Alejandro Pauly

VASA: An algebra for vague spatial data in databases

Many geographical applications deal with objects in space that cannot be adequately described by determinate, crisp spatial concepts because of their intrinsically indeterminate and vague nature. Geographical information systems and spatial database systems are currently unable to cope with this kind of data. To support the efficient representation, querying, and manipulation of vague spatial data in a database context, we present a formal data model called vague spatial algebra (VASA). This algebra comprises a set of vague spatial data types for vague points, vague lines, and vague regions together with a comprehensive collection of vague spatial operations and vague topological predicates. One of VASAs main benefits is that its formal framework is based on well known, general, and exact models of crisp spatial data types. This enables an exact definition of the vague spatial model since we can build upon an already existing theory of spatial data types. In particular, crisp spatial data types turn out to be a special case of their vague counterparts. In addition, our approach enables executable specifications for the operations, which can be immediately used as implementations. The article offers a precise and conceptually clean foundation for implementing a DBMS extension for vague spatial data and demonstrates the embedding of these new data types as attribute data types in a database schema as well as the incorporation of vague spatial operations and predicates into queries formulated in an SQL-like query language. All concepts have been verified in a prototype implementation.

Topological predicates between vague spatial objects

Topological predicates are an important element of database systems that allow manipulation of spatial data. Based on the necessity for such systems to handle uncertainty, we introduce a general mechanism that identifies vague topological predicates. This definition forms part of a formal data model referred to as VASA (Vague Spatial Algebra), in which the data types vague regions, vague lines, and vague points are defined in terms of existing definition of crisp spatial data types. Following this trend, the mechanism presented here identifies vague topological predicates on the basis of well defined crisp topological predicates. An example implementation of the mechanism for vague regions is given.

Dimension-refined topological predicates

Topological predicates, as derived from the 9-intersection model, have been widely recognized in GIS, spatial database systems, and many other geo-related disciplines. They are based on the evaluation of nine Boolean predicates checking the intersections of the boundary, interior, and exterior of a spatial object with the respective parts of another spatial object for inequality to the empty set. In this paper, we replace each Boolean predicate, which is a topological invariant, by another topological invariant. This new invariant is given as a function yielding the dimension of the respective intersection in the 9-intersection matrix, resulting in a dimension matrix. The goal of this paper is to determine the definition and semantics of all predicates that can be derived from this matrix for all combinations of spatial data types. It turns out that these dimension-based predicates are special refinements of the aforementioned topological predicates; hence, we call them dimension-refined topological predicates. We show that these predicates allow us to pose a class of more fine-grained topological queries.

Vague Spatial Data Types, Set Operations, and Predicates

Many geographical applications deal with spatial objects that cannot be adequately described by determinate, crisp concepts because of their intrinsically indeterminate and vague nature. Current geographical information systems and spatial database systems are unable to cope with this kind of data. To support such data and applications, we introduce vague spatial data types for vague points, vague lines, and vague regions. These data types cover and extend previous approaches and are part of a data model called VASA (Vague Spatial Algebra). Their formal framework is based on already existing, general exact models of crisp spatial data types, which simplifies the definition of the vague spatial model. In addition, we obtain executable specifications for the operations which can be immediately used as implementations. This paper gives a formal definition of the three vague spatial data types as well as some basic operations and predicates. A few example queries illustrate the embedding and expressiveness of these new data types in query languages.

Preserving local topological relationships

Topological relationships between objects in space are of great importance in many disciplines. Recently, topological relationships have been defined for complex spatial objects. However, this definition only expresses topological relationships between complex spatial objects as a whole (global view); therefore,topological information between the individual components (local view)that compose the objects is lost. In this paper we propose a novel, hybrid model of topological relationships for composite regions that provides access to the global topological relationships as well as the local topological relationships that exist between the simple regions that are the components of the composite regions involved.

ROSA: an algebra for rough spatial objects in databases

A fundamental data modeling problem in geographical information systems and spatial database systems refers to an appropriate treatment of the vagueness or indeterminacy features of spatial objects. Geographical applications often have to deal with spatial objects that cannot be adequately described by the determinate, crisp concepts exclusively available in these systems since these objects have an intrinsically indeterminate and vague nature. The goal of this paper is to show that rough set theory can be leveraged in an elegant manner to seamlessly model this kind of spatial data. Our approach introduces novel rough spatial data types for rough points, rough lines, and rough regions that can be employed as attribute types in database schemas. These data types are part of a data model called ROSA (ROugh Spatial Algebra). Their formal framework is based on already existing, general, exact models of crisp spatial data types, which simplifies the definition of the rough spatial model. In addition, we obtain executable specifications for the operations on rough spatial objects; these can be immediately used as implementations. This paper gives a formal definition of the three rough spatial data types as well as some basic operations.

Identifying topological predicates for vague spatial objects

Many geographical applications deal with spatial objects that cannot be adequately described by determinate, crisp concepts because of their intrinsically indeterminate and vague nature. GIS and spatial database systems are currently unable to handle this kind of data. Based on recent work on vague spatial data types, which are part of a formal data model called VASA (Vague Spatial Algebra) and which leverage exact models of crisp spatial data types, this paper introduces a general mechanism for identifying topological predicates for vague spatial objects by means of topological predicates for crisp spatial objects. We illustrate this mechanism by deducing these predicates for vague points.

Local topological relationships for complex regions

Topological relationships between spatial objects are important for querying, reasoning, and indexing of data within spatial databases. These relationships are qualitative and respond to questions about the relative positions (e.g., disjointedness or containment) of spatial objects. Several models have been proposed that effectively define formal sets of topological relationships between simple spatial data types. The generalization of topological relationship models to complex spatial data types, which are roughly defined as multi-component versions of their simple counterparts, has raised awareness of the fact that these models only provide a global view of topological relationships whereas details of the topological relationships between individual components of the spatial objects involved are often ignored. In this paper, we introduce a fine-grained view on topological relationships between complex regions. Our model focuses on leveraging information about the local topological relationships that hold between the components of two spatial objects, thereby providing a localized view of the overall global topological relationship.

Ensuring the semantic correctness of complex regions

Ensuring the semantic and topological correctness of spatial data is an important requirement in geographical information systems and spatial database systems in order to preserve spatial data quality and enable correct operation execution. Spatial objects like complex regions are usually represented as an ordered sequence of segments (sequence view) to support and ease the computation of spatial operations by means of plane sweep algorithms. The semantic correctness of such a sequence is usually simply assumed but is not easy to see. In this paper, we present a novel and efficient algorithm to discover the cyclic structure and check for the semantic correctness of the sequence representation of a complex region by determining its cyclic structures (component view) in terms of multiple faces possibly containing holes. The algorithm producing the component view is also interesting for object construction, manipulation, and visualization.