Connected coverage, which reflects how well a target field is monitored under the base station, is the most important performance metrics used to measure the quality of surveillance that wireless sensor networks (WSNs) can provide. To facilitate the measurement of this metrics, we propose two novel algorithms for individual sensor nodes to identify whether they are on the coverage boundary, i.e., the boundary of a coverage hole or network partition. Our algorithms are based on two novel computational geometric techniques called localized Voronoi and neighbor embracing polygons. As compared to previous work, our algorithms can be applied to WSNs of arbitrary topologies. They are also truly distributed and localized by merely needing the minimal position information of one-hop neighbors and a limited number of simple local computations, and thus are of high scalability and energy efficiency. We show the correctness and efficiency of our algorithms by theoretical proofs and extensive simulations.