Uncertainty in visibility: a scoping review of the probable and fuzzy viewshed for observer location optimization

Abstract

Although the probable and fuzzy viewshed have been recognized as critical in visibility analysis, they remain underutilized in practical applications such as surveillance drone positioning, telecommunications tower placement, and helicopter battle-position selection. Traditional approaches often assume a binary (boolean) notion of visibility, overlooking real-world factors like uncertainty in terrain data, partial occlusion from vegetation, or the effect on visibility by light sources, atmospheric haze, and target size. This scoping review systematically maps research on non-boolean visibility models and identifies several key gaps. First, there is a lack of methods that integrate both probabilistic and fuzzy approaches for observer placement. Second, while research has addressed DEM uncertainty and vegetation, few studies combine multiple factors or apply their methods to multi-observer or path-planning problems. Finally, research into 3D applications remains sparse, even though such work is critical for tasks like military helicopter missions or surveillance drone flights. Consequently, we highlight the need for more robust modeling of combined visibility factors and clearer strategies for incorporating both probable and fuzzy criteria in real-world operational settings. Bridging these gaps will enable more accurate and reliable visibility analyses across diverse domains, from city planning to helicopter mission planning.