This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Existing models of spatial relations do not consider that different concepts exist on different levels in a hierarchy and in turn that the spatial relations in a given scene area function of the specific concepts considered. One approach to determining the existence of a particular spatial relation is to compute the corresponding high level concepts explicitly using map generalization before inferring the existence of the spatial relation in question. We explore this idea through the development of a model of the spatial relation “

Murphy [

A set of polygons corresponding to houses in a housing estate and a number of lines corresponding to roads are represented. The grey line represents the access road for the housing estate in question. Data taken from OpenStreetMap.

Our cognitive capacity to infer this spatial relation of

The layout of this paper is as follows. In

This section is divided into three parts. In

Implicit information derived from spatial data can be used to support many applications such as map generalisation (where this process is known as data enrichment) [

As stated by Luscher

A spatial relation is a means of modeling a particular property of the spatial relationship which exists between two or more objects. Spatial relations may be categorized as topological, metric and order relations [

Research on the topic of spatial relations is motivated by a broad spectrum of possible application areas. Spatial relations can be used to describe constraints which specify a subset of spatial objects. For example, one may specify the subset of objects which fall within a given radius of a point using a metric relation [

As stated by Cohn and Hazarika [

Spatial relations may also be categorised as

In (

The International Cartographic Association defined generalisation as “The selection and simplified representation of detail appropriate to the scale and/or purpose of the map” [

The goal of map generalization is to produce a suitable map representation subject to a set of constraints [

Map generalization is performed through the application of one or a number of generalization operators. Jones [

Aggregation by connecting objects is generally performed in two steps. The first step of

The two polygons in (

Many authors have proposed methodologies which perform both steps of object grouping and merging [

As discussed in the introduction existing models of spatial relations do not consider that different concepts exist on different levels in a hierarchy and in turn that the spatial relations in a given scene are a function of the specific concepts considered. We propose that there exists two possible approaches to modeling a particular spatial relation. The first is to model the necessary higher level concepts explicitly using map generalization before inferring the existence of the spatial relation in question. The second approach is to model the necessary higher level concepts implicitly using a set of lower level concepts before inferring the existence of the spatial relation in question. For example, a housing estate may be modeled implicitly by set containing all houses belonging to the estate in question.

In this section we explore the former of these approaches by presenting a model of the spatial relation

The proposed generalisation method performs only the task of object merging and assumes the set of objects which require merging is known

The three polygon in (

Given a set of polygons a constrained Delaunay triangulation is computed and all edges internal to polygons are removed. For example a scene containing three polygons and its corresponding triangulation are displayed in

The above merging operator does not prevent the introduction of intersections between the result of merging and other objects in the scene. For example consider the scene in

The merging of the polygons in (

In this section we describe the function

In order to compute

In each figure the set of 8 rays corresponding to a point

In order to compute

Let

Computing

In this section we evaluate the model of the spatial relation

A set of polygons corresponding to houses in a housing estate and a number of lines corresponding to roads are represented. The grey lines represent the access roads for the housing estate in question. Data taken from OpenStreetMap.

The data used in this study was taken from OpenStreetMap (OSM) (

The results of merging the polygons in (

OSM test scenes with the corresponding

Examining

Like all qualitative relations,

To demonstrate the usefulness of the proposed model we computed the accuracy with which it could classify the roads in the test scenes as access or non-access roads. Classification was performed using a

This work represents the first attempt to model spatial relations in the presence of concepts which exist on different levels in a hierarchy. As such we believe it points the direction for future research in this area. Some possible future research directions include the following. Firstly it would be beneficial to consider other spatial relations, besides

In this work we proposed to model higher level concepts by explicitly computing the concepts in question using map generalization. However, as discussed in

Research presented in this paper was primarily funded by the Irish Research Council for Science Engineering and Technology (IRCSET) EMPOWER program. It was also in part funded by the Irish Environmental Protection Agency (EPA) STRIVE programme (Grant 2008-FS-DM-14-S4) and a Strategic Research Cluster Grant (07/SRC/I1168) from Science Foundation Ireland under the National Development Plan. The authors would like to sincerely thank the anonymous reviewers who’s efforts significantly improved the quality of the research presented.