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Update notebooks directory
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ami-sc
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notebooks/DiscreteWaveletTransform.ipynb
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338
notebooks/DiscreteWaveletTransform.ipynb
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@ -1,306 +0,0 @@
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{
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"cells": [
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"***\n",
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"\n",
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"**PCA - Test Notebook**\n",
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"\n",
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"The following notebook serves as a template and testing code for the implementation of the Principal Component Analysis (PCA).\n",
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"\n",
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"***"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- **Required Libraries:**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import cv2\n",
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"import numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(460, 860, 3)"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Load an image for testing purposes.\n",
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"test_img = cv2.imread(\"../data/fire_dataset/fire_images/fire.1.png\")\n",
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"test_img.shape"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Visualize the image.\n",
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"cv2.imshow(\"Test Image\", test_img)\n",
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"cv2.waitKey(0)\n",
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"cv2.destroyAllWindows()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"- Red Channel Dimensions: (460, 860)\n",
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"- Green Channel Dimensions: (460, 860)\n",
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"- Blue Channel Dimensions: (460, 860)\n"
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]
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}
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],
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"source": [
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"# Get the channels of the image.\n",
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"b, g, r = cv2.split(test_img)\n",
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"\n",
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"# Check the dimensions of the channels.\n",
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"print(\"- Red Channel Dimensions:\", r.shape)\n",
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"print(\"- Green Channel Dimensions:\", g.shape)\n",
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"print(\"- Blue Channel Dimensions:\", b.shape)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Normalize each channel so that each value is in the scale of [0, 1].\n",
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"# Each value (pixel) can have a maximum value of 255.\n",
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"r_norm = r / 255\n",
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"g_norm = g / 255\n",
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"b_norm = b / 255"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(3, 395600)"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# \"Flatten\" the channels.\n",
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"r_norm = r_norm.reshape([-1])\n",
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"g_norm = g_norm.reshape([-1])\n",
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"b_norm = b_norm.reshape([-1])\n",
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"\n",
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"# Stack the individual arrays to a single array.\n",
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"flat_rgb = np.vstack([r_norm, g_norm, b_norm])\n",
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"flat_rgb.shape"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- To perform a Principal Component Analysis (PCA), we must first center the data.\n",
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"- This is done by subtracting the mean $\\mu$.\n",
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"\n",
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"$$x' = x - \\mu$$\n",
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"\n",
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"- We consider each pixel as a sample, living in a 3-channel (3D) space.\n",
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"- This means we have a $3 \\times n$ array:\n",
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" - The rows are the dimensions.\n",
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" - The columns are the pixels.\n",
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"- The mean is calculated *across columns*.\n",
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"- We do not need to standardize because data is already in the same scale."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(3, 395600)"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Center the data.\n",
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"x_center = flat_rgb - np.mean(flat_rgb, axis = 1, keepdims = True)\n",
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"x_center.shape"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- Compute the covariance matrix of the centered data as follows:\n",
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"\n",
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"$$C = \\dfrac{1}{N} X \\: X^T$$\n",
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"\n",
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"- We get a $D \\times D$ matrix (in this case, $3 \\times 3$)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(3, 3)"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"cov = np.cov(x_center)\n",
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"cov.shape"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- Now, we must perform the eigendecomposition of the covariance matrix.\n",
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"- We get $3$ eigenvalues associated with the $3$ corresponding eigenvectors."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"eigenvalues, eigenvectors = np.linalg.eig(cov)"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- NumPy does not return the eigenvalues and eigenvectors in sorted order.\n",
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"- We must sort them manually."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Sort the eigenvalues and eigenvectors in order of increasing variance kept.\n",
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"# The \"-\" is needed for ascending order.\n",
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"idx = np.argsort(-eigenvalues)\n",
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"eigenvalues = eigenvalues[idx]\n",
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"eigenvectors = eigenvectors[:,idx]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(9,)"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# \"Flatten\" the eigenvectors for the model.\n",
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"eigenvectors = eigenvectors.reshape([-1])\n",
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"eigenvectors.shape"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"***\n",
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"\n",
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"- The theory is that each eigenvector is a *summary* of each channel (one eigenvector per channel).\n",
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"- Each eigenvector captures the variation in each channel.\n",
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"- It should be an accurate representation of the relevant parts of the channel.\n",
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"- The model should be able to differentiate between a *fire* and a *non-fire* image using the eigenvectors.\n",
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"- This also means we do not need the pixels anymore. We can give the eigenvectors directly to the model."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Fire_Detection",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.3"
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},
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"orig_nbformat": 4
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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12
notebooks/README.md
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12
notebooks/README.md
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# `/notebooks`
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***
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## Directory Contents
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- `./README.md`:
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- This file.
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- `./XGBoost_Model.ipynb`:
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- Full training and hyperparameter tuning process for the XGBoost model used in the motion detection code.
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- `./DiscreteWaveletTransform.ipynb`:
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- Example analysis for the histogram generation and wavelet decomposition.
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