The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science

In recent years there has been increasing interest in constructing cognitive vision systems capable of interpreting the high level semantics of dynamic scenes. Purely quantitative approaches to the task of constructing such systems have met with some success. However, qualitative analysis of dynamic scenes has the advantage of allowing easier generalisation of classes of different behaviours and guarding against the propagation of errors caused by uncertainty and noise in the quantitative data. Our aim is to integrate quantitative and qualitative modes of representation and reasoning for the analysis of dynamic scenes. In particular, in this paper we outline an approach for constructing cognitive vision systems using qualitative spatial-temporal representations including prototypical spatial relations and spatio-temporal event descriptors automatically inferred from input data. The overall architecture relies on abduction: the system searches for explanations, phrased in terms of the learned spatio-temporal event descriptors, to account for the video data.

The Double Cross calculus has been proposed for the purpose of navigation based on qualitative information about spatial configurations. Up until now, however, no results about algorithmic properties of this calculus are known. First, we

The granularity of spatial calculi and the resulting mathematical properties have always been a major question in solving spatial tasks qualitatively. In this paper we present the Oriented Point Relation Algebra (OPRAm), a new orientation calculus with adjustable granularity. Since our calculus is a relation algebra in the sense of Tarski, fast standard inference methods can be applied. One of the major problems—depending on the environment, the robots ’ capabilities and the tasks to be solved—is the choice of the granularity of an applied calculus. To present, granularity had to be chosen at the start and could not be changed on the fly. In a dynamically changing environment under real time conditions it is necessary to choose a coarse but still adequate granularity of the spatial representation: only in that case irrelevant feature changes fail to trigger unnecessary inference steps. A qualitative, coarse abstraction suppresses tiny changes in the environment and leads to fast computation. 1

This paper proposes a method for reconstructing qualitative positions of multiple vision sensors from qualitative information observed by the vision sensors, i.e., motion directions of moving objects. In order to directly acquire the qualitative positions of points, the method proposed in this paper iterates the following steps: 1) observing motion directions (left or right) of moving objects with the vision sensors, 2) classifying the vision sensors into ######### ########## ##### based on the motion directions, 3) acquiring ##### ##### ###########, and 4) propagating the constraints. Compared with the previous methods, which reconstruct the environment structure from quantitative measurements and acquire qualitative representations by abstracting it, this paper focuses on how to acquire qualitative positions of landmarks from low-level, simple, and reliable information (that is, qualitative). The method has been evaluated with simulations and also verified with observation errors

Qualitative formalisms, suited to express qualitative temporal or spatial relationships between entities, have gained wide acceptance as a useful way of abstracting from the real world. The question remains how to describe spatio temporal concepts, such as the interaction between disconnected moving objects, adequately within a qualitative calculus and more specifically how to use this in geographical information systems. In this paper, the Basic Qualitative Trajectory Calculus (QTCB) for representing and reasoning about moving objects is presented. QTCB enables comparisons between positions of objects at different time points to be made. The calculus is based on few primitives (i.e., distance and speed constraints), making it elegant and theoretically simple. To clarify the way in which trajectories are represented within QTCB, specific cases of movements (e.g. circular movement) are presented. To illustrate the naturalness of QTC, a “predator-prey” example is studied.

Abstract. We study an alternative to the prevailing approach to modelling qualitative spatial reasoning (QSR) problems as constraint satisfaction problems. In the standard approach, a relation between objects is a constraint whereas in the alternative approach it is a variable. By being declarative, the relation-variable approach greatly simplifies integration and implementation of QSR. To substantiate this point, we discuss several specific QSR algorithms from the literature which in the relation-variable approach reduce to the customary constraint propagation algorithm enforcing generalised arc-consistency. 1

We develop a theory for ternary point-based calculi such that the relations are invariant when all points are mapped by rotations, scalings or translations and propose methods to determine arbitrary transformations and compositions of such relations. We argue that calculi based on such relation systems should satisfy two criteria. First, the relation system should be closed under transformations, compositions and intersections and have a finite base that is jointly exhaustive and pairwise. This implies that the well-known path consistency algorithm can be used to conclude implicit knowledge without any loss of information. If this is the case, we call the calculus practical. Second, we say that a relation system is natural if all relations and their complements give rise to sets of points that are connected. The main result of the paper is then the identification of a maximally refined calculus amongst the practical natural RST calculi, which turns out to be very similar to Ligozat’s flip-flop calculus. From that it follows, e.g., that there is no finite refinement of the TPCC calculus by Moratz et al that is closed under transformations, composition, and intersection.

In this paper, we present some preliminary results about the connections existing between qualitative and discrete constraint networks. We present a natural encoding of any qualitative network N into a discrete one P such that the constraints of N become the variables of P and the constraints of P are defined by the weak composition table of the used qualitative algebra. We then introduce some properties about the (global) consistency of networks, circumscribing conditions under which the two models are equivalent. We also relate some domain filtering consistencies (such as generalized arc consistency) of discrete networks encoding qualitative ones with ◦-consistency, where ◦ denotes the weak composition of the qualitative calculus.

In the previous two decades, a number of qualitative constraint calculi have been developed, which are used to represent and reason about spatial configurations. A common property of almost all of these calculi is that reasoning in them can be understood as solving a binary constraint satisfaction problem over infinite domains. The main algorithmic method that is used is constraint propagation in the form of the path-consistency method. This approach can be applied to a wide range of different aspects of spatial reasoning.