
   "source": [
    "As you can see, the accuracy metric changes, while the Jaccard Index does not. Obviously the accuracy metric depends on the amount of zero-value pixels in the label image. We just visualize the cropped images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dde2cf25-3480-43aa-92a5-d1de6cf5169b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tr>\n",
       "<td>\n",
       "<img src=\"data:image/png;base64,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\"></img>\n",
       "</td>\n",
       "<td style=\"text-align: center; vertical-align: top;\">\n",
       "<b><a href=\"https://www.napari-hub.org/plugins/napari-segment-blobs-and-things-with-membranes\" target=\"_blank\">nsbatwm made  made </a>image</b><br/>\n",
       "<table>\n",
       "<tr><td>shape</td><td>(50,&nbsp;50)</td></tr>\n",
       "<tr><td>dtype</td><td>int32</td></tr>\n",
       "<tr><td>size</td><td>9.8 kB</td></tr>\n",
       "<tr><td>min</td><td>0</td></tr><tr><td>max</td><td>3</td></tr>\n",
       "</table>\n",
       "\n",
       "</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "StackViewNDArray([[0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  ...,\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reference_labels[20:,20:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3505144b-d036-4d12-a903-15c8358f8ace",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tr>\n",
       "<td>\n",
       "<img 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\"></img>\n",
       "</td>\n",
       "<td style=\"text-align: center; vertical-align: top;\">\n",
       "<b><a href=\"https://www.napari-hub.org/plugins/napari-segment-blobs-and-things-with-membranes\" target=\"_blank\">nsbatwm made  made </a>image</b><br/>\n",
       "<table>\n",
       "<tr><td>shape</td><td>(50,&nbsp;50)</td></tr>\n",
       "<tr><td>dtype</td><td>int32</td></tr>\n",
       "<tr><td>size</td><td>9.8 kB</td></tr>\n",
       "<tr><td>min</td><td>0</td></tr><tr><td>max</td><td>3</td></tr>\n",
       "</table>\n",
       "\n",
       "</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "StackViewNDArray([[0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  ...,\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0],\n",
       "                  [0, 0, 0, ..., 0, 0, 0]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_labels[20:,20:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "217cf4bd-25f2-4135-9539-59f895d71f38",
   "metadata": {},
   "source": [
    "## Explanation\n",
    "When comparing the equations of accuracy $A$ and Jaccard index $J$, it is obvious that both do the same kind-of, but only accuracy includes the number of zero-value pixels in both label images. These pixels are the true-negatives $TN$.\n",
    "\n",
    "$$\n",
    "  A =\\frac{TP + TN}{FN + FP + TP + TN}\n",
    "$$\n",
    "\n",
    "$$\n",
    "  J =\\frac{TP}{FN + FP + TP}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95691bdb-c2eb-43b5-94da-1c5aae1bf44a",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "Compute the [Dice coefficient](https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient) of `test_labels` compared to `reference_labels`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3cccf21-d0a3-4b78-8074-c8881807f287",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.19"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}