A survey of qualitative spatial representations

Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work

Order in space: a general formalism for spatial reasoning

In this paper we propose a general approach for reasoning in space. The approach is composed of a set of two general constraints to govern the spatial relationships between objects in space, and two rules to propagate relationships between those objects. The approach is based on a novel representation of the topology of the space as a connected set of components using a structure called adjacency matrix which can capture the topology of objects of different complexity in any space dimension. The formalism is used to explain spatial compositions resulting in indefinite and definite relations and it is shown to be applicable to reasoning in the temporal domain. The main contribution of the formalism is that it provides means for constructing composition tables for objects with arbitrary complexity in any space dimension. A new composition table between spatial objects of different types is presented. A major advantage of the method is that reasoning between objects of any complexity can be achieved in a defined limited number of steps. Hence, the incorporation of spatial reasoning mechanisms in spatial information systems becomes possible

Magnification Control in Self-Organizing Maps and Neural Gas

We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms: localized learning, concave-convex learning, and winner relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case the results hold only for the one-dimensional case.Comment: 24 pages, 4 figure

Qualitative Distances and Qualitative Description of Images for Indoor Scene Description and Recognition in Robotics

The automatic extraction of knowledge from the world by a robotic system as human beings interpret their environment through their senses is still an unsolved task in Artificial Intelligence. A robotic agent is in contact with the world through its sensors and other electronic components which obtain and process mainly numerical information. Sonar, infrared and laser sensors obtain distance information. Webcams obtain digital images that are represented internally as matrices of red, blue and green (RGB) colour coordinate values. All this numerical values obtained from the environment need a later interpretation in order to provide the knowledge required by the robotic agent in order to carry out a task. Similarly, light wavelengths with specific amplitude are captured by cone cells of human eyes obtaining also stimulus without meaning. However, the information that human beings can describe and remember from what they see is expressed using words, that is qualitatively. The research work done in this thesis tries to narrow the gap between the acquisition of low level information by robot sensors and the need of obtaining high level or qualitative information for enhancing human-machine communication and for applying logical reasoning processes based on concepts. Moreover, qualitative concepts can be added a meaning by relating them to others. They can be used for reasoning applying qualitative models that have been developed in the last twenty years for describing and interpreting metrical and mathematical concepts such as orientation, distance, velocity, acceleration, and so on. And they can be also understood by human-users both written and read aloud. The first contribution presented is the definition of a method for obtaining fuzzy distance patterns (which include qualitative distances such as near , far , very far and so on) from the data obtained by any kind of distance sensors incorporated in a mobile robot and the definition of a factor to measure the dissimilarity between those fuzzy patterns. Both have been applied to the integration of the distances obtained by the sonar and laser distance sensors incorporated in a Pioneer 2 dx mobile robot and, as a result, special obstacles have been detected as glass window , mirror , and so on. Moreover, the fuzzy distance patterns provided have been also defuzzified in order to obtain a smooth robot speed and used to classify orientation reference systems into open (it defines an open space to be explored) or closed . The second contribution presented is the definition of a model for qualitative image description (QID) based on qualitative models of shape, colour, topology and orientation. This model can qualitatively describe any kind of digital image and is independent of the image segmentation method used. The QID model have been tested in two scenarios in robotics: (i) the description of digital images captured by the camera of a Pioneer 2 dx mobile robot and (ii) the description of digital images of tile mosaics taken by an industrial camera located on a platform used by a robot arm to assemble tile mosaics. In order to provide a formal and explicit meaning to the qualitative description of the images generated, a Description Logic (DL) based ontology has been designed and presented as the third contribution. Our approach can automatically process any random image and obtain a set of DL-axioms that describe it visually and spatially. And objects included in the images are classified according to the ontology schema using a DL reasoner. Tests have been carried out using digital images captured by a webcam incorporated in a Pioneer 2 dx mobile robot. The images taken correspond to the corridors of a building at University Jaume I and objects with them have been classified into walls , floor , office doors and fire extinguishers under different illumination conditions and from different observer viewpoints. The final contribution is the definition of a similarity measure between qualitative descriptions of shape, colour, topology and orientation. And the integration of those measures into the definition of a general similarity measure between two qualitative descriptions of images. These similarity measures have been applied to: (i) extract objects with similar shapes from the MPEG7 CE Shape-1 library; (ii) assemble tile mosaics by qualitative shape and colour similarity matching; (iii) compare images of tile compositions; and (iv) compare images of natural landmarks in a mobile robot world for their recognition

Spectral Theory for Networks with Attractive and Repulsive Interactions

There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;, the behavior of groups, or cliques, in social networks; the study of optimal convergence for consensus algorithm; and many other examples. Frequently the problems involve computing the index of a matrix, i.e. the number of positive and negative eigenvalues, and the dimension of the kernel. In this paper we consider one of the most common examples, where the matrix takes the form of a signed graph Laplacian. We show that the there are topological constraints on the index of the Laplacian matrix related to the dimension of a certain homology group. In certain situations, when the homology group is trivial, the index of the operator is rigid and is determined only by the topology of the network and is independent of the strengths of the interactions. In general these constraints give upper and lower bounds on the number of positive and negative eigenvalues, with the dimension of the homology group counting the number of eigenvalue crossings. The homology group also gives a natural decomposition of the dynamics into "fixed" degrees of freedom, whose index does not depend on the edge-weights, and an orthogonal set of "free" degrees of freedom, whose index changes as the edge weights change. We also present some numerical studies of this problem for large random matrices.Comment: 27 pages; 9 Figure

Spatial reasoning via active observation

This paper presents a model for space in which an autonomous agent acquires information about its environment. The agent uses a predefined exploration strategy to build a map allowing it to navigate and deduce relationships between points in space. The shapes of objects in the environment are represented qualitatively. This shape information is deduced from the agent\u27s motion. Normally, in a qualitative model, directional information degrades under transitive deduction. By reasoning about the shape of the environment, the agent can match visual events to points on the objects. This strengthens the model by allowing further relationships to be deduced. In particular, points that are separated by long distances, or complex surfaces, can be related by line-of-sight. These relationships are deduced without incorporating any metric information into the model. Examples are given to demonstrate the use of the model

Generation of navigation graphs for indoor space

This article proposes a comprehensive approach to computing a navigation graph for an indoor space. It focuses on a single floor, but the work is easily extensible to multi-level spaces. The approach proceeds by using a formal model, based on the combinatorial map but enhanced with geometric and semantic information. The process is almost fully automatic, taking as input the building plans providing the geometric structure of the floors and semantics of the building, such as functions of interior spaces, portals, etc. One of the novel aspects in this work was the use of combinatorial maps and their duals to provide a compact formal description of the topology and connectivity of the indoor structure represented by a connected, embedded graph. While making use of existing libraries for the more routine computational geometry involved, the research develops several new algorithms, including one for computing the local kernel of a region. The process is evaluated by means of a case study using part of a university building

Areas of Same Cardinal Direction

Cardinal directions, such as North, East, South, and West, are the foundation for qualitative spatial reasoning, a common field of GIS, Artificial Intelligence, and cognitive science. Such cardinal directions capture the relative spatial direction relation between a reference object and a target object, therefore, they are important search criteria in spatial databases. The projection-based model for such direction relations has been well investigated for point-like objects, yielding a relation algebra with strong inference power. The Direction Relation Matrix defines the simple region-to-region direction relations by approximating the reference object to a minimum bounding rectangle. Models that capture the direction between extended objects fall short when the two objects are close to each other. For instance, the forty-eight contiguous states of the US are colloquially considered to be South of Canada, yet they include regions that are to the North of some parts of Canada. This research considers the cardinal direction as a field that is distributed through space and may take on varying values depending on the location within a reference object. Therefore, the fundamental unit of space, the point, is used as a reference to form a point-based cardinal direction model. The model applies to capture the direction relation between point-to-region and region-to-region configurations. As such, the reference object is portioned into areas of same cardinal direction with respect to the target object. This thesis demonstrates there is a set of 106 cardinal point-to-region relations, which can be normalized by considering mirroring and 90° rotations, to a subset of 22 relations. The differentiating factor of the model is that a set of base relations defines the direction relation anywhere in the field, and the conceptual neighborhood graph of the base relations offers the opportunity to exploit the strong inference of point-based direction reasoning for simple regions of arbitrary shape. Considers the tiles and pockets of same cardinal direction, while a coarse model provides a union of all possible qualitative direction values between a reference region and a target region