Insights into geographical window based SSIM for comparison of OD matrices

The rich structural information of travel patterns in terms of number of trips distributed to different destinations within a region is an essential element that cannot be ignored during any statistical assessments such as comparison of Origin-Destination (OD) matrices. While most of the traditional indicators fail to compare the structural differences between OD matrices, Structural Similarity (SSIM) index outperforms them by comparing the structure, mean and standard deviations within one single formulation. In the existing literature with respect to OD matrices comparison, the application of SSIM is still theoretical in nature and there is no clarity on the level of acceptability of SSIM values due to its sensitivity towards the local window size. Thus SSIM in the context of OD matrices has to be further refined especially by emphasising on the size and physical significance of local window and local SSIM values, so that it can be applied best in practice. In this light, the paper proposes a practical approach for computing SSIM based on geographical windows that has a physical significance in terms of size and shape of windows, geographical correlation and its potential to analyse local travel patterns due to different travel distributions in different sections of the network. Also, using real Bluetooth zonal OD matrices from Brisbane network, the study also demonstrates the potential of SSIM over traditional indicators.