Likelihood Function for Multi-target Color Tracking Using Discrete Finite Mixtures

Abstract

Color-based object trackers have been proved robust and versatile in visual tracking applications. There are different techniques used in the literature to compare the color similarity between the current object being tracked and a reference model and the most common being a Gaussian approximation of the color histogram distribution and a distance measure based on the Bhattacharyya coefficient to accomplish for the target correspondence task. This approach requires constant updating in order to preserve the invariability of the color model and therefore requires ad-hoc techniques for estimating the parameters of the Gaussian likelihood and the histogram update model. In this paper, we present a more general approach to color-based object tracking using a finite mixture of discrete multivariate distributions. More particularly, the Dirichlet Compound Multinomial (DCM) or Polya density is used to directly model random color histograms from a single target. Conversely, a mixture of Polya distributions is proposed as a multi-target color likelihood. The approach presented in this work only requires to estimate the parameters of the DCM mixture, with a single component of the mixture representing the color distribution of a single object. We demonstrate the improvement obtained with this method compared to the more traditional Gaussian assumption in real scenes, solving complex problems like changes in illumination and perspective.