Abstract Geographic space is a large scale space which is beyond the human perception, and can not be seen from a single viewpoint. Maps and drawings provide one way of perceiving and understanding geographic spaces. Here another approach to spatial cognition is addressed. The approach, space syntax, is proved to be of great value in predicting human spatial behaviour in urban environments. The discussion is instrumental in explaining some previous findings in space syntax studies, and can also be seen as a contribution to Naive geography. The basic assumption is that human spatial cognition in some sense is determined by spatial configuration, and spatial cognition again determines human spatial behaviour like pedestrian movement in urban environments. Thus, by analysing urban morphological properties, pedestrian rates are predictable.

Keywords: Spatial cognition, space syntax, naïve geography.

1. Introduction

Spatial cognition is the human understanding and perception of geographic space. Geographical space is a large-scale space, it is "a space whose structure is at a significantly larger scale than the observations available at an instant. Thus, to learn the large-scale structure of the space, the traveller must necessarily build  a cognitive map of the environment by integrating observations over extended periods of time, inferring spatial structure from perceptions and effects of actions." (Kuipers and Levit 1990). Thus, geographic space differentiates from small scale space or ‘table-top’ space, in which objects are thought of being manipulable or explorable from a single point of view. One could have a global view of the small scale space. Urban environments can be seen as a kind of geographic space either at the architecture scale or city scale.

The traditional view on spatial cognition is said to be based on cognitive maps (Lynch 1960) - a mental map about the geographic space. However, it is generally agreed that the cognitive map is not entirely maplike (Kuipers 1982, pp. 202). Maps are based on Euclidean geometry, i.e. spatial objects are represented with precise co-ordinates along objects edges or outlines. However, spatial cognition is not necessarily based on metric measures, for instance, spatial adjacency cannot be perceived by a metric measure, as trivial distance difference might exclude a site from a particular neighbourhood.

In the context of this paper, a new kind of map called an axial map using the space syntax approach is introduced, which, we believe, has more resemblance to a cognitive map. The axial map, or more precisely the space syntax approach, is well used to predict human spatial behaviour both at the architectural and city scale. Therefore the paper is intended to provide cognitive evidence as to why human behaviour is predictable using the space syntax approach, rather than how people explore the urban system with an axial map. The basic assumption is that spatial configuration (morphological structure) is the driving force for human activity within urban environments, and it is this that first influences human cognition, and further determines human activity within urban environments.

The work presented here is also motivated by naïve geography in the field of spatial information theory, a theoretical basis for GIS. Naive geography (Egenhofer and Mark 1995) is defined as the body of knowledge that people have about the surrounding geographic world. It is considered to be the fundamentals of next generation GIS, which can be used by average citizens without extensive training. Naive geography intends to incorporate people’s concepts about space and time and to mimic human thinking.

The remainder of this paper continues with a brief introduction to the space syntax approach used as a powerful tool for urban morphological analysis (Jiang 1998). In the main part of this paper, sections 3 and 4, we elaborate on the plausity of the space syntax approach both as a computational and cognitive model. Section 5 presents our conclusions and points out some directions for further research.

2. Space syntax approach

Space syntax is based on the fact that an urban environment is an interconnected space where everywhere links to everywhere else. The space syntax approach provides an urban morphological representation by looking at only public spaces (open space). These public spaces look like a beady ring system, in which space widens to form irregular beads, and narrows to form strings, while at the same time joining back to itself so that there are always choices of routes from any one space to any other space (Hillier and Hanson 1984, pp. 90).

Based on the analogy of the beady ring system, there are two ways to represent urban environments by only concentrating on public spaces: convex polygons and axial lines. A convex polygon is a polygon that no line drawn between any pair of points within that polygon goes outside of the polygon. The axial line is the longest straight line which chains convex polygons. Axial lines are said to be also linked to the notion of visibility. Both kinds of representation are named convex maps and axial maps respectively. Figure 1 shows the open space of an irregular street grid and its axial representation - axial map.

The above axial representation gives the opportunity to measure a particular property of the urban environment; connectivity indexes, control value and integration are some of these morphological properties. Connectivity is the measure of how well an axial line is intersected by others. In principle, there is no non-intersected line in any urban environment, i.e. each space is accessible from every other space in the city. In the mean time, experience tells us that the length of the axial line has some correlation  to connectivity indexes, that is, these are more possibilities for lengthy lines to be intersected by others.

A modification of connectivity is control value, which measures how each axial line controls its immediate neighbours, i.e. those lines intersected by the current one. Both connectivity and control are local measures, since they only take into account relationships between a space and its immediate neighbours.

Integration of a line is by definition a value which indicates the degree to which a line is more integrated, or segregated,  from a system as a whole. The measure is actually based on a more basic notion called depth. Depth is more generally a topological distance in a graph. If two lines are directly connected, then the distance between them is equal to one, and the distance of a pair of lines which are not directly connected is the shortest path between them. Integration is a global measure, as the calculation of integration is based on the total depth from the current. However, if a number of depth, instead of all depth, is considered, then the integration is called local integration.

Finally the axial maps can be coloured from red through the spectrum to blue depending either on connectivity or on integration. Thus red lines are well connected or well integrated, and blue lines are not well connected and most segregated with spectrum representing something in between.

In summary, global integration is a key morphological variable, and its value of a space can be measured based on the number of other spaces that must be traversed in order to reach all the other parts of the system. Connectivity, as well as local integration,  on the other hand, measures local morphological property of a system. In some sense, control value is a modified connectivity measure which takes into account the connection of each neighbour of a space. Thus, global integration is a global measure describing the relation of each space to the system as a whole, while connectivity and local integration are local measures describing the relationship of each space to its neighbours.

The development of space syntax theory basically consists of two parts: (1) the formalisms of geographic models for urban environments; and (2) the test and analysing of formal models. The above discussion only covers the first part. As far as the second part concerned, extensive empirical studies have been made over the past decade with spatial syntax research (e.g. Hillier 1997). The rest of this paper concentrate on the computational and cognitive aspects of the model.

3. The computational model of space

You may have sensed from the above introduction to the space syntax that the theory is based on the graph theory, or more precisely that the actual morphological computation is based on the associated graph of the axial map. Figure 2 shows a simple version of an axial map and the associated graph. With the figure, it is relatively easy to understand the morphological measures introduced above. First of all, connectivity is the number of nodes directly linked to each individual node. For instance, line 1 (or node 1 in the associated graph) in figure 2 has connectivity of 3, and line 2 has connectivity of 1.

Figure 2: An axial map and the associated graph

The control value for a line is determined according to the following calculation,
  ............(1)
where n is the number of immediate neighbours of a space, and Cj is the connectivity of the jth immediate neighbour of the space.

According to the definition of depth, for each axial line, all other lines should be traversed in order to retain the so called mean depth (MD),
.....................(2)
where  n is the number of spaces and is the total depth of the ith axial line.

For measuring integration and segregation property, MD is sufficient. Relative Asymmetry (RA) is employed to standardise MD between 0 and 1.
......................(3)

What keeps space syntax a plausible model for spatial cognition is that it is a computational model. In other words, with the computational model by analysing morphological structure human spatial behaviour is predictable. For instance, extensive empirical studies over the past decade have demonstrated that pedestrian rates strongly correlate to local integration value (Hillier et al. 1993).

4. The cognitive model of space

In this section, we attempt to elaborate on some cognitive issues using the space syntax approach, e.g. why human behaviour is predictable? Space syntax is also considered as a contribution to naive geography, because it is not only computationally plausible, as shown above,  but is also cognitively plausible as discussed below.

Figure 3: Closed spaces and open spaces

4.1 Closed spaces vs open spaces

Geographic spaces, particularly urban environments, are complex spaces which can be viewed from two stands: closed spaces and open spaces. As shown in Figure 3, closed spaces are spatial entities such as buildings, plots, and street blocks; open spaces are mainly streets. Traditional maps represent geographic spaces both with closed spaces and open spaces in a paper sheet, while GIS represent these spaces layer by layer. Space syntax concentrates on the representation of open spaces in a unique way which differentiates it from maps and GIS.

Open spaces are all interconnected, one can travel from everywhere to everywhere else. It is this kind of characteristics that keep space syntax in a unique way in modelling urban environments, or geographic space in more general term. From the cognitive point of view, concentration on open spaces at least has following advantages. It is useful to analyse and understand the morphological structure; It facilitates the perception of human activities in urban environments.

One of spatial knowledge is cognitive knowledge, which is essentially ‘map-like’, and includes knowledge of relative positions, distances and angles (Mark 1997). However, we argue that maps are poor in perceiving spatial configuration, while axial maps, a special map based on open spaces, are good in analysing the morphological properties of urban environments. The study of spatial configuration is instrumental in predicting human behaviour, for instance, pedestrian movements in urban environments.

4. 2 Vista spaces vs urban environments

Space syntax starts the representation of  urban environments from what can be seen from a single viewpoint. The viewable space is called a vista space which is represented as an axial line. Thus an urban environment is a set of all vista spaces, and is represented visually as an axial map, or mathematically an interconnected graph. Therefore, the property of an urban environment can be inferred from individual vista spaces. Compared to spatial modelling using Euclidean geometry in which the geographic objects are represented as a series of co-ordinates and spatial inference is based on the complex computation, the space syntax approach is object oriented.

An axial map is an economic representation of urban form, which is a kind of morphological representation. Krafta (1997, pp.2) refers to the kind of morphological representation as a configurational representation, i.e. "a representation of the urban spatial reality given by a few categories of components (e.g. the axial line) and rules (the adjacency) which tie each component to all others in such a way that a change in any one of these basic elements reflects on the entire system". Therefore, morphological representation differs from maps and the like (photographs, or drawings) in the sense that it is a systematic description of urban environments.

Regarding the economic representation, Krafta gave a plausible analogy - "x ray" of  urban environments. Axial maps can be seen as the approximate skeleton of urban environments. That is, with the axial map representation, it is possible to think about the basic form of urban environments. For instance, figure 4 shows a series of axial maps of Oxford at different times from the 14 century up to the present, where the grey scale of lines represents the global integration, i.e. the darker, the more integrated. From the figure, the basic spatial morphological structure is readable, for instance where the integrated areas are and where the segregated areas are.

The difference between morphological representations and maps, has been rooted in long standing debate, i.e. whether geographic space should be viewed as something measurable with a ruler or whether the only important information is the relationships between objects in that space. Human thinking is not metric based. If you are asked where your home is, you may answer by saying in which region (hierarchical reasoning), and by (topological relation) a certain street. Therefore, topological relationship is frequently used in daily life. Incorporation of this sort of knowledge into a GIS is so called common-sense reasoning. This strikes me to be a possible explanation of how people in general perceive space when they are walking or driving over the urban space, i.e. one vista space is perceived as one unit in human mind, and the urban space is a collection of all vista spaces. With this explanation, it is understandable that pedestrian rates are predictable using the local morphological properties.

Street networks seem to have similar roles as axial maps in structural description, however, we are not convinced with this as named streets are in a sense "artificial". Maps are the most efficient and effective way of communicating metric properties of large scale space, whilst the axial maps are more likely to resemble human spatial reasoning and perception processes.

4.3 Distance and spatial adjacency

Distance is the central concept of spatial cognition, and it plays an important role in human activity. As stated by Montello (1997, pp. 297), "it helps us orient ourselves and locate places during navigation. It is used to evaluate costs of travelling from one place to another, and it helps us utilise resources efficiently (time, money, food). Clearly, knowledge of distances in the environment ‘effect the decision to stay or go.. the decision of where to go... [and] the decision of which route to take’ (Cadwallader 1976: pp. 316). It therefore seems likely that an understanding of the perception and explanation of spatial behaviour."

The distance that space syntax concerns itself with is a sort of topological distance (Buckley and Harary 1990), i.e. the distance of two intersected axial lines is one, and distance of non-intersected lines is the shortest path between them. The paradigm about distance set by space syntax conforms well to cognitive distance. This is summarised as a so called segmentation feature, i.e. routes with increasing numbers of right-angle turns were shown to be psychologically longer than routes with fewer right-angle turns (Sadalla and Magel 1980). Figure 4 illustrates two routes from point A to point B, people in general follow the route with more turns have a longer distance estimate than another route with only one turn. Again this strikes me as an indication of the resemblance between topological relationship to human perception.

Figure 5: Distance estimates influenced by the route structuring

As the global integration is derived from the mean depth, the mean shortest distance is from a node to every other node in a graph. The notion well conforms to the conclusion in cognitive science that when travelling in an urban environment, the choices of routes reflects the human desire to minimise functional distance (Deutsch and Isard 1961).

Spatial adjacency is a special kind of spatial relationships, and it is a very important feature which is frequently discussed in current GIS. It is mainly dealt with by computational geometry (e.g. Berg et al. 1997), which is regarded as a geometry for GIS. In raster format, to define adjacency, we must specify a   or   pixels grid, or we have to intentionally set up topological relationships of spatial objects in vector format. As summarised by Gold (1995) that "raster adjacency is based on adjacent regular tiles - usually squares of space; vector adjacency depends on the detection of line intersection in order to form a polygonal graph and it is this graph that forms the conventional GIS ‘topology’".

Space adjacency is a basic rule to form axial maps, i.e. two axial lines intersected are regarded as adjacency. The existence of this adjacency relationship is expressed as an edge of the dual graph. This edge connects two nodes, each node representing a vista space.

Spatial syntax seems to be reasonable in measuring spatial adjacency. Space adjacency can be measured with metric distance, for example by drawing a circle around a point object, or drawing a buffer along a line or polygon object. If a spatial adjacency is modelled metrically, then the trivial distance difference may exclude a site from the neighbourhood. Thus, metric measure is a poor measure for spatial adjacency as shown in figure 6. In terms of metric distance points 1, 2 and 3 are neighbours of the central points. However, when considering connection, point 3 is excluded from its neighbours because of poor connection, while point 5 is included in the neighbours. We believe that the neighbours in the right hand are more realistic. There has been increasing attention to solving spatial adjacency from setting appropriate (topological) data structure (Okaba 1994, Gold 1992).

 a: metric space             b: topological space

Figure 6: The concept of neighbour in both metric and topological space

Now coming back to space syntax, it is understandable that people living by the dominated street may have relatively bigger neighbourhood feelings and in the opposite way, the people living in less dominated streets may have less neighbourhood feelings. This may be a basic hypothesis which needs to be investigated in the future.

5. Summary and Conclusions

In spite of the fact that spatial cognition is an important aspect of GIS, and that there has increasing research activity in this respect, no satisfying model for the  prediction of spatial behaviour has been developed to date. This paper provides such a model that shows that human spatial behaviour in general is predictable in urban environments. Extensive empirical studies have been made over the past decade at Bartlet School of Graduate Studies, of University College London in this field.

Configurational representation of urban systems ( or more generally geographic space) is a sort  of representation which differentiates it from other visual representations we are used to. Maps and the like are a kind of metric representation which do not result in more information as far as spatial cognition is concerned, whilst configurational representation based  on topological relationships may be more informative in the sense of spatial cognition.

Space syntax provides an alternative way to understanding geographic space. The distinguished property of space syntax is the same as that of naive geography, i.e. treats topological relationships as prior to measurements. As already  recognised (Egenhofer and Mark 1995), there is a big gap between what a human user wants to do with a GIS and the spatial concepts offered by the GIS. The space syntax approach introduced here yields an alternative to spatial apprehension, and it can be employed to make predictions of human behaviour. By implementing an extension of space syntax approach, we have successfully brought the approach to GIS users for morphological analysis (Jiang 1998).

Space syntax has proved to be a substantial model for urban studies, but it is not without problem. Amongst others, the following two points are critical. Firstly, the notion of axial lines are quite fuzzy, although we attempt to regard it as the representation of vista space in this paper. Secondly, the generation of axial maps for an urban system is still manual, and there is no efficient automatic way to do it. Although there are some principles to draw axial lines, it is hard to guarantee the consistency of axial maps. For instance, the claim (Hillier and Hanson 1984) that an axial map is the least set of longest axial lines is not proven.

Acknowledgement

This paper is part of Virtual ENvironments for Urban Environments (VENUE) project, financially supported by a grant from Joint Information System Committee (JISC).

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 Related publications:

1. (with Batty M. and M. Thurstain-Goodwin), Local Movement: Agent-Based Models of Pedestrian Flows, CASA Working Paper Series, 68 pages, 1998.

2. Cartographic Visualisation: Analytical and Communication Tools, Cartography, December, pp. 1-11, 1996.

3. (with A. Brown, and F. J. Ormeling), Some Perceptual Aspects of Colouring Uncertainty, in: M. J. Kraak and M. Molenaar (eds.) Advances in GIS Research II, Taylor & Francis, pp. 477 - 490, 1996.

4. Advanced Visualisation and Virtual Reality for Exploring Complex Social Phenomena, position paper for Workshop on Advanced Visualisation and Virtual Reality in the Social Sciences, 9 - 11 September 1998, Weetwood Hall, University of Leeds.

5. Multi-agent Simulations for Pedestrian Crowds, Proceedings of European Simulation Symposium, Nottingham, Oct. 26-28, 1998.

6. Axwoman: An ArcView Extension for Urban Morphological Analysis, Proceedings of Geoinformatics’98, June, Beijing, 1998.http://andes.esri.com/arcscripts/details.cfm?CFGRIDKEY=-2057687617 

7. Urban Morphology: A Set of Theory and Tools for Urban Sustainable Development, Proceedings of 3rd Annual Meeting of Chinese Young Scientists, August, Beijing, 1998.