Density-based modeling of visual features is very common in computer vision research due to the uncertainty of observed data; so accurate and simple density representation is essential to improve the quality of overall systems. Even though various methods, either parametric or non-parametric, are proposed for density modeling, there is a significant trade-off between flexibility and computational complexity. Therefore, a new compact and flexible density representation is necessary, and the dissertation provides a solution to alleviate the problems as follows.

First, we describe a compact and flexible representation of probability density functions using a mixture of Gaussians which is called Kernel Density Approximation (KDA). In this framework, the number of Gaussians components as well as the weight, mean, and covariance of each Gaussian component are determined automatically by mean-shift mode-finding procedure and curvature fitting. An original density function estimated by kernel density estimation is simplified into a compact mixture of Gaussians by the proposed method; memory requirements are dramatically reduced while incurring only a small amount of error. In order to adapt to variations of visual features, sequential kernel density approximation is proposed in which a sequential update of the density function is performed in linear time.

Second, kernel density approximation is incorporated into a Bayesian filtering framework, and we design a Kernel-based Bayesian Filter (KBF). Particle filters have inherent limitations such as degeneracy or loss of diversity which are mainly caused by sampling from discrete proposal distribution. In kernel-based Bayesian filtering, every relevant probability density function is continuous and the posterior is simplified by kernel density approximation so as to propagate a compact form of the density function from step to step. Since the proposal distribution is continuous in this framework, the problems in conventional particle filters are alleviated.

The sequential kernel density approximation technique is naturally applied to background modeling, and target appearance modeling for object tracking. Also, the kernel-based Bayesian filtering framework is applied to object tracking, which shows improved performance with a smaller number of samples. We demonstrate the performance of kernel density approximation and its application through various simulations and experiments with real videos.