Distance Transform-Based Skeleton Extraction and Its Applications in Sensor Networks

We study the problem of skeleton extraction for large-scale sensor networks with reliance purely on connectivity information. Existing efforts in this line highly depend on the boundary detection algorithms, which are used to extract accurate boundary nodes. One challenge is that in practical this could limit the applicability of the boundary detection algorithms. For instance, in low node density networks where boundary detection algorithms do not work well, the extracted boundary nodes are often incomplete. This paper brings a new view to skeleton extraction from a distance transform perspective, bridging the distance transform of the network and the incomplete boundaries. As such, we propose a distributed and scalable algorithm for skeleton extraction, called DIST, based on DIStance Transform, while incurring low communication overhead. The proposed algorithm does not require that the boundaries are complete or accurate, which makes the proposed algorithm more practical in applications. First, we compute the distance transform of the network. Specifically, the distance (hop count) of each node to the boundaries of a sensor network is estimated. The node map consisting of the distance values is considered as the distance transform (the distance map). The distance map is then used to identify skeleton nodes. Next, skeleton arcs are generated by controlled flooding within the identified skeleton nodes, thereby connecting these skeleton arcs, to extract a coarse skeleton. Finally, we refine the coarse skeleton by building shortest path trees followed by a prune phase. The obtained skeleton is robust to boundary noise or shape variations. Besides, we present two specific applications that benefit from the extracted skeleton: identifying complete boundaries and shape segmentation. First, with the extracted skeleton using DIST, we propose to identify more boundary nodes to form a meaningful boundary curve. Second, the utilization of the derived skeleton to segment the network into approximately convex pieces has been shown to be effective.