=Paper=
{{Paper
|id=Vol-3743/paper4
|storemode=property
|title=Representing Spatial Uncertainty and Allowing for Probabilistic Topological Functions with SUFF, an Extension to GeoSPARQL (short paper)
|pdfUrl=https://ceur-ws.org/Vol-3743/paper4.pdf
|volume=Vol-3743
|authors=Nicholas John Car
|dblpUrl=https://dblp.org/rec/conf/geold/Car24
}}
==Representing Spatial Uncertainty and Allowing for Probabilistic Topological Functions with SUFF, an Extension to GeoSPARQL (short paper)==
https://ceur-ws.org/Vol-3743/paper4.pdf
Representing spatial uncertainty and allowing for
probabilistic topological functions with SUFF, an
extension to GeoSPARQL
Nicholas J. Car1,*
1
KurrawongAI, Brisbane Australia
Abstract
The Spatial Uncertainty for Features & Functions (SUFF) Model is a small extension ontology to
GeoSPARQL that allows for spatial uncertainty, sometimes called fuzziness, in the representation of
spatial geometries and for probabilistic topological calculations using them. It introduces ontological
elements that allow standard GeoSPARQL geometries to be associated in new ways, allowing for different
forms of handling uncertainty, including for visualisation. It describes how standard topological func-
tions, such as those made available in Semantic Web form by GeoSPARQL, may be applied to collections
of geometries and yield probabilistic results.
Keywords
GeoSPARQL, geospatial, Semantic Web, OWL, OGC, uncertainty, probabilistic, Levels of Measurement
1. Introduction
The GeoSPARQL standard [1] provides classes and properties for the representation of spatial
information in Semantic Web [2] form. The main classes are Feature and Geometry with the
former holding conceptual information about a spatial objects and the latter representations
of its spatial projection, such as a polygon defined with coordinates. Predicates for indicating
different forms of geometry projection serialization, topological relations between features or
geometries and scalar spatial values, such as area, are also provided.
In addition to its ontology, GeoSPARQL defines a set of functions - topological, spatial
aggregate and others - that systems can implement to calculate the relations between features
and other spatial information.
GeoSPARQL does not specifically cater for spatial uncertainty or probabilistic topological
functions: the only forms of geometry handled are the the simple features - [3] types of POINT,
LINESTRING, POLYGON, MULTIPOLYGON etc.. - and topological functions return binary results
- for example either a polygon is disjoint with another or it is not.
GeoSPARQL is not, by itself, completely sufficient for any particular task and does not attempt
to provide a user with all the ontological elements they would need for specialised work, instead,
GeoSPARQL is expected to be used with other Semantic Web models which together provide the
GeoLD2024: 6th International Workshop on Geospatial Linked Data at ESWC 2024
*
Corresponding author.
$ nick@kurrawong.ai (N. J. Car)
https://kurrawong.ai (N. J. Car)
0000-0002-8742-7730 (N. J. Car)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
necessary elements. For example, if a user wanted to represent the area of a lake, GeoSPARQL
provides the class Feature to represent the lake - a spatial object - the hasArea predicate to
indicate a scalar area value but no predicates to indicate units of measure or particualr measures:
these may be taken from a dedicated metrology ontology, perhaps Quantities, Units, Dimensions
& Types 1 .
This allows GeoSPARQL to be extended by uses to meet particular needs and this paper does
this for spatial uncertainty.
This paper describes how, by use with a small extension to GeoSPARQL of only few predicates
known as the Spatial Uncertainty for Features & Functions (SUFF) ontology that we have defined,
2 , GeoSPARQL can represent fuzzy spatiality and allow for probabilistic topological functions as
well as providing several other capabilities, such as position obfuscation with specific tolerances.
2. Motivation
The motivation for this work is encountered regularly in spatial data work: many projects need
to represent spatial uncertainty - fuzziness - and would benefit from topological functions that
work well with uncertain spatial data.
Some examples of spatial objects for which the author has recently needed to represent with
uncertain positions are: Australian Indigenous (Aboriginal) peoples’ traditional land areas;
mineral occurrence areas; informal, named geographical objects; and species distribution maps.
None of these are well served with crisp - certain - representations of position. For example,
using a crisp polygon to represent the extent of an Aboriginal traditional land area will not
capture the fact that no such areas ever had/have precise boundaries.
A second example is mineral occurrences in the earth’s crust that change in concentration
over distance. Their extents are usually estimated by sampling - surface collection or drillhole
sample extraction. No simple points or individual polygons can represent gradients and extent
estimations.
Data analysers may be called on to work with information that would best be represented
with uncertainty but none is given. This forces them to add fuzziness to visualisations by
blurring polygon boundaries or by representing point locations with a polygon - perhaps circle
- perhaps itself with a blurred boundary. This addition of fuzziness on top of the original data
may be done differently by different analysts or by using different spatial data software and no
two representations of the data including these fuzzy additions are guaranteed to be the same.
This paper, and the SUFF ontology, aim to both provide the ontological elements necessary for
representations of several forms of uncertain spatial information within data and instructions
on how to extend common topological functions to work with those representations. This will
allow data analysts to be provided with all the information necessary to produce consistent
fuzzy representations of spatial information, regardless of who they are or what tools they are
using.
1
https://qudt.org
2
https://w3id.org/profile/suff
3. SUFF Model
The SUFF Model is a small ontology that describes hot to represent spatial uncertainty. To do
this it defines only a few new predicates and no new classes and instead indicates how to use
existing classes and predicates from GeoSPARQL and other ontologies to do this.
An overview of the SUFF Model, showing reused and new model elements, is given in Figure 1.
Figure 1: An overview of the SUFF Model.
The SUFF Model is available online at https://w3id.org/suff and detailed information about
the model, it’s element definitions, examples of use and validation of data created conforming
to it are all given there.
3.1. Model Logic Overview
The basic premise of the SUFF Model is that multiple GeoSPARQL Geometry objects can be
linked to a Feature to contain different representations of its position which may correspond
to different confidences in the position. Different relationships between the multiple geometries
can also be used to allow for different interpretations of their relative confidence of position.
These different interpretations are also mapped to specific visualisations so that the relationship
from data to visualisation is deterministic.
The model describes how topological functions to determine spatial relationships, such as
the such as the simple features [3] family of relations, can be performed against the features
linked to multiple geometries.
3.2. Use of multiple geometries
Multiple GeoSPARQL Geometry objects are grouped in a GeoSPARQL Geometry Collection
which is then linked to a GeoSPARQL Feature through GeoSPARQL’s hasGeometry predicate
but the range value of the predicate must be loosened to allow for this use, i.e. not just Geometry.
Fuzziness in the feature’s position is then
given by blurring (interpolating) between
the individual geometry’s boundaries. The
manner of blurring can be indicated by link-
ing a concept from the Levels of Measure-
ment vocabulary to the geometry collecting
with the SUFF hasUncertaintyRelations
predicate and certainty at a particular ge-
ometry’s boundary may be indicated di-
rectly by the data creator using the standard
rdf:value predicate, or it may be calculated
by the geometry’s relative position in the col-
lection.
Figure 2 shows multiple polygons, A, B, C &
D giving different estimates for the position of
a Feature. The reasons for particular geome-
tries might be given as citations of scholarly
works, or descriptive text, or as complex data
objects, such as sampling result . Figure 2: Multiple polygons - one per Geome-
try linked to a single Feature can in-
3.3. Levels of Measurement dicate variation in fuzziness: the fur-
ther apart the boundaries are in any
Levels of Measurement is a classification sys- place, the greater the spatial uncer-
tem used to indicate the nature of information tainty there. The right side A/B bound-
within variables [4]. Four levels are defined: ary is comparatively certain.
Nominal, Ordinal, Interval and Ration (see the
Levels of Measurement vocabulary for the def-
initions) and different calculations about the
relative values of geometries in a collection can be made, based on the level indicated for the
collection (see the SUFF Model’s Rules Section for details).
If the level for a given geometry collection is not given, the Nominal is assumed and each
geometry is assigned equal certainty with the 0 to 1 range divided by the number of geometries.
Visually these would be stacked so coincident geometries’ opacities would be added.
If ordering is specifically assigned to the geometries, such as https://www.w3.org/TR/shacl/’s
order predicate, then the level of the collection is at least Ordinal and certainty per geometry
is the 0 - 1 range divided by no. geometries + 1 times the geometry order, so for 3 geometries:
0.25, 0.5 & 0.75. Interval ordering sees specific uncertainty values given by the user and Ratio
values are given but a 0 and a 1 are required too.
3.4. Evidence for position
Evidence for a particular geometry may be given using schema.org’s citation predicate or
other conventional form of referencing. For evidence to be used for ordering for the Ordinal
form, it must be numeric and the value indicator predicate as well as order direction must be
given. This will replace use of rdf:value.
3.5. Functions
Topological relations defined in GeoSPARQL may be computed between spatial objects with
fuzzy geometries and the method is described in the SUFF Model’s Rules Section. A summary is
that for the calculation of a relation between a feature A with fuzzy position and a standard
feature B, the relation must be calculated for each geometry of A’s in its linked collection and
B and then an answer may be given with a probability based on the certainty of the highest
geometry / B result, or the lowest, depending on the particular relation.
Consider the topological relation Simple Features Within [3]: If polygon A is within the
outermost 1 of 4 polygons with the Ordinal level for feature B, then we may say A is within
B with a probability of 0.25 since 1 / 4 (polygons) is 0.25. If A is within the two outermost
polygons of feature B and second outermost polygon is assigned the certainty of 0.4 using
SUFF’s certainty predicate, then we can say A is within B with a probability of 0.4.
A graphical representation of some within calculations is given in Figure 3.
Figure 3: A: Polygon ‘X’ is within the feature represented with multiple pink geometries with a probability
of 0.5 since it is within 1 of 2 geometries and no certainty information is give. Polygon ‘Y’ is within
the feature with a probability of 1 since it is within 2 of 2 geometries. B: ‘X’ is within the feature with
probability 0.6 since the most certain geometry it is within is that of 0.6.
4. Conclusions
The SUFF Model is a very small extension to GeoSPARQL. It introduces very few novel modelling
elements and addresses problems long solved by many spatial analysis and many software
packages. However, it moves the point of uncertainty definition from the user of spatial data to
the data itself and thus has the potential to allow for systematically-presented fuzzy data. It
also provides a method for standard topological functions calculations with fuzzy data.
References
[1] Nicholas J. Car, Timo Homburg, Matthew Perry, John Herring, Frans Knibbe, Simon J.D.
Cox, Joseph Abhayaratna, Mathias Bonduel, OGC GeoSPARQL - A Geographic Query
Language for RDF Data, OGC Implementation Standard OGC 22-047, Open Geospatial
Consortium, 2023. URL: http://www.opengis.net/doc/IS/geosparql/1.1.
[2] T. Berners-Lee, J. A. Hendler, O. Lassila, The semantic web: A new form of web content
that is meaningful to computers will unleash a revolution, Scientific American (2001). URL:
https://doi.org/10.1038/scientificamerican0501-34.
[3] J. R. Herring, Simple feature access - Part 1: Common architecture, OpenGIS Implementation
Standard, Open Geospatial Consortium, 2010. URL: http://www.opengis.net/doc/is/sfa/1.2.1.
[4] W. Kirch (Ed.), Level of MeasurementLevel of measurement, Springer Netherlands, Dor-
drecht, 2008, pp. 851–852. doi:10.1007/978-1-4020-5614-7\_1971.