Quantitative indices based on 3D discrete wavelet transform for urban complexity estimation using remotely sensed imagery

Urbanization in most developing countries is gradually increasing. Quantitative estimation of urbanization to a standardized level is crucial for analysing the relation between urbanization and other factors, since urban growth affects diverse and complex natural and socio-economic phenomena. Spatially and spectrally, remotely sensed imageries covering urban areas display different characteristics from those of rural or mountainous areas. A three-dimensional discrete wavelet transform (3D DWT) scheme is regarded as useful for analysing both spatial and spectral information. In addition, the energy parameter of wavelet coefficient by 3D DWT indicates channels regarding dominant spatial and spectral frequency, extracted from the original image sets. Based on these spatial and spectral features and the energy parameter of 3D wavelet coefficients, three kinds of urban complexity index are proposed. Of the three indices, the third index is the most useful to quantitatively interpret urban complexity. These indices can be used for a basis to analyse the relationship between feature groups within urban environments.