An optimum framework for entities tracking in populations

The entities tracking within populations is a task encountered in many scenarios such as observations of the biological cells, studying behaviors of crowds, and evaluating transactions on the Internet. This paper outlines the optimality of a tracking process where associations between the entities in consecutive populations observed at discrete time instances must be determined. As the sub-optimum tracking methods are prone to the propagation of association errors, the optimum tracking is defined as a Maximum A posteriori Probability (MAP) or a Maximum Likelihood (ML) estimation problem over the set of time-varying attributes associated to each entity in the population. A subset of these attributes can be then also used to evaluate the characteristics of individuals in the population as one direct application of the entities tracking.