A fuzzy approach to visibility maps creation over digital terrains

Abstract

The construction of inter-visibility models for a terrain is an important tool for environmental and animal studies. Efficient crisp algorithms are known to address this problem directly on a raster digital elevation map (DEM) of the study area. Randomness plays an important role: several factors like vegetation, height of the observer, presence of unmapped human artifacts, etc. cannot be modeled in advance into a traditional DEM model. We propose the use of fuzzy terrain models to incorporate uncertainty and unpredictable variability of the landscape. Accordingly, we propose a suitable definition of visibility to obtain inter-visibility models. An algorithm that uses approximation of fuzzy numbers with a discrete family of intervals is proposed. The proposed model produces sound results and can be extended to model complex situations like triangulating a radio source using two directional receivers. All of these situations are difficult to manage with a precise stochastic model and are a frequent occurrence in animal behavior studies under field conditions. The proposed techniques have been implemented inside a user-friendly software package that may easily exchange data with the most common GISs. We report also some experimental results obtained using over artificial terrain under controlled noise and under-sampling conditions.