Introduction_to_pooling_and_cov_layers_using_numpy.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "xauvSk9ESqVB",
        "outputId": "7918a8d7-2ac3-42c9-9e65-dae78d669409"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Visual Introduction to CNN: Convolution and Pooling\n",
        "\n",
        "# Convolutional Neural Networks (CNNs) are powerful models for image analysis. Let's explore the convolutional and pooling operations.\n",
        "\n",
        "# Input Image\n",
        "input_image = np.array([[1, 1, 0, 0, 0, 0],\n",
        "                       [0, 1, 1, 0, 0, 0],\n",
        "                       [0, 0, 1, 1, 0, 0],\n",
        "                       [0, 0, 0, 1, 1, 0],\n",
        "                       [0, 0, 0, 0, 1, 1],\n",
        "                       [0, 0, 0, 0, 0, 1]])\n",
        "\n",
        "# Display the input image\n",
        "plt.imshow(input_image, cmap='gray')\n",
        "plt.title('Input Image')\n",
        "plt.axis('off')\n",
        "plt.show()\n",
        "\n",
        "# Convolutional Operation (Edge Detection)\n",
        "kernel = np.array([[1, 0, -1],\n",
        "                   [1, 0, -1],\n",
        "                   [1, 0, -1]])\n",
        "\n",
        "output_conv = np.zeros_like(input_image)\n",
        "\n",
        "for i in range(input_image.shape[0] - kernel.shape[0] + 1):\n",
        "    for j in range(input_image.shape[1] - kernel.shape[1] + 1):\n",
        "        output_conv[i, j] = np.sum(input_image[i:i+kernel.shape[0], j:j+kernel.shape[1]] * kernel)\n",
        "\n",
        "# Display the output of the convolutional operation\n",
        "plt.imshow(output_conv, cmap='gray')\n",
        "plt.title('Convolutional Operation')\n",
        "plt.axis('off')\n",
        "plt.show()\n",
        "\n",
        "# Max Pooling Operation\n",
        "pool_size = 2\n",
        "\n",
        "output_pool = np.zeros((output_conv.shape[0] // pool_size, output_conv.shape[1] // pool_size))\n",
        "\n",
        "for i in range(0, output_conv.shape[0], pool_size):\n",
        "    for j in range(0, output_conv.shape[1], pool_size):\n",
        "        output_pool[i // pool_size, j // pool_size] = np.max(output_conv[i:i+pool_size, j:j+pool_size])\n",
        "\n",
        "# Display the output of the max pooling operation\n",
        "plt.imshow(output_pool, cmap='gray')\n",
        "plt.title('Max Pooling Operation')\n",
        "plt.axis('off')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let explore more Kernels "
      ],
      "metadata": {
        "id": "Tgd3dPzWTkyP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Visual Introduction to CNN: Convolution with Multiple Kernels\n",
        "\n",
        "# Convolutional Neural Networks (CNNs) use multiple kernels to extract different features from an image. Let's visualize this process.\n",
        "\n",
        "# Input Image\n",
        "input_image = np.array([[1, 1, 0, 0, 0, 0],\n",
        "                       [0, 1, 1, 0, 0, 0],\n",
        "                       [0, 0, 1, 1, 0, 0],\n",
        "                       [0, 0, 0, 1, 1, 0],\n",
        "                       [0, 0, 0, 0, 1, 1],\n",
        "                       [0, 0, 0, 0, 0, 1]])\n",
        "\n",
        "# Display the input image\n",
        "plt.imshow(input_image, cmap='gray')\n",
        "plt.title('Input Image')\n",
        "plt.axis('off')\n",
        "plt.show()\n",
        "\n",
        "# Convolutional Operation with Multiple Kernels\n",
        "kernels = np.array([[[1, 1],\n",
        "                     [0, 1]],\n",
        "                    \n",
        "                    [[-1, 0],\n",
        "                     [0, 1]]])\n",
        "\n",
        "output_conv = np.zeros_like(input_image)\n",
        "\n",
        "for k in range(kernels.shape[0]):\n",
        "    for i in range(input_image.shape[0] - kernels.shape[1] + 1):\n",
        "        for j in range(input_image.shape[1] - kernels.shape[2] + 1):\n",
        "            output_conv[i, j] += np.sum(input_image[i:i+kernels.shape[1], j:j+kernels.shape[2]] * kernels[k])\n",
        "\n",
        "# Normalize output for visualization\n",
        "output_conv = (output_conv - np.min(output_conv)) / (np.max(output_conv) - np.min(output_conv))\n",
        "\n",
        "# Display the output of the convolutional operation\n",
        "plt.imshow(output_conv, cmap='gray')\n",
        "plt.title('Convolutional Operation')\n",
        "plt.axis('off')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 839
        },
        "id": "Hi_WRVe3TnZO",
        "outputId": "e40f38a3-3763-4273-ade4-11bc2b761aaa"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ixF3-NBCSrGL"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}