A Computational approach to ‘The Image of the City’

In The Image of the City Lynch describes how individuals perceive and recall features in urban spaces. The most distinctive elements in the urban landscape - categorised in paths, nodes, edges, districts and landmarks - give shape to individuals’ mental representation of the city. Lynch’s approach has stimulated research into spatial cognition, urban design and artiﬁcial intelligence, and still represents an essential pillar in the analysis of urban dynamics. Nevertheless, an explicit link between The Image of the City and GIScience has not been completely explored yet. In this paper, a computational approach to The Image of the City is proposed. Diﬀerent perspectives in spatial cognition and GIS research are integrated, to obtain a complete Image of the City, in which the most salient elements are shared by a large part of citizens. Nodes, paths and districts were identiﬁed through network science techniques. Methods drawn from the information approach to The Image of the City are used to detect landmarks, integrating the complexity of points of reference in their visual, structural and semantic components, as conceptualised by Lynch and successive research. The methods were applied to the central area of Boston and built using freely available spatial datasets. Results were compared to Lynch’s maps to evaluate the methodology: beside a considerable discrepancy with regard to landmarks, a good correspondence for paths, nodes, edges and districts was


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A number of research communities have been involved in the quantitative formulation of memorability and in extracting cognitively salient urban features.
These approaches can potentially contribute to the development of a framework for extracting Lynch's five elements. 50 The relationship between the external space and the mental representation social phenomena is the driving force of Space Syntax, a set of theories and techniques 'for the representation, quantification, and interpretation of spatial configuration in buildings and settlements ' [21, p. 363]. In this perspective, the street layout and the configuration of space have a strong impact on the 55 Shannon's information theory, on the other, for studying how the mental image is formed from specific urban elements. In this information approach, legible cities are composed of informative and significant artefacts or urban configurations. City nodes, paths or districts are 'information carriers' that shape the mental image. Here, the original measure of information [50] -a form of entropy 85 that quantitatively measures the unexpectedness of an event -is adjusted with an index that incorporates semantic information. This component represents the result of biological, cultural, social and pragmatic categorisation processes.

Space Syntax
Their theory reinvigorates the idea that city elements may be remembered for symbolic and social meanings [1], but also for their pragmatic functions. 90 Moreover, it introduces a computational framework to The Image of the City that takes into account the combination of these traits and their contribution to the legibility of cities. The drawback of their approach is that it contemplates a measure of entropy, suitable for the city-or district-level but unfitting for computing the individual scores of the elements. 95

Automatic Landmark Extraction
Sorrows and Hirtle [52] refine the notion of landmark. The authors differentiate visual landmarks -objects used as spatial points of reference for their visibility -from cognitive landmarks -relevant for their uncommon and meaningful content -and structural landmarks -recognisable for their advantageous 100 and prominent position in the space. This work has inspired a vein of research in GIS community interested in automatic identification of landmarks for wayfinding design and navigational support: Raubal and Winter [45] advance a model that measures the salience of buildings in relation to perceptual and cognitive properties. Winter [58] ameliorates the model, recommending to consider 3d 105 visibility as another property. Elias [9] presents a similar approach based on machine learning algorithms that inspect geometric, topological and semantic attributes of buildings to establish landmark hierarchies. Furthermore, Winter et al. [59] integrate the previous approaches to construct a hierarchy of landmarks, emphasising the distinction between local-landmarks and city-wide 110 (global) landmarks.
In summary, while these works have moved landmark research forward, the other Lynchian elements are of little interest and rarely mentioned here.

Contributions and Gaps
Even though automatic landmark identification models have been dissemi-115 nating [46], presumably due to their potential applicability in navigation systems design, none of the approaches have offered a set of methods and tools to quantitatively derive the five elements of The Image of the City.
• Space Syntax, when reformulating The Image of the City, has mostly considered visual aspects, neglecting important implications regarding the 120 genuine human-environment interactions and focused on paths identification.
• The information approach, whilst being based on the usage of geospatial dataset, returns a macro-level index of legibility.
• Edges have generally received a little attention, or been considered a par-125 ticular type of landmark and assessed for their structural properties [e.g. 47,45]; districts have been translated in Voronoi partitions, whose cognitive salience is disputable.
• More importantly, in the literature discussed above, when an application of the methodologies is presented, the dataset usually refers to small areas, 130 it is created ad-hoc by the researchers or based on questionnaires, which makes it hard to reproduce the study for new areas.

Methodology
In the following section, network science techniques are presented for the detection of nodes, paths and districts, from the street configuration. In addition, 135 a comprehensive landmark detection method is proposed following Sorrows and Hirtle's framework [52] and the models discussed above. These approaches were enriched performing a 3d visibility analysis and integrated with insights derived from the information approach; semantic and pragmatic properties were here considered for the first time in a large geo-dataset. Lastly, a set of rules to

Nodes
Nodes are the strategic foci into which the observer can enter, and which are the intensive foci to and from which he is travelling. They may be primarily junctions, places of a break in transportation, a crossing or convergence of paths  In our approach betweenness centrality was calculated in an undirected planar graph, as: Where, in an undirected graph G, n jk is the number of shortest paths between the vertexes j and k, and n jk (i) is the number of shortest paths between the vertexes j and k that pass through i. Paths are the main lines of movement in the city; they guide people's move-170 ment, supporting orientation. In low-legibility contexts, when a path is not characterised by vivid activities or peculiar properties, perceptual continuity comes into play: people rely on this functional quality to successively travel across the city. The concept of continuity recalls the idea that people tend to choose routes that minimise angular change rather than distance [49,16,23]. In 175 this sense, angular betweenness is described as the best predictor of pedestrian and vehicular movement when only the street network is at disposal of the researcher [5]. Betweenness centrality, as defined above (see eq.1), was computed for vertexes in a dual graph representation so generated:

Paths
• Street segments are converted to vertexes;

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• When two street segments cross each other in the road network, a link connecting the corresponding vertex in the dual representation is created.
• The amplitude of the angle of incidence formed by two street segments is assigned to the corresponding link as weight.
Finally, the centrality values of the vertexes in such a network were reas-185 signed to the originating segments. Therefore, it is assumed that the major paths are those which minimise angular change in travels across the city. Here, we did not take into account the road-type class (e.g., major-road, secondary- Space Syntax suggests that the topology of the street network is associated with people's perception of places and regions: Law [29] illustrates a process for generating sub-graphs from the street topology applying community detection techniques. The so formed Street-based Local Areas (SLA) [55] are regions whose 200 internal homogeneity has social and functional foundations [15].
In this discussion, it is assumed that the different districts of a city can be identified analysing the road layout. The modularity optimisation function [3] is adopted to extract SLAs. This algorithm optimises modularity [15], an index that measures the goodness of a network division. Modularity (Q) computes 205 the difference between the edges within a community and the expected numbers of edges in a network with the same structure but random connections.
When the number of within-community edges is nothing more than random, the structure of the communities is poor and Q is equal to zero. Otherwise, greater the difference, greater Q, stronger the division. On the contrary, high 210 values of Q represent strong division amongst well-structured communities. The implementation of the modularity optimisation technique follows these steps for more details): 1. Every node i is considered a community.
2. For each node i, the algorithm evaluates the gain in modularity (Q) that 215 would be obtained by joining the node with each of the neighbour communities j.
3. If no possible gain is detected, the node i stays in its original community, otherwise, it is placed in the community, wherein the modularity gain would be maximised. The function was run in an undirected dual graph. Partitions were extracted from a network where weights were based on the angles of incidence between 225 pairs of segments, as described above. Thereby, districts are the sub-graphs obtained from the street network, optimising modularity.

Landmarks
Landmarks are point references considered to be external to the observer. The cultural meaning of a building was obtained counting the number of listed 250 historic elements located within its boundaries. Finally, pragmatic significance was calculated following a simplification of the information approach, as an index of unexpectedness: Where, in a buffer of x metres around the building b, N b is the frequency 255 of the land use class of b and N is the number of buildings. The scores of the indexes were scaled and combined in the relative component, and, subsequently, in the overall score (see table 1 for details).

Edges
Edges are linear elements not considered as paths: they are usually, bound- Edges are authentic organising features whose primary trait is linear continuity. Nevertheless, edges could be permeable and crossable, they can coincide 265 and align with paths. In the current analysis, the following linear elements, with a predefined minimum length, were extracted as edges: • Sections of railway structures as bypasses or other visible structures.
• Sections of motorways.

The case study
The methods delineated above were applied to the city centre of Boston, MA (USA), on the area studied by Lynch ( figure 1). The results of the analysis are presented, discussed and compared to the map depicted by Lynch, who asked 275 30 residents and workers to describe customary itineraries and experiences, and recognise places (see figure 2).
Our analysis mainly relies on the street network and buildings footprints.
While the datasets are Boston-specific, the sources employed are generic (and often available as open data) so to allow application of this approach for other 280 case study areas. The sources are:

Nodes, paths and districts
We found some crucial nodes (   In Boston edges seem to play two roles. On one hand the river and the harbour define the shape of the city centre; on the other hand, the motorways, 385 besides reinforcing the peninsula profile, represent interruptions, separate different areas and obstruct movement. The Central Artery is described by Lynch's

Discussion and conclusion
The aim of this work was to provide a quantitative formulation of Lynch's Image of the City, easily incorporable in GIS environments, that may favour a 410 more explicit inclusion of The Image of the City in GIScience. In The Image of the City, Lynch introduces and describes five elements -nodes, paths, districts, landmarks and edges -that give shape to the mental representation of the city.
A complete computational approach to The Image of the City was presented here and tested on a large and freely available urban-dataset, integrating a range 415 of methods derived from previous research. The mental image of Boston was drawn ranking artefacts on the basis of network and geospatial measures. We explicitly took into consideration a semantic component in landmark extraction lastly, the criteria advanced to pull out edges produced satisfying results, against the ones presented in The Image of the City.
Having said that, the complexity of human cognition and perception can-  The work has shown that the development of a computational form of The Image of the City is feasible. The methodology devised here can be applied to other cities and urban contexts very easily, manipulating just the input data and a few parameters. This approach makes it possible to reveal images of cities, investigated so far with qualitative and time-consuming procedures. We argue 465 that this tool may support spatial planning decisions in urban design, providing important insights as concerns city livability, quality of life [30], the adequate mix of land-uses, the ease of navigation and orientation.