Research

Visibility Graph Analysis

On this page...

• An introduction to visibility graph analysis
  • Methodology
  • Application
  • Addendum
  • References
  • Who is working on it
  • How can I analyse spaces for myself?
  • Bibliography

On this site...

• About UCL Depthmap
• Pictures
• Early Results
• Report on VGA Use

An introduction to visibility graph analysis

Methodology

Visibility graph analysis is a spatial analysis technique for urban and building spaces pioneered at the VR Centre, which may also be applied to landscapes.

The method involves taking a selection of points across a space, and forming graph edges between those points if they are mutually visible, to form a visibility graph. As such, the technique is similar to those used previously in landscape analysis by De Floriani et al. (1994), or in computation geometry (see for example, deBerg et al. 1997), although we take a grid of many (thousands) of points across the space rather than selecting a few key locations.

Having constructed the visibility graph, we then take measures of various features of the graph. So far, having been inspired by Hillier and Hanson's (1984) work, we have concentrated on the integration of a point in the graph. The integration is a normalised (inverse) measure of the mean shortest path from the point to all other points in the system. However, we have also expanded to other measures, in particular those of Watts and Strogatz (1998) in determining whether systems as a whole are 'small worlds' or not: these measures are mean shortest path length (again), and a measure called the clustering coefficient, which is a measure of local density of edges for a location. For details of our application of the measures, please see to Turner et al. (2001).

Due to historical reasons, we first talked of 'Isovist Integration Analysis' (Turner and Penn, 1999), a misnomer which has unfortunately taken hold. This was due to our starting off with isovists, and then joining isovists which had overlapping centres --- the result is identical to the visibility graph --- and then taking the integration measure. Our preferred terminology now would be 'Visibility Graph Analysis Integration', or 'VGA Integration'.

Application

Our first analysis was of the Tate Gallery. We first compared the first ten-movement trace of people entering the Tate (from Hillier et al. 1996) with the pattern of VGA integration for gallery. The results were surprising: visual inspection showed that the highest integration values corresponded well with where movement occured (see the figure below). We then went on to compare our results with other data obtained by Hillier et al.. A detailed description, with full results from the analysis is included in Turner and Penn (1999), and a revised analysis is also presented in Turner et al. (2001).

Ten-minute movement trace compared with visibility graph analysis integration of the Tate Gallery. Note how most movement occurs in the most visually integrated areas, identified by the analysis.

At the time of our analysis, Tate Gallery was being explored principally by Ruth Conroy as part of her PhD thesis (Conroy 2000), indeed, she supplied the model we used. Although not directly concerned with visibility graph analysis, Conroy explores how isovists affect the movement of people within virtual environments.

The T-shape example, shown at the top of the page, was developed as an example for the Syntax Symposium paper, and has since been rehashed many times. The only useful thing it shows is that integration is not directly proportional to neighbourhood size (see the Environment and Planning B paper for details).

Following our initial experimentation, the analysis was tested in earnest by two MSc students, Maria Doxa from the Bartlett, and Fotini Kontou from Geomatic Engineering. Doxa (1998) applied the technique to public building spaces --- the National Theatre and the Royal Festival Hall --- where, due to the buildings' open plan nature, it was difficult to divide the spaces effectively into 'convex spaces', in order to perform conventional space syntax analysis, and for this reason, she turned to visibility graph analysis instead. Kontou (1998) provided the first detailed report on the use of visibility graph analysis, where she applied it to movement patterns found with the Harrods department store. Her findings are summarised in Chapman et al. (1999).

In conjuction with Doxa and O'Sullivan, we then went on to extend the methodology and think about the consequences of our applications. The results are published in Turner et al. (2001). It was at this time that we formalised the technique as 'visibility graph analysis' and found its relationship to previous work in landscape analysis and computational geometry. At this time we were also finding out about the limitations of the methodology. In particular, experiments by the Space Syntax Laboratory showed that the method was a less successful 'people movement predictor' when used in urban rather than building contexts --- integration is weighted to large open areas, whereas people movement is not. Doxa has proposed returning to a more topological analysis, using the methodology to identify spaces --- not just to solve this problem, but also to enhance spatial description. Meanwhile, Turner has proposed moving away from the integration metric to graph analyses based on the shape of the graph distribution rather than the actual numbers of nodes at different depths.

Since its inception, VGA has been used primarily by Space Syntax Limited in design projects, although it is now being taken up by PhD students within UCL and other commercial outfits. The summary presented here will almost certainly be out of date before it is published on the web, especially the tentative thoughts about the future of the methodology. Please see 'Who is using it' to find out who is doing what at the moment.

AT, April 2000

Addendum

Since this piece was written, we have also discovered an earlier implementation of visibility graph analysis of architectural systems, by Braaksma and Cook (1980). In a similar manner to Krüger et al (1979), Braaksma and Cook map the visibility relationships of components within a space; they lay them out as a 'covisibility' matrix that identifies which components can see each which, and analyse the matrix. As such, the methods of analysis mirror ours. However, Braaksma and Cook's application differs in one crucial respect to our implementation of visibility graph analysis; we analyse the open space between the built form, while Braaksma and Cook, as with others such as Krüger et al or De Florianni et al (1994) map the intervisibility of built components.

Our method follows Benedikt, and starts from isovists taken within form, and attempts to build graphs of these (i.e., as the title of Turner et al, 2001 suggests, moving from isovists to visibility graphs). This is why we have always classed it as a space syntax method, as it essentially categorises the possible occupiable spaces of the built environment by their (in this case, visual) relationships to other occupiable spaces. The result is that outcomes are proposed to deal with how people might interact with space. Either moving through it (as described in Turner and Penn, 1999 and Desyllas et al, 2001), or standing, discussing or generally occupying it (see, for example, Doxa's, 2001, analysis of the usage of the Royal Festival Hall).

Our terminology has moved on again. We now tend to call our specific implementation of VGA "dense grid visibility graph analysis", since we start with a dense grid of isovist locations to build the graph (although, obviously, one could start with other arrangements of point locations within open space). VGA has led us to talk about "Visual Integration" (the analogue of axial integration), or "visual depth" (number of visibility turns from one location to another), or even "visual connectivity" (for "neighbourhood size", or the approximate isovist area, as in space syntax, "connectivity" is used to discuss the number of lines connected to another).

AT, January 2004

References

Chapman, D, Kontou, F, Penn, A, and Turner, A, 1999, "Automated viewshed analysis for configurational analysis of retail facilities", In Proceedings 19th International Cartographic Conference, Ottawa, Canada.
Conroy, R, 2000 Spatial Navigation in Immersive Virtual Environments, unpublished PhD thesis, Bartlett Faculty of the Built Environment, University College London, London (forthcoming)
deBerg, M, van Kreveld, M, Overmars, M, and Schwarzkopf, O, 1997 Computational Geometry (Springer-Verlag, Berlin)
De Floriani, L, Marzano, P, and Puppo E, 1994, Line-of-sight communication on terrain models International Journal of Geographical Information Systems 8(4) 329--342.
Doxa, M, 1998 The Character of Interior Public Space: Morphologies of Movement and Co-Presence and the Potential for Interaction in Public Buildings, unpublished MSc Thesis, Bartlett Faculty of the Built Environment, University College London, London.
Hillier, B and Hanson, J, 1984 The Social Logic of Space (Cambridge University Press, Cambridge)
Hillier, B, Major, M D, Desyllas, J, Karimi, K, Campos, B, and Stonor, T, 1996, "Tate Gallery, Millbank: a study of the existing layout and new masterplan proposal", Technical Report, Bartlett School of Graduate Studies, University College London, London.
Kontou, F, 1998 Does space matter? - Investigating spatial configuration using space syntax & GIS tools, unpublished MSc Thesis, Department of Geomatic Engineering, University College London, London.
Turner, A, Doxa, M, O'Sullivan, D, and Penn, A, 2001, From isovists to visibility graphs: a methodology for the analysis architectural space Environment and Planning B: Planning & Design 28(1) 103--121.
Turner, A and Penn, A, 1999 "Making isovists syntactic: isovist integration analysis" In Proceedings 2nd International Symposium on Space Syntax, Universidad de Brasil, Brazil.
Watts, D J and Strogatz, S H, 1998, Collective dynamics of 'small-world' networks Nature 393(4 June) 440--442.

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Who is working on VGA

VGA is being researched around the world, with active work on investigation of the technique in Chile, Italy and the UK among others. Commercially, two companies, Space Syntax Limited , and Intelligent Space use the method to help understand the social usage of space.

People

Work includes validation of the technique (under Prof. Margarita Greene, Chile), understanding how spatial structure is linked to visual structure (under Prof. Valerio Cutini, Italy), applications by students within the Bartlett and outside, as well as work by researchers in Canada, Germany and Norway.

Related Research

Benedikt originated research into isovists. He is director of the Center of American Architecture and Design at the University of Texas.

Peponis and his research team at Georgia Tech have produced a software package called Spatialist which performs many visual analysis tasks, including isovist production, and spatial analysis related to their research.

Sofia Psarra is working on innovative techniques of spatial classification by investigating the intervisibilty of points on the perimeter of isovists in both theoretical and real layouts.

Of course, isovist analysis and graph analysis are also still central to Space Syntax methodology as a whole.

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How can I analyse spaces for myself?

UCL has developed UCL Depthmap, a program to perform visibility graph analysis. The program runs on Windows NT, 2000 and XP.

Space Syntax Limited has been appointed to distribute the UCL Depthmap software. If you would like a copy of UCL Depthmap for educational use, please contact licensing@spacesyntax.com.

In addition, several similar programs have been written by researchers closely connected with UCL. These include Omnivista, written for Mac users, which also calculates isovist paths through systems. Contact the author, Nick 'Sheep' Dalton for details. Intelligent Space Partnership have implemented 'Fathom', which calculates many visibilty graph measures, and Sanjay Rana has written a plug-in program for ArcView called Isovist Analyst while at UCL. Isovist Analyst can be downloaded from the CASA website.

Gerald Franz at the Max Planck Institute for Biological Cybernetics in Tübingen, Germany has developed a GNU public license implementation called ajanachara to analyse VRML models. ajanachara can be obtained compiled for both Linux and Windows, in addition to the source code.

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Selected Bibliography

A selection of recommended reading on VGA:

• Turner, A. and Penn, A., 1999, Making isovists syntactic: isovist integration analysis. In Proceedings 2nd International Symposium on Space Syntax

• Turner, A., Doxa, M., O'Sullivan, D. and Penn, A., 2001, From isovists to visibility graphs: a methodology for the analysis of architectural space. Environment and Planning B: Planning and Design 28:103–121

• O'Sullivan, D. and Turner, A., 2001, Visibility graphs and landscape visibility analysis. International Journal of Geographical Information Science 15:221–237

• Desyllas, J., Duxbury, E., 2001, Axial maps and visibility graph analysis: a comparison of their methodology and use in models of urban pedestrian movement In Proceedings 3rd International Symposium on Space Syntax, Georgia Institute of Technology, GA, May 2001.

• Doxa, M., 2001, Morphologies of co-presence and interaction in interior public space in places of performance: the Royal Festival Hall and the Royal National Theatre, London In Proceedings 3rd International Symposium on Space Syntax, Georgia Institute of Technology, GA, May 2001.

• Cutini, V., 2003, "Lines and squares: Towards a configurational approach to the morphology of open spaces"
  In Proceedings 4th International Symposium on Space Syntax, UCL, London, June 2003.