Kernels and Convolution.ipynb

kernels-and-convolution.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/thepatrickniyo/2a0632f5dc0fc1a0338fb2cf0fdce0f2/kernels-and-convolution.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MjQI6ZcWPqg5"
      },
      "outputs": [],
      "source": [
        "#!/usr/bin/env python3\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "IMAGE = np.array([[1,0,0.13,0.16,0,1],\n",
        "          [0,0.13,0,0,1,0],\n",
        "          [0.6,0.13,0.06,1,0,0], # Added a 0 to match column count\n",
        "          [0,1,1,1,1,0],\n",
        "          [1,0,1,1,1,0], # Removed extra 1 to match column count\n",
        "          [1,1,0,0,1,1]])\n",
        "\n",
        "def convolve_grayscale_valid(image, kernel):\n",
        "    h, w = image.shape\n",
        "    kh, kw = kernel.shape\n",
        "\n",
        "    # Calculate the dimensions of the output convolved image\n",
        "    output_h = h - kh + 1\n",
        "    output_w = w - kw + 1\n",
        "\n",
        "    convolved_image = np.zeros((output_h, output_w))\n",
        "\n",
        "    for i in range(output_h):\n",
        "        for j in range(output_w):\n",
        "            overlapped_area = image[i:i+kh, j:j+kw]\n",
        "            convolved_image[i,j] = np.sum(overlapped_area * kernel)\n",
        "\n",
        "    return convolved_image"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Theory number Anesu\n",
        "\n",
        "By the size of the convolved\n",
        "\n",
        "9*9 image\n",
        "3*3 Kernel\n",
        "\n",
        "4*4 conv_img\n",
        "\n",
        "og_img_width - kernel_width+1\n",
        "\n",
        "7*7 conv_img"
      ],
      "metadata": {
        "id": "Q-B2aiIwRNc5",
        "outputId": "b062b7f4-1ebf-46a1-c35a-20d34acb9529",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 106
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "SyntaxError",
          "evalue": "invalid syntax (ipython-input-1-2377775834.py, line 3)",
          "traceback": [
            "\u001b[0;36m  File \u001b[0;32m\"/tmp/ipython-input-1-2377775834.py\"\u001b[0;36m, line \u001b[0;32m3\u001b[0m\n\u001b[0;31m    By the size of the convolved\u001b[0m\n\u001b[0m       ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#!/usr/bin/env python3\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from tensorflow import keras # <--- Add this import\n",
        "\n",
        "def convolve_grayscale_valid(image, kernel):\n",
        "    # image is now a single 2D array (height, width)\n",
        "    h, w = image.shape\n",
        "\n",
        "    kh, kw = kernel.shape\n",
        "\n",
        "    # Let's initialize the variables for height and width\n",
        "    new_h = h - kh + 1\n",
        "    new_w = w - kw + 1\n",
        "\n",
        "    # convolved_image is now a single 2D array\n",
        "    convolved_image = np.zeros((new_h, new_w))\n",
        "\n",
        "    for i in range(new_h):\n",
        "        for j in range(new_w):\n",
        "            # No need for batch dimension (:) anymore\n",
        "            overlapped_area = image[i:i+kh, j:j+kw]\n",
        "            convolved_image[i, j] = np.sum(overlapped_area * kernel)\n",
        "\n",
        "    return convolved_image\n",
        "\n",
        "if __name__ == '__main__':\n",
        "    # Load MNIST dataset directly using Keras\n",
        "    # The dataset comes as (training_images, training_labels), (test_images, test_labels)\n",
        "    (images, _), (_, _) = keras.datasets.mnist.load_data()\n",
        "\n",
        "    # Normalize images: pixel values typically range from 0-255.\n",
        "    # We convert them to float32 and scale them to 0-1 for better processing.\n",
        "    images = images.astype('float32') / 255.0\n",
        "\n",
        "    # Select only the first image from the dataset for demonstration\n",
        "    single_image = images[0]\n",
        "    print(\"Original image shape:\", single_image.shape)\n",
        "\n",
        "    # Define the kernel for edge detection (e.g., Sobel-like vertical edge detector)\n",
        "    kernel = np.array([[1, 0, -1],\n",
        "                       [1, 0, -1],\n",
        "                       [1, 0, -1]])\n",
        "\n",
        "    # Perform the convolution on the single image\n",
        "    convolved_single_image = convolve_grayscale_valid(single_image, kernel)\n",
        "    print(\"Convolved image shape:\", convolved_single_image.shape)\n",
        "\n",
        "    # Display the original and convolved images\n",
        "    plt.figure(figsize=(10, 5))\n",
        "\n",
        "    plt.subplot(1, 2, 1)\n",
        "    plt.imshow(single_image, cmap='gray')\n",
        "    plt.title(\"Original Image\")\n",
        "    plt.axis('off') # Hide axes for cleaner image display\n",
        "\n",
        "    plt.subplot(1, 2, 2)\n",
        "    plt.imshow(convolved_single_image, cmap='gray')\n",
        "    plt.title(\"Convolved Image (Edge Detection)\")\n",
        "    plt.axis('off') # Hide axes\n",
        "    plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 480
        },
        "id": "9jgYyPzxROyP",
        "outputId": "5c65bdf9-2393-4d4a-8340-896f03583b28"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "\u001b[1m11490434/11490434\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 0us/step\n",
            "Original image shape: (28, 28)\n",
            "Convolved image shape: (26, 26)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}