Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

TL;DR

This paper introduces a novel method for approximating visibility probabilities between imprecise points in a 2D space with obstacles, using polygonal approximations of density functions to address a complex geometric probability problem.

Contribution

It proposes a new approach to approximate probability density functions with polygons for visibility analysis among imprecise points amid obstacles.

Findings

Effective polygonal approximation of density functions

Accurate estimation of visibility probabilities

Novel computational geometry approach

Abstract

Let $p$ and $q$ be two imprecise points, given as probability density functions on $\mathbb R^2$, and let $\cal R$ be a set of $n$ line segments (obstacles) in $\mathbb R^2$. We study the problem of approximating the probability that $p$ and $q$ can see each other; that is, that the segment connecting $p$ and $q$ does not cross any segment of $\cal R$. To solve this problem, we approximate each density function by a weighted set of polygons; a novel approach to dealing with probability density functions in computational geometry.