Terrain prickliness: theoretical grounds for high complexity viewsheds

TL;DR

This paper introduces the prickliness attribute to measure terrain complexity for viewshed analysis, providing algorithms for its computation and validating its effectiveness on real terrains.

Contribution

It defines prickliness as a new topographic measure and develops optimal algorithms for its computation on different terrain models, enhancing viewshed complexity analysis.

Findings

Prickliness correlates with viewshed complexity.

Algorithms efficiently compute prickliness for various terrain types.

Validated on diverse real-world terrains.

Abstract

An important task in terrain analysis is computing \emph{viewsheds}. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the \emph{prickliness}, that measures the number of local maxima in a terrain from all possible angles of view. We show that the prickliness effectively captures the potential of 2.5D TIN terrains to have high complexity viewsheds. We present optimal and (under standard assumptions) near-optimal algorithms to compute it for 1.5D and 2.5D TIN terrains, respectively, and efficient approximate algorithms for raster DEMs. We validate the usefulness of the prickliness attribute with experiments in a large set of real terrains.