intersection_over_union_(1).ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ali3brt/-Ali3brt-s-Machine-Learning-and-Deep-Learning-Projects/blob/main/intersection_over_union_(1).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w1Tys8Cz7Ut0"
      },
      "source": [
        "# Intersection over Union (IoU)\n",
        "\n",
        "Intersection over Union (IoU) is also known as Jaccard Index, have a look at Wikipedia for a great explanation - [Wikipedia](https://en.wikipedia.org/wiki/Jaccard_index)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "4nnKhy5E7Ut1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "68e0a175-a194-44cf-a11c-6d2d2290c4ff"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m650.7/650.7 kB\u001b[0m \u001b[31m10.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m950.8/950.8 kB\u001b[0m \u001b[31m7.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h"
          ]
        }
      ],
      "source": [
        "!pip  install -q keras-cv\n",
        "import numpy as np\n",
        "import tensorflow as tf\n",
        "import matplotlib.pyplot as plt\n",
        "import keras_cv"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "NUtLRfqY7Ut2"
      },
      "outputs": [],
      "source": [
        "# Define the bounding boxes\n",
        "box1 = np.array([50, 50, 100, 100])  # [x1, y1, x2, y2]\n",
        "box2 = np.array([75, 75, 150, 150])  # [x1, y1, x2, y2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "KGgOR7li7Ut2"
      },
      "outputs": [],
      "source": [
        "# Calculate the intersection and union\n",
        "x1 = max(box1[0], box2[0])\n",
        "y1 = max(box1[1], box2[1])\n",
        "x2 = min(box1[2], box2[2])\n",
        "y2 = min(box1[3], box2[3])\n",
        "intersection = max(0, x2 - x1) * max(0, y2 - y1)\n",
        "area1 = (box1[2] - box1[0]) * (box1[3] - box1[1])\n",
        "area2 = (box2[2] - box2[0]) * (box2[3] - box2[1])\n",
        "union = area1 + area2 - intersection"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "3MJMhqbc7Ut3"
      },
      "outputs": [],
      "source": [
        "# Calculate the IoU\n",
        "iou = intersection / union"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "Hkub2mO77Ut3",
        "outputId": "01c5b42b-94ab-4b15-9112-2d63ff390d2d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 463
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plot the bounding boxes and intersection/union\n",
        "fig, ax = plt.subplots()\n",
        "rect1 = plt.Rectangle((box1[0], box1[1]), box1[2] - box1[0], box1[3] - box1[1], linewidth=1, edgecolor='r', facecolor='none')\n",
        "rect2 = plt.Rectangle((box2[0], box2[1]), box2[2] - box2[0], box2[3] - box2[1], linewidth=1, edgecolor='b', facecolor='none')\n",
        "ax.add_patch(rect1)\n",
        "ax.add_patch(rect2)\n",
        "plt.title('Intersection over Union (IoU)')\n",
        "plt.plot([x1, x2], [y1, y1], linewidth=1, color='k')\n",
        "plt.plot([x1, x2], [y2, y2], linewidth=1, color='k')\n",
        "plt.plot([x1, x1], [y1, y2], linewidth=1, color='k')\n",
        "plt.plot([x2, x2], [y1, y2], linewidth=1, color='k')\n",
        "plt.text(0.5 * (box1[0] + box1[2]), box1[1] - 10, 'Ground Truth Area = %d' % area1, horizontalalignment='center', verticalalignment='top', fontsize=12, color='r')\n",
        "plt.text(0.5 * (box2[0] + box2[2]), box2[1] - 10, 'Prediction Area = %d' % area2, horizontalalignment='center', verticalalignment='top', fontsize=12, color='b')\n",
        "plt.text(40, 130, f'Intersection = {intersection}', fontsize=10, color='k')\n",
        "plt.text(40, 120, f'Union = {union}', fontsize=10, color='k')\n",
        "plt.text(40, 110, f'IoU = {iou:.3f}', fontsize=10, color='k')\n",
        "plt.text(100, 110, f'False Positive', fontsize=10, color='b')\n",
        "plt.text(60, 60, f'False Negative', fontsize=10, color='r')\n",
        "plt.text(78, 80, f'True Positive', fontsize=10, color='k')\n",
        "plt.axis('off')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hV2z9mig7Ut4"
      },
      "source": [
        "### Implementation with Keras\n",
        "\n",
        "#### Detection (bounding boxes) input\n",
        "\n",
        "To calculate the IoU for bounding boxes, with the coordinate of the edges, kerascv [compute_iou](https://keras.io/api/keras_cv/bounding_box/utils/compute_iou/) will do."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "TV7C4_sc7Ut4",
        "outputId": "1fb84688-326d-4392-9800-0365f6038ac8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 50,  50, 100, 100]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "# wrap box1 in axis 0 to make it a batch of size 1\n",
        "box1 = np.expand_dims(box1, axis=0)\n",
        "box1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "skxtPqN47Ut5",
        "outputId": "f2a2eb2a-6112-4d67-b1d1-b623299dcdf3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 75,  75, 150, 150]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "# wrap box1 in axis 0 to make it a batch of size 1\n",
        "box2 = np.expand_dims(box2, axis=0)\n",
        "box2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "44qCm7lD7Ut5",
        "outputId": "a922a930-d76b-40a4-efd4-e989e5907160",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.08333334]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "keras_cv.bounding_box.compute_iou( boxes1=box1, boxes2=box2, bounding_box_format='xyxy').numpy()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZtPYAn-X7Ut5"
      },
      "source": [
        "#### Segmentation (pixels) Input\n",
        "\n",
        "Note that in Keras `IoU`, `BinaryIoU` and `meanIoU` have a different input than the bounding box edges - that is the prediction per pixel.\n",
        "In Keras:\n",
        "* `BinaryIoU` calculates the IoU over a single binary class ([docs](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/BinaryIoU))\n",
        "* `IoU` calculates IoU over a single class ([docs](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/IoU))\n",
        "* `meanIoU` calculates the mean IoU over multiple classes ([docs](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/MeanIoU))\n",
        "\n",
        "The formula for all of these three is:\n",
        "```\n",
        "iou = true_positives / (true_positives + false_positives + false_negatives)\n",
        "```\n",
        "\n",
        "For example, assume you are trying to predict if each pixel is cat, dog, or background.\n",
        "You have 80% background pixels, 10% dog, and 10% cat.\n",
        "The model predicts 100% background."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D2AOq6iG7Ut5"
      },
      "source": [
        "#### IoU"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "TVtlrVKY7Ut5",
        "outputId": "69c8b5e1-4a61-465b-9d26-522b99ea1f7d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.3333333"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "m = tf.keras.metrics.IoU(num_classes=2, target_class_ids=[0])\n",
        "m.update_state([0, 0, 1, 1], [0, 1, 0, 1])\n",
        "m.result().numpy()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sKv8sdPe7Ut6"
      },
      "source": [
        "Let's analyze:\n",
        "\n",
        "|Ground Truth|Prediction|Outcome|\n",
        "|------------|----------|-------|\n",
        "|0|0|True Positive|\n",
        "|0|1|False Negative|\n",
        "|1|0|False Positive|\n",
        "|1|1|True Negative|\n",
        "\n",
        "So according to the formula:\n",
        "\n",
        "```\n",
        "iou = 1/(1+1+1) = 0.33\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6PJ7t-zi7Ut6"
      },
      "source": [
        "#### Binary IoU"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "Jcn8H2Br7Ut6",
        "outputId": "0b27bd0b-7341-4738-fb87-3afe0ad9d0ec",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.33333334"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "m = tf.keras.metrics.BinaryIoU(target_class_ids=[0, 1], threshold=0.3)\n",
        "m.update_state([0, 1, 0, 1], [0.1, 0.2, 0.4, 0.7])\n",
        "m.result().numpy()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rcs4xab87Ut6"
      },
      "source": [
        "**To the Student**: To understand why the calculation is over both labels, see the docs of `BinaryIoU` for `target_class_ids`.\n",
        "\n",
        "Let's analyze:\n",
        "\n",
        "|Ground Truth|Prediction|Outcome with respect to label 0|Output with respect to label 1|\n",
        "|------------|----------|-------------------------------|------------------------------|\n",
        "|0|0.1<0.3 => 0|True Positive|True Negative|\n",
        "|1|0.2<0.3 => 0|False Positive|False Negative|\n",
        "|0|0.4>0.3 => 1|False Negative|False Positive|\n",
        "|1|0.7>0.3 => 1|True Negative|True Positive|\n",
        "\n",
        "So according to the formula:\n",
        "\n",
        "```\n",
        "iou = 1/(1+1+1) + 1/(1+1+1)= (0.33 + 0.33)/2 = 0.33\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "raWhgdl07Ut6"
      },
      "source": [
        "#### MeanIoU"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "PzwVdnTH7Ut6",
        "outputId": "8839bce4-b7c5-4ad9-b31b-59c9b8a699f9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.33333334"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "m = tf.keras.metrics.MeanIoU(num_classes=2)\n",
        "m.update_state([0, 0, 1, 1], [0, 1, 0, 1])\n",
        "m.result().numpy()\n"
      ]
    }
  ],
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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