Background Subtraction Using Gaussian Mixture Models (GMM)

In computer vision, background subtraction is a widely used technique for separating foreground objects from the background in video streams. Among various implementation approaches, Gaussian Mixture Models (GMM) provide a robust method that can model complex background scenes and adaptively update the background model to accommodate environmental changes. In the GMM approach, each pixel in the video sequence is modeled as a mixture of Gaussian distributions, where each distribution represents a potential background component. The algorithm typically maintains 3-5 Gaussian distributions per pixel to capture multimodal backgrounds like waving trees or flickering screens. Key parameters including mean, covariance, and weight for each distribution are continuously updated using an online learning mechanism, often implemented through an expectation-maximization (EM) approach or incremental version of the algorithm. The implementation generally involves comparing new pixel values against existing distributions, where matches are used to update parameters while unmatched values may spawn new distributions. A common practice involves ordering distributions by their weight/variance ratio and selecting the top distributions as background components. The OpenCV library provides cv2.createBackgroundSubtractorMOG2() function which implements an optimized version of this algorithm with automatic parameter adjustment and shadow detection capabilities. This adaptive modeling allows the system to handle gradual lighting changes, periodic motions, and long-term scene variations while maintaining sensitivity to genuine foreground objects. The model parameters evolve over time through recursive updating equations, enabling real-time performance suitable for surveillance systems and motion detection applications.