Representing short-term observations of moving objects by a simple visual language

Abstract

In a variety of dynamical systems, formations of motion patterns occur. Observing colonies of animals, for instance, for the scientist it is not only of interest which kinds of formations these animals show, but also how they altogether move around. In order to analyse motion patterns for the purpose of making predictions, to describe the behaviour of systems, or to index databases of moving objects, methods are required for dealing with them. This becomes increasingly important since a number of technologies have been devised which allow objects precisely to get traced. However, the indeterminacy of spatial information in real world environments also requires techniques to approximate reasoning, for example, in order to compensate for small and unimportant distinctions which are due to noisy measurements. As a consequence, precise as well as coarse motion patterns have to be dealt with.

A set of 16 atomic motion patterns is proposed. On the one hand, a relation algebra is defined on them. On the other hand, these 16 relations form the basis of a visual language using which motion patterns can easily be dealt with in a diagrammatic way. The relations are coarse but crisp and they allow imprecise knowledge about motion patterns to be dealt with, while their diagrammatic realisation also allow precise patterns to get handled. While almost all approaches consider motion patterns along arbitrary time intervals, this paper in particular focuses on short-term motion patterns as we permanently observe them in our everyday life.

The bottom line of the current work, however, is yet more general. While it has been widely argued that it makes sense to use both sentential and diagrammatic representations in order to represent different things in the same system adequately (and hence differently), we argue that it makes even sense to represent the same things differently in order to grasp different aspects of one and the same object of interest from different viewpoints. We demonstrate this by providing both a sentential and a diagrammatic representation for the purpose of grasping different aspects of motion patterns. It shows that both representations complement each other.

Introduction

In a variety of dynamical systems formations of motion patterns occur. The need to deal with them arise for several reasons: patterns of animal movements are investigated providing a detailed picture of seasonal variability in the scale and patterns of movements [1]; movement patterns are used as an indicator of cognitive function, depression, and social involvement among people with Alzheimer's disease [2]; spatiotemporal databases require moving objects, such as people, animals, vehicles, or even hurricanes, forest fires, and oil spills to be stored, queried, and retrieved [3]. In particular the need to query such databases indicates the importance of means which are simple to handle by human users. It is our aim to provide a formalism which suffices both the need for a simple tool for describing motion patterns and a thorough computational tool to reason about them. To be clear, in this paper by motion patterns we mean changes in the formation of a number of objects. While there is a great body of work about formations (equally configurations), there is still a lack of methods in order to describe changes of formations—especially when making short-term observations of changing formations. For the description of a traffic scenario, for example, it is less useful to describe a static configuration than to describe how a given formation just changes by considering relative directions of moving objects.

Difficulties in verbalising motion patterns for the purpose of communicating spatiotemporal situations, or in order to index spatiotemporal databases, indicate the importance of means which are simple to handle by human users. Any representation of motion patterns requires both spatial and temporal aspects to be considered. Representing spatiotemporal information, in such a way that in spite of all difficulties the interface between man and machine keeps simple, is a specific problem pertaining to the field of human–computer interaction. We refer to it as to the spatiotemporal representation problem of human–computer interfaces. It relates to the question as to what extent a specific knowledge representation influences human–computer interactions.

From the point of view of cognitive psychology, it has been argued that for human beings graphics serve a variety of functions, amongst others, attracting attention, supporting memory, providing models, and facilitating inference and discovery [4]. From the point of view of the knowledge representation community, it has been argued, that the everyday commonsense knowledge about the spatiotemporal behaviour of objects is captured by qualitative reasoning methods [5]. Reconciling these two views amounts to provide a graphical set of motion patterns which simultaneously form the basis of some qualitative representation. By this means, we will solve a sub-problem of the spatiotemporal representation problem of human–computer interfaces, namely that one for motion patterns. For this purpose we focus on knowledge representation issues and leave questions about the appropriateness of the proposed representation for human users to investigations about human–computer interactions. However, those investigations will built upon the representation we will introduce below, and the diagrammatic realisation of the introduced representation gives first insights in how appropriate the representation is from the point of view of human–computer interfaces since the proposed motion pattern relations can be easily memorised, drawn, and graphically combined.

The main body of this paper is organised as follows. In Section 2 approaches to motion patterns are discussed and it is shown how they lack dealing with an interesting subclass of motion patterns. In the following sections, we shall introduce a representation for this class of motion patterns: Section 3 brings in a set of atomic motion patterns, and a relation algebra, described in Section 4, allows those patterns to be dealt with. After that, Section 5 compares this algebra with a diagrammatic representation, showing what advantages both representations have. Section 6 illustrates the calculus by some examples and we conclude in Section 7 by discussing strengths and weaknesses of our method.