Visibility graphs and landscape visibility analysis

Visibility analysis based on viewsheds is one of the most frequently used GIS analysis tools. In this paper we present an approach to visibility analysis based on the visibility graph. A visibility graph records the pattern of mutual visibility relations in a landscape, and provides a convenient way of storing and further analysing the results of multiple viewshed analyses for a particular landscape region. We describe how a visibility graph may be calculated for a landscape. We then give examples, which include the interactive exploration ofa landscape, and the calculation of new measures of a landscape?s visual properties based on graph metrics ? in particular, neighbourhood clustering coefficient and path length analysis. These analyses suggest that measures derived from the visibility graph may be of particular relevance to the growing interest in quantifying the perceptual characteristics of landscapes

Fast approximation of visibility dominance using topographic features as targets and the associated uncertainty

An approach to reduce visibility index computation time andmeasure the associated uncertainty in terrain visibility analysesis presented. It is demonstrated that the visibility indexcomputation time in mountainous terrain can be reduced substantially,without any significant information loss, if the lineof sight from each observer on the terrain is drawn only to thefundamental topographic features, i.e., peaks, pits, passes,ridges, and channels. However, the selected sampling of targetsresults in an underestimation of the visibility index ofeach observer. Two simple methods based on iterative comparisonsbetween the real visibility indices and the estimatedvisibility indices have been proposed for a preliminary assessmentof this uncertainty. The method has been demonstratedfor gridded digital elevation models

Coupling between time series: a network view

Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of two coupled time series. The correspondence between the two time series is mapped to a network, "the cross-visibility graph", to demonstrate the correlation between them. We applied the algorithm to several correlated and uncorrelated time series, generated by the linear stationary ARFIMA process. The results demonstrate that the cross-visibility graph associated with correlated time series with power-law auto-correlation is scale-free. If the time series are uncorrelated, the degree distribution of their cross-visibility network deviates from power-law. For more clarifying the process, we applied the algorithm to real-world data from the financial trades of two companies, and observed significant small-scale coupling in their dynamics