This article outlines a novel method for comparing the spatial shapes of urban units, termed “spatial signatures.” This approach allows for a granular and nuanced understanding of urban morphology by classifying areas based on both their physical form and functional characteristics. The method relies on a three-step process: defining a suitable spatial unit, characterizing each unit based on form and function, and employing cluster analysis to group similar units into distinct spatial signatures.
Defining the Spatial Unit: Enclosed Tessellation Cells (ETCs)
The foundation of this comparative method lies in the selection of an appropriate spatial unit. Traditional units like administrative boundaries or arbitrary grids fail to capture the inherent complexity of urban form. This method utilizes Enclosed Tessellation Cells (ETCs), offering a more granular and morphologically sensitive unit of analysis.
ETCs are generated by partitioning space using physical barriers like streets, railways, and rivers, creating enclosed areas. These enclosures are further subdivided by building footprints, acting as anchors for a morphological tessellation algorithm, akin to Voronoi tessellation. The resulting ETCs are:
- Indivisible: Containing at most one building, preventing further meaningful subdivision.
- Internally Consistent: Reflecting a single signature type due to their granularity.
- Geographically Exhaustive: Covering the entire study area without gaps.
Fig. 1: ETC Delineation Process. From enclosing components (A) to enclosures (B), incorporating buildings (C) to final ETCs (D).
Characterizing Urban Form and Function
Each ETC is characterized based on two core components:
Form: Urban Morphometrics
Form is quantified using urban morphometrics, involving the numerical description of buildings, streets, ETCs, and enclosures. Six categories of characteristics are analyzed:
- Dimensions
- Shapes
- Spatial Distribution
- Intensity
- Connectivity
- Diversity
This results in 59 individual morphometric characters. To account for spatial heterogeneity, each character is represented by three summary variables (quartiles) reflecting the weighted distribution of values within a defined spatial context surrounding each ETC. This contextualization allows for the identification of contiguous clusters even in diverse urban areas.
Fig. 2: Spatial Context Definition for ETC Characterization. A neighborhood of 10 topological steps is used, weighted by inverse distance between poles of inaccessibility.
Function: Open Data and Transfer Methods
Functional characterization leverages available open data related to land cover, population, points of interest, and accessibility. Various transfer methods are employed to link data from different sources (grids, administrative boundaries) to ETCs:
- Areal Interpolation
- Building-Based Dasymetric Areal Interpolation
- Network-Constrained Accessibility
- Euclidean Accessibility
- Zonal Statistics
As with form, contextual versions of functional characters are generated to reflect spatial patterns.
Cluster Analysis: Identifying Spatial Signatures
The final step involves using K-Means cluster analysis to group ETCs with similar form and function characteristics into distinct spatial signatures. The contextual summaries of form and function variables are standardized and used as input for the clustering algorithm.
The optimal number of clusters is determined using the clustergram method and validated with internal validation measures. Initial clustering results in 10 broad categories, further subdivided to provide a more detailed classification of urban areas. Contiguous ETCs belonging to the same cluster are combined to form spatial signature geometries.
Fig. 3: Clustergram and Goodness of Fit Metrics. The analysis suggests 10 clusters as the optimal solution.
This method provides a robust framework for comparing the spatial shapes of urban units, enabling a deeper understanding of urban structure and its evolution. The resulting spatial signatures offer a valuable tool for urban planning, analysis, and research.
