Detecting the Topological Development in a Complex Moving Region

Exploring the topology of a region object requires the mathematical study of its geometric properties that are preserved under deformations. A moving region whose location and extent change over time can undergo several topological changes such as the splitting of a region or the formation of a hole. The study of this kind of changes is important in many applications, e.g., for the topology control of wireless sensor networks and the processing of animation images in multimedia applications. Since we often lack the ability of capturing the location, extent, and shape changes of a moving region during its lifespan, it is challenging to detect these changes. Further, for a complex moving region containing multiple components, it is difficult to determine which component before a change corresponds to which component after the change. In this article, we propose a model pursuing a three-phase strategy to determine the topological changes of a complex moving region represented by a sequence of snapshots called observations. The first phase partitions the observations into several evaluation units. The second phase uniquely maps each unit before the change to exactly one unit after the change. The third phase interprets the topological changes by integrating all basic topological changes from the evaluation units. We also show the detailed algorithms of this three-phase strategy which turn out to be efficient. Finally, a case study illustrates our concepts.