Perceptual hashing meets Hilbert curves: An innovative dimensionality reduction method for intercity morphological complexity comparison

Abstract

A high-frequency city, born in the era of smart sensors and geo-big data, epitomises a self-organised urban form that sustains vitality, balances functions, and resilience, while confronting urban science with unprecedented complexity and heterogeneity. Differences in scale, morphology, and function across cities accumulate, reinforcing this rapidly evolving data landscape and shaping a dynamic, complex high-frequency urban system. To address this challenge, this study innovatively develops a framework for structural simplification and dimensionality reduction that combines perceptual hashing with the Hilbert curve, emphasising methodological novelty in bridging computational efficiency and spatial semantics. Through key feature extraction, spatial order mapping, and dimensional-size transformation, the framework distils essential information and progressively projects complex high-dimensional data onto two- and one-dimensional spaces. At its core, the framework introduces two novel forms of representation – Urban QR codes and Urban barcodes – that enable compact presentation and efficient comparison of urban spatial features. Validation using comprehensive nighttime light imagery shows that the framework not only preserves the core characteristics of spatial patterns during dimensionality reduction but also achieves high consistency with existing clustering studies. Processed imagery further demonstrates potential as a structural supplement for multimodal data integration, while the framework itself opens new avenues for cross-scale comparison and multi-city analysis of high-dimensional, high-frequency urban data.