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Background Subtraction using Gaussian Mixture Models (GMM)

This project implements a custom Gaussian Mixture Model (GMM) for background subtraction in images and videos. GMM is a probabilistic model that represents a mixture of multiple Gaussian distributions, commonly used for modeling pixel distributions in background subtraction tasks.

Table of Contents

• Project Overview
• Installation
• Usage
• Project Structure
• Results
• References

Project Overview

This implementation focuses on using a GMM for background subtraction in visual data. The primary steps include:

1. Building the GMM Class: Implements GMM from scratch with methods for initialization, expectation-maximization (E-step and M-step), and prediction.
2. Video Frame Processing: Helper functions to display video frames or save them to a file, enabling analysis and visualization of GMM-based background subtraction.
3. Application to Background Subtraction: Uses pixel distributions modeled by GMM to separate foreground (moving objects) from the background.

Installation

To run this project, you will need the following dependencies:

pip install numpy matplotlib opencv-python

Usage

1. Implement the GMM:

   • The GMM class provided in Background Subtraction.ipynb contains methods for GMM-based background subtraction.

2. Run the Notebook:

   • Execute the notebook to fit the GMM model to visual data. The notebook includes:
     • Class definitions for the GMM.
     • Helper functions for frame display and saving.

3. Display and Save Frames:

   • The helper functions display_frames and save_frames help visualize and save the background subtraction results.

Sample Commands

# Instantiate and fit GMM
gmm = GMM(n_components=3, tol=1e-4, max_iter=100)
gmm.fit(data)

# Display results as video
display_frames(frames, fps=10)

# Save results
save_frames(frames, fps=10, output_path='./results', file_name='background_subtraction_result')

Project Structure

Background Substraction.ipynb   # Main notebook with GMM implementation and example usage
README.md                       # Project README file

Results

Example output showing background subtraction results using GMM and averaging:

Background Subtraction Results - Frame Averaging
Background Subtraction Results - GMM

References

• Gaussian Mixture Models - scikit-learn
• Understanding GMMs - YouTube Video 1
• Introduction to GMMs - YouTube Video 2

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