Delineating Boundaries for Imprecise Regions

Abstract

In geographic information retrieval, queries often name geographic regions that do not have a well-defined boundary, such as "Southern France." We provide two algorithmic approaches to the problem of computing reasonable boundaries of such regions based on data points that have evidence indicating that they lie either inside or outside the region. Our problem formulation leads to a number of subproblems related to red-blue point separation and minimum-perimeter polygons, many of which we solve algorithmically. We give experimental results from our implementation and a comparison of the two approaches.

Reasoning about Fuzzy Temporal and Spatial Information from the Web

“…In some approaches, a single crisp boundary is constructed to represent a vague region, assuming that the vagueness of the boundary is not important for the intended application. In [198], for example, an algorithm is discussed to find a reasonable polygon for a vague region R, based on a set of points that are assumed to lie in the region, and a set of points that are assumed to lie outside the region. These sets are extracted automatically from web pages containing phrases like x is located in R. Another way of obtaining such a polygon is proposed in [15], pursuing a similar strategy.…”

Peeling Meshed Potatoes

“…In particular, the closely-related turning functions have been used to compare the shape of polygons [2,16]. Closer to our application, Reinbacher et al [17] consider minimizing the total angular change as a shape criterion to delineate imprecise regions with compact shapes.…”

Delineating imprecise regions via shortest-path graphs

“…As mentioned in the previous subsection, common representations are fuzzy boundaries [10,13,20], crisp boundaries [21], and the egg-yolk model [4,8]. Each approach has its own advantages and disadvantages.…”

“…An important consideration is whether a vernacular region is required to be connected or not. Some existing methods explicitly take this requirement into account [21], others explicitly do not use it [8]. We believe that in most cases connectedness is a desirable property and, hence, a method should be capable of guaranteeing it.…”

“…For some countries this data may be available, but it is a severe restriction for worldwide application. The dual of a Voronoi diagram, a Delaunay triangulation, is also used to delineate vague regions [21]. However, this approach again relies on negative samples.…”