Tracking System for Living Beings and Objects: Integration of Accessible Mathematical Contributions and Graph Theory in Tracking System Design

Abstract

This paper presents a theoretical framework for a tracking system, wherein we generalize the formulation of a tracking system de- signed for living beings and objects. Many tracking systems are typically developed within specific frameworks, either for tracking in limited or unlimited space. The latter often relies on technical tools dedicated to tracking living beings or objects. In this study, we propose a system theory that formulates the task of tracking both living beings and ob- jects. Graphical modeling is widely employed in tracking to establish correct connections between the elements to be tracked and other com- ponents in the system. However, basing a tracking system on graphs in both its theoretical and practical aspects remains the optimal method for achieving a high-performing, relevant, and adaptable system in vari- ous situations. This paper introduces a tracking system based on graph learning and hypergraphs, fully leveraging direct and indirect relations while considering the order between multiple system links. Tracking is thus formulated as a search problem on graphs and hypergraphs, with vertices representing the elements of the system (living beings or ob- jects), and edges representing the types of connections between these elements. We define a law governing the relationships between the ver- tices, managing the shared data between the elements of the system and other processes. Furthermore, examples of single and multi-context track- ing situations demonstrate that the proposed system, in its theoretical foundation, outperforms existing systems.