A Level Set Framework for Visibility Related Variational Problems

We introduce a framework and construct algorithms based on it to handle optimization problems that deal with the maximization of visibility information for observers when obstacles to vision are present in the environment. This framework uses at its core the approach developed in [14] which adopts the level set framework of [10] to construct a function that encodes visibility information in a continuous way. This continuity allows for powerful techniques to be used in the discrete setting for interpolation, integration, differentiation, and set operations. Thus, through the application of [14], several level set tools, gradient flow, derivative discretizations, and solvers for ordinary differential equations, we produce our visibility framework for optimization and demonstrate its flexibility with algorithms tackling different model problems in the subject.