Bounded Asymmetrical Student´s-t Mixture Model

The finite mixture model based on the Student´s-t distribution, which is heavily tailed and more robust than the Gaussian mixture model (GMM), is a flexible and powerful tool to address many computer vision and pattern recognition problems. However, the Student´s-t distribution is unbounded and symmetrical around its mean. In many applications, the observed data are digitalized and have bounded support. The distribution of the observed data usually has an asymmetric form. A new finite bounded asymmetrical Student´s-t mixture model (BASMM), which includes the GMM and the Student´s-t mixture model (SMM) as special cases, is presented in this paper. We propose an extension of the Student´s-t distribution in this paper. This new distribution is sufficiently flexible to fit different shapes of observed data, such as non-Gaussian, nonsymmetric, and bounded support data. Another advantage of the proposed model is that each of its components can model the observed data with different bounded support regions. In order to estimate the model parameters, previous models represent the Student´s-t distributions as an infinite mixture of scaled Gaussians. We propose an alternate approach in order to minimize the higher bound on the data negative log-likelihood function, and directly deal with the Student´s-t distribution. As an application, our method has been applied to image segmentation with promising results.