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 diferent forms of handling uncertainty, including for visualisation. It describes how standard topological functions, such as those made available in Semantic Web form by GeoSPARQL, may be applied to collections of geometries and yield probabilistic results.
The GeoSPARQL standard [
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 - [
GeoSPARQL is not, by itself, completely suficient 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 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.
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 diferently by diferent analysts or by using diferent 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. 1https://qudt.org 2https://w3id.org/profile/suf
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.
The SUFF Model is available online at https://w3id.org/suf 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.
The basic premise of the SUFF Model is that multiple GeoSPARQL Geometry objects can be linked to a Feature to contain diferent representations of its position which may correspond to diferent confidences in the position. Diferent relationships between the multiple geometries can also be used to allow for diferent interpretations of their relative confidence of position. These diferent 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 [
Levels of Measurement is a classification
system used to indicate the nature of information
within variables [
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.
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.
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 [
A graphical representation of some within calculations is given in Figure 3.
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.