Computing 3-D From-Region Visibility Using Visibility Integrity

Visibility integrity (VI) is a measurement of similarity between the visibilities of regions. It can be used to approximate the visibility of coherently moving targets, called group visibility. It has been shown that computing visibility integrity using agglomerative clustering takes O(n4 log n) for n samples. Here, we present a method that speeds up the computation of visibility integrity and reduces the time complexity from O(n4 log n) to O(n2). Based on the idea of visibility integrity, we show for the first time that the visibility-integrity roadmap (VIR), a data structure that partitions a space into zones, can be calculated efficiently in 3-D. More specifically, we offer two different offline approaches, a naive one and a kernel-based one, to compute a VIR. In addition, we demonstrate how to apply a VIR to solve group visibility and group following problems in 3-D. We propose a planning algorithm for the camera to maintain visibility of group targets by querying the VIR. We evaluate our approach in different 3-D simulation environments and compare it to other planning methods.