Conceptual Neighborhood Graph Research Articles

Approximate Query Answering Based on Topological Neighborhood and Semantic Similarity in OpenStreetMap

In this paper we focus on a pictorial query language, referred to as Geographical Pictorial Query Language (GeoPQL), and we revise its formal semantics by considering the polygon-polyline, polyline-polyline, and polygon-polygon topological relationships. This work proposes the Approximate Answering Engine (AAE) within a Distributed System, referred to as GeoPQLJSON (GeoPQLJ). The AAE provides approximate answers to query with empty results by following two directions: the Operator Conceptual Neighborhood (OCN) graph, and the OpenStreetMap (OSM) attribute hierarchy, giving maximum flexibility to the user choices. According to the former, the geo-operators of the queries can be replaced with the ones labeling the adjacent nodes of the OCN graph. By following the latter, the system evaluates the OSM attribute semantic similarity according to the information content approach, and proposes possible attribute replacements to the user. Note that the presence of OSM attributes allows the quick and direct access to large amount of geographical data, without requiring in our case the use of the topological elements. The functionalities of the Distributed GeoPQLJ System are illustrated by several query examples.

Binary topological relations on the digital sphere

Topological relations are the predominant backbone of qualitative spatial reasoning, focusing to date mostly on objects that are embedded in R2. With the advent of ball-shaped screen technologies and the growing importance of globally situated data, the digital sphere, known as T2, becomes a viable embedding. While topological relations have been investigated for a spherical embedding S2 within a continuous framework, the lack of a full account of the relations in T2 prevents more refined query systems on global discrete data. This paper extends the concept of spherical topological relations to the digital spherical embedding, building on the model of a planar digital region in Z2 whose boundary comprises the pixels along the region's margin. With the 9-intersection and its detailed descendant, the 9+-intersection, 29 relations between two digital regions are derived. This set of binary digital spherical relations is jointly exhaustive and pairwise disjoint. The relations' conceptual neighborhood graph, capturing the similarity among the relations, further highlights that 18 of the 29 relations are refinements of those found in S2. These topological relations between digital regions coincide with the binary relations found between broad-boundary regions when the broad boundaries are of uniform thickness, a scenario preventing the inclusion of an entire interior of one region within the boundary of the other. Five different rationales for coarsening are investigated, each leading to a different group of the relations along the conceptual neighborhood graph.

Approximate answering of queries involving polyline–polyline topological relationships

In geographic information systems, pictorial query languages are visual languages which make easier the user to express queries by free-hand drawing. In this perspective, this article proposes an approach to provide approximate answers to pictorial queries that do not match with the content of the database, that is, the results are null. It addresses the polyline–polyline topological relationships and is based on an algorithm, called Approximate Answer Computation algorithm, which exploits the notions of Operator Conceptual Neighborhood graph and 16-intersection matrix. The operator conceptual neighborhood graph represents the conceptual topological neighborhood between Symbolic Graphical Objects and is used for relaxing constraints of queries. The nodes of the operator conceptual neighborhood graph are labeled with geo-operators whose semantics has been formalized. The 16-intersection matrix provides enriched query details with respect to the well-known Dimensionally Extended 9-Intersection Model proposed in the literature. A set of minimal 16-intersection matrices associated with each node of the operator conceptual neighborhood graph, upon the external space connectivity condition, is defined and the proof of its minimality is provided. The main idea behind each introduced notion is illustrated using a running example throughout this article.

The cognition of change: scaling deformations in mind and spatial theories

The dynamics of the earth and its inhabitants have become a core topic and focus in research in the spatial sciences. The spatio-temporal data avalanche challenges researchers to provide efficient and effective means to process spatio-temporal data. It is of vital importance to develop mechanisms that allow for the transition of data not only into information but also into knowledge. Knowledge representation techniques from artificial intelligence play an important role in laying the foundations for theories dealing with spatio-temporal data. Specifically, the advances in the area of qualitative spatial representation and reasoning (QSTR) have led to promising results. Categorical distinctions of spatio-temporal information identified by QSTR calculi potentially correspond to those relevant to humans. This article presents the first behavioral evaluation of qualitative calculi modeling geographic events associated with scaling deformations of entities, that is, changes in size by either expansion or contraction. Examples of such dynamics include a lake flooding its surroundings or an expanding oil spill in the ocean. We compare four experiments using four different semantic domains. Each domain consists of two spatially extended entities: one entity is undergoing scaling deformations while the other is static. We kept the formal QSTR characterization, which are paths through a topologically defined conceptual neighborhood graph, identical across all semantic domains. Our results show that for geographic events associated with scaling deformations (a) topological relations are not equally salient cognitively; (b) domain semantics has an influence on the conceptual salience of topological relations.

Evolution of Region Connection Calculus to VRCC-3D+

Qualitative spatial reasoning (QSR) is useful for deriving logical inferences when quantitative spatial information is not available. QSR theories have applications in areas such as geographic information systems, spatial databases, robotics, and cognitive sciences. The existing QSR theories have been applied primarily to 2D. The ability to perform QSR over a collection of 3D objects is desirable in many problem domains. Here we present the evolution (VRCC-3D+) of RCC-based QSR from 2D to both 3D (including occlusion support) and 4D (a temporal component). It is time consuming to construct large composition tables manually. We give a divide-and-conquer algorithm to construct a comprehensive composition table from smaller constituent tables (which can be easily handcrafted). In addition to the logical consistency entailment checking that is required for such a system, clearly there is a need for a spatio-temporal component to account for spatial movements and path consistency (i.e. to consider only smooth transitions in spatial movements over time). Visually, these smooth movement phenomena are represented as a conceptual neighborhood graph. We believe that the methods presented herein to detect consistency, refine uncertainty, and enhance reasoning about 3D objects will provide useful guidelines for other studies in automated spatial reasoning.

QRPC: A new qualitative model for representing motion patterns

The Qualitative Rectilinear Projection Calculus (QRPC), a new representation model based on planar trajectories, is presented in this work for describing qualitatively motion patterns. Several models have been developed for this purpose and by comparing them with our proposal we show that the proposed model results in an intuitive approach for representing, in any context, the kinematical behavior of two objects in motion on the plane through the possible relationships among the rectilinear projection of their trajectories. The paper is centered on the formal definition of the set of geometric relations in terms of the front–back and left–right dichotomies, and how by the composition of these relations, it can be possible enumerate an exhaustive set of qualitative states and the possible transitions among them. The complete iconic representation of the set of qualitative states defines the Conceptual Neighborhood Graph of the QRPC model. In order to illustrate how this qualitative representation can be used to analyze and describe the relative motion of two objects, some examples extracted from the traffic engineering field have been studied.

Spatial Information Theory Meets Spatial Thinking: Is Topology the Rosetta Stone of Spatio-temporal Cognition?

Topology is the most commonly used spatial construct to bridge the gap between formal spatial information theory and systems on the one side and (human) spatial cognition and thinking on the other. To this end, we find topological calculi in virtually all research areas pertinent to spatial information science such as ontological modeling, geographic information retrieval, or image analysis and classification. Manifold behavioral experiments have been conducted to assess the cognitive adequacy of topological calculi with varying results. Our contribution here is unique for two reasons: first, we are addressing, behaviorally, the role of topology in the crucial area of spatio-temporal information; second, we are evaluating the role of topology across different semantic domains. We report five experiments that were conducted in the framework we developed (Klippel and Li 2009), which combines critical constructs from spatial information theory and cognitive science. Topologically equivalent movement patterns were specified across five domains using paths through a conceptual neighborhood graph. This approach allows us to disentangle the role of topology from the influence of semantic context. The results show that topology plays an important yet not semantic-independent role in characterizing the cognitive conceptualization of geographic events.

Semantic Approach for the Spatial Adaptation of Multimedia Documents

With the proliferation of heterogeneous devices (desktop computers, personal digital assistants, phones), multimedia documents must be played under various constraints (small screens, low bandwidth, etc). Taking these constraints into account with current document models is impossible. Hence, generic source documents must be adapted or transformed into documents compatibles with the target contexts. The adaptation consists of modifying this specification of the document in a minimal way to lead it to satisfy the target profile. The profile defines constraints that must be satisfied by the document to be played. At this level, the transgressive adaptation becomes necessary when no specification model exists to satisfy this profile. We focus on the spatial dimension of a multimedia document and we provide an approach for the spatial adaptation that permits to best preserve the initial document semantic. In the proposed transgressive adaptation, the relations that do not comply with the target profile are not most often replaced by the closest ones due to the fact that their immediate neighboring relations have the same similarity degree whereas there may exist differences between them. In this paper, we extend this approach to, firstly, best preserve the proximity between the adapted and the original documents by weighting the arcs of the conceptual neighborhood graphs and secondly, to deal with complex relations models by integrating the concept of the relations relaxation graphs that permit to handle the distances defined within the relations.

Topologically Characterized Movement Patterns: A Cognitive Assessment

In this paper, we discuss the role of topology as a predictor for the conceptualization of dynamically changing spatial configurations (referred to as movement patterns). We define meaningful units of movement patterns as paths through a topologically defined conceptual neighborhood graph. Topology plays a central role in formal approaches to human cognition and in predicting cognitive similarity ratings—although primarily for static spatial configurations. Formal specifications of the role of topology for characterizing movement patterns do exist, yet there is paucity of behavioral validation. To bridge this gap, we conducted an experiment based on the grouping paradigm to assess factors that underlie conceptualizations of movement patterns. The experiment was designed such that paths through the conceptual neighborhood graph were distinguished by topologically differentiated ending relations. We believe topology can make an important contribution in explaining movement conceptualizations. One recently formulated topology-based contribution is the endpoint hypothesis, asserting that a cognitive focus is placed on event ending relations. We discuss the results of our experiment in relation to previous experiments targeted toward a framework for modeling the cognitive conceptualization of dynamically changing spatial relations.

Topological relations between directed lines and simple geometries

Directed lines are fundamental geometric elements to represent directed linear entities. The representations of their topological relations are so different from those of simple lines that they cannot be solved exactly with normal methods. In this paper, a new model based on point-set topology is defined to represent the topological relations between directed lines and simple geometries. Through the intersections between the start-points, end-points, and interiors of the directed lines and the interiors, boundaries, and exteriors of the simple geometries, this model identifies 5 cases of topological relations between directed lines and points, 39 cases of simple lines, and 26 cases of simple polygons. Another 4 cases of simple lines and one case of simple polygons are distinguished if considering the exteriors of the directed lines. All possible cases are furthermore grouped into an exclusive and complete set containing 11 named predicts. And the conceptual neighborhood graph is set up to illustrate their relationship and similarity. This model can provide a basis for natural language description and spatial query language to present the dynamic semantics of directed lines relative to the background features.

Identifying factors of geographic event conceptualisation

The present paper examines whether the formal topological characterisation of spatial relations between moving geographic regions provides an adequate basis for the human conceptualisation of motion events for those regions. The paper focuses on gradual changes in topological relationships caused by continuous transformations of the regions (specifically, translations). Using a series of experiments, the conceptualisation and perception of conceptual neighborhoods is investigated. In particular, the role of conceptual neighborhoods in characterising motion events is scrutinised. The experiments employ a grouping paradigm and a custom‐made tool for presenting animated icons. The analysis examines whether paths through a conceptual neighborhood graph sufficiently characterise the conceptualisation of the movement of two regions. The results of the experiments show that changes in topological relations—as detailed by paths through a conceptual neighborhood graph—are not sufficient to characterise the cognitive conceptualisation of moving regions. The similarity ratings show clear effects of perceptually and conceptually induced groupings such as identity (which region is moving), reference (whether a larger or a smaller region is moving), and dynamics (whether both regions are moving at the same time).

The four intersection-and-difference model for line-line topological relations

The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cartographic generalization. To develop a sound and effective approach to describe line-line relations, it is first necessary to define the topology of an individual line, i.e., local topology. The concept of connective degree is used for the identification of topological differences in the geometric structure of a line. The general topological definition of a line is given, i.e., endpoints set and interior point set. This definition can be applied to the embedded spaces of different dimensions, whether co-dimension is equal to or larger than zero. On this basis, a generic model called the 4 intersection-and-difference is set up for the description of basic line-line topological relations, upon which a conceptual neighborhood graph is built with consideration of topological distance. It is concluded that the proposed model can represent the property of topological changes, and basic relations between line segments in IR1 and IR2.

Approximate topological relations

In spatial data models for various applications, such as geographical information systems (GISs), the importance of topological relations is widely recognized. Topology makes very general statements about the structure and the relations of spatial objects. A refinement of topology by means of other geometric aspects can help to bend the various models that have been developed for topological relations towards a more effective description of geographic space. The introduction of broad boundaries is a direction to define approximate topological relations between spatial objects. In this paper, approximate topological relations are destined to capture boundary uncertainty, variations over time, proximity measures, and vector-raster representations. Approximate topological relations are structured in conceptual neighborhood graphs that have a twofold interpretation: two neighboring relations are at topological distance 1 in terms of the nine-intersection model and can be obtained, one from the other, by an elementary continuous deformation.