The representation of places with vague or ill-de ned boundaries continues being an issue for information systems. Despite the presence of multiple representation methods, it is still unclear how to determine which approach is best suited for a particular task. This paper proposes a set of characteristics based on the application domain, conceptual, and logical levels and di erentiates the approaches according to these characteristics. We demonstrate how they are matched with the task requirements and in uence the choice of representation method.
Representing `place' poses challenges, more so when the extents or boundaries
cannot be well-de ned. Although humans are capable of interpreting what is
being referenced in such cases, handling these in information systems is more
complex. Some of the associated problems are discussed in literature under
discipline of spatial vagueness and uncertainty, especially their philosophical
and representational aspects. The former aspects address whether vagueness is
intrinsic to the real world or just a feature of language[
No single representation can claim to be applicable for all cases. The methods
di er in the way assumptions are made about space, the underlying formal models,
applicability of data models and the kinds of reasoning they allow. Selecting the
right one for a given task is a matter of tness for purpose and requires that
the method's capabilities are matched to the requirements. Requirements vary
and can be speci ed in numerous ways. A consistent way of specifying these
requirements is needed. Our approach is to specify these in terms of the model
characteristics. The characteristics themselves may be de ned at di erent levels
similar to the levels of data abstraction in an information system [
Lake Carnegie in Australia is ephemeral. Depending on the amount of precipitation the lake may or may not be lled with water (Fig. 1). Though a lake in vernacular terms, in dry seasons it is reduced to a muddy marsh1. This presents a problem, since it is now unclear where exactly the boundaries of the lake lie.
Suppose a user needs a representation of Lake Carnegie. We examine a few questions that need to be answered to arrive at a clear understanding of what needs to be represented. 1. What is a `lake' ? First, the semantics of the term `lake' need to be clear. Is it a single contiguous body of water or does it include smaller scattered pools in the vicinity as well? Do the requirements dictate that water be present in the lake all year round? This is treated as the rst step towards arriving at a solution. 2. What is the purpose of representation? Requirements for an ecologist di er from that of a cartographer. An ecologist is likely to be interested in the variation of the lake over time; a fuzzy spatial extent rather than precisely de ned boundaries being of importance. A cartographer is more interested in the lake as a crisp object. 3. What data sources are available? The choice of representation is in uenced by the data sources. A di erent method is needed for a representation built up from satellite imagery, than another which uses water level observations from sensors scattered through the lake. 1 http://www.nasa.gov/multimedia/imagegallery/image_feature_817.html (a) Apr 2011
(b) Sep 2011
As one can infer, varying user needs and requirements must be met with a suitable method to represent the same place. From the myriad of possibilities, one needs a way to identify the right representation approach. Next, we brie y propose certain characteristics and explain how these characteristics can be used to distinguish among representation methods as the rst step to this end. 3
From the di erent levels of abstraction, we identify characteristics which will serve as the criteria to di erentiate between methods. Some commonly used methods for representing vague places are then brie y analyzed based on these. 3.1
Starting from the di erent levels of abstraction, we propose the following
characteristics for use in deciding upon the correct method to employ for representation
of vague entities.
1. Conceptualization of space - The adopted perspective of vagueness (whether
it is linguistic or ontic) a ects the choice of the representational and semantic
framework [
Base representations - We coin this term to refer to those methods which abstract or crisp the vague place. Possible ways are to de ne the feature a priori according to some metric, or reduce it to a simple feature type (point, line or polygon), a minimum bounding rectangle (MBR) which covers the entire extent of the space where the entity is located, or through tessellations of space. These are usually in the form of vector data. Examples may be seen in VGI where a real world feature is outlined by contributors (from GPS tracks or tracing from aerial imagery), or in gazetteers where a feature is simply located by a representative point. Here vagueness is not preserved, and they are generally not classi ed under methods for vagueness representation. They are included here for the sake of completeness since they are often applied and prove adequate in some cases. The methods themselves do not provide any theory for reasoning.
Probabilistic methods - These methods derive the membership value of an
individual in a set through a statistically de ned probability function. These are
used mainly to handle uncertainty. The underlying stochastic model assumes
that phenomena are crisp and knowable, with the result that no measurable way
for metrics such as precision in the case of vagueness exist [
Fuzzy-set methods - These are based on Fuzzy-set theory and ideal for
modelling objects which have graduating or indeterminate boundaries [
Rough sets - The basis for rough sets is the indiscernibility relation { where a
collection of elements is indiscernible from another. Rough sets use a three-valued
logic (true; f alse; maybe) to determine the membership of a point to a region as
opposed to the binary notion of membership (true; f alse) in classical set theory.
Similar to the egg-yolk model, a region may be represented by its determinate
lower approximation and an indeterminate upper approximation [
Supervaluation - The idea behind supervaluation is to account for the di erent
possible interpretations of a vague predicate when multiple interpretations for a
vague region exist. The positive extension is where all interpretations are true.
Its inverse the negative extension is the region where no interpretation is true.
The remaining regions constitute the penumbra [
We take the example of Lake Carnegie and consider two di erent sets of requirements for representations.
{ The cartographer imagines the lake to be a single contiguous body of water with a crisp boundary, though the reality is di erent. Satellite imagery is used as source of data. No reasoning needs to be performed. { The ecologist views the lake as a non-crisp object de ned by level of water.
Water level observation data from sensors is available. The need is to generate a surface exhibiting water presence over a period of time.
In the rst case, the space is conceptualized as a crisp body. Data from satellite imagery is a raster, from which the boundary needs to be derived. One obvious solution is to simply trace the outline from the image, resulting in a base representation. The suggested approach in this case is however to use fuzzy-set modelling with -cuts. By varying , di erent boundaries (each of which is crisp) can be obtained. One such representation by using fuzzy membership of pixel values and obtaining a crisp boundary is seen in Fig. 2a.
In the second case, the lake is conceptualized depending on its objective property (water level). Spatial distribution of the data source, sensors which provide observations, can be thought of as consisting of points (vector). Since the user needs to obtain interpolated values in order to obtain a lake surface, application of probabilistic methods is suitable here. A probabilistic representation simulated from randomly distributed sensors with arbitrary observations is shown in Fig. 2b, with outline of the lake from OpenStreetMap 2 for reference.
This is a trivial example, but the same principles apply in other cases as well. For example, in the Tell Us Where3 project dataset, it would be possible to obtain a representation of places with noncrisp boundaries. This however has not been attempted here owing to sampled locations in the current dataset being insu cient in number to demonstrate our cause. 5
Various representation methods have been proposed in literature for the representation of places with vague boundaries. It is important to enable decision makers to adopt the right method based on their needs. The approach taken here uses multiple levels of abstraction to specify the requirements in a consistent manner. The levels allow identi cation of characteristics with which di erent methods can be analyzed. Di ering requirements in the modelling of a vague region such as a lake can lead to di erent possible solutions as presented in the lake use case. 6
This research was carried out under the International Research Training Group on Semantic Integration of Geospatial Information (IRTG-SIGI) and is funded by the DFG (German Research Foundation), GRK 1498. 2 http://www.openstreetmap.org 3 http://telluswhere.net