Upper bound projection and Stochastic isovists: a solution to the comparison of Visibility Graph Analysis systems

Nick S. Dalton, Ruth Dalton, Sam McElhinney, Panagiotis Mavros

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Visibility graph analysis (VGA) (Turner et al., 2001) is a widespread technique in the space syntax community, used to evaluate urban and building designs. To compare different spatial configurations, architects and researchers have relied on the use of the measure integration, based on D-value relativisation. This paper points out that this form of relativisation was developed originally for convex and axial analysis, the graphs of which have different structural properties compared to the kinds of networks found in typical VGA graphs. Using a new technique of incrementally increasing visibility graph density, we show that the integration value for a fixed point does not remain constant as the size of the graph/network increases. Using several graphs, we empirically demonstrate this non-consistency. We evaluate Tecklenburg (Teklenburg et al., 1993), NAIN (Hillier et al., 2012) and depth-decay methods of relativisation and show that these processes do not empirically produce the necessary stability required. From this, we conclude that it is difficult to compare integration values for VGA analyses using the traditional measure of integration based on known relativisation techniques.
To solve this, we introduce the notion of Restricted Random Visibility Graph Analysis or R-VGA. A fixed number of randomly distributed points spread over the system. Using R-VGA as a gold standard, we then introduce a new empirical relativisation called upper bound projection relativisation (UBPR) specifically for the relativisation of gridded, non-gridded and other dense isovist graphs. In conclusion, we suggest that traditional integration relativisation (the D-value) will always create only approximate solutions. Using UBPR, it is now possible for researchers to accurately compare different spatial models of different sizes.
Original languageEnglish
Title of host publicationProceedings 13th International Space Syntax Symposium
EditorsAkkelies van Nes, Remco E. de Koning
Place of PublicationBergen, Norway
PublisherWestern Norway University of Applied Sciences
Number of pages19
ISBN (Electronic)9788293677673
Publication statusPublished - 12 Aug 2022
Event13th International Space Syntax Symposium - Western Norway University of Applied Sciences (HVL), Bergen, Norway
Duration: 20 Jun 202225 Jun 2022


Conference13th International Space Syntax Symposium
Abbreviated titleSpace Syntax Symposium
Internet address


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