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

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.