Background Segmentation and Motion Detection

Gaussian Mixture Model

All generated data points are derived from a mixture of a finite Gaussian distributions that has no known parameters.
A Gaussian mixture of three normal distributions:

As human's height as an example, height is typically modeled as a normal distribution for each gender with a mean of approximately 5'10" for males and 5'5" for females.
Given only the height data and not the gender assignments for each data point, the distribution of all heights would follow the sum of two scaled (different variance) and shifted (different mean) normal distributions.

Mathematically, Gaussian mixture models are an example of a parametric probability density function, which can be represented as a weighted sum of all densities of Gaussian components.
The parameters for Gaussian mixture models are derived either from maximum a posteriori estimation or an iterative expectation-maximization algorithm from a prior model which is well trained.

OpenCV: MEAN SHIFT TRACKING

Adaptive background mixture models for real-time tracking

Chris Stauffer and W.E.L Grimson

Abstract

This paper discusses modeling each pixel as a mixture of Gaus- sians and using an on-line approximation to update the model.

Introduction

The non-adaptive methods of backgrounding is useful only in highly-supervised, short-term tracking applications without significant changes in the scene.

A standard method of adaptive backgrounding is averaging the images over time, creating a background approximation which is similar to the current static scene except where motion occurs.

Rather than explicitly modeling the values of all the pixels as one particular type of distribution, we simply model the values of a particular pixel as a mixture of Gaussians.

We consider the values of a particular pixel over time as a “pixel process”. The “pixel process” is a time series of pixel values,