Speaker: Rostislav Goroshin

Title: Solutions to Visibility Optimization Problems using Variational Methods in a Level-Set Framework


The continuous visibility level set function introduced by Tsai, Osher, et al. allows for gradient based and variational formulations of many classical visibility based problems. In this work we propose solutions to two such problems. The first asks where to position n-observers such that the area visible to these observers is maximized. The second problem is to determine the shortest route an observer should take through a map such that every point in the map is visible from at least one vantage point on the route. These problems are known as the "art gallery" and "watchmen route" (inspection route) problems, respectively. We propose a greedy iterative algorithm, formulated in the level set framework as the solution to the art gallery problem. Finally, we propose a variational solution to the inspection route problem which achieves complete visibility coverage of the domain while attaining a local minimum of path length.