K-means Enhanced Density Gradient Analysis for Urban and Transport Metrics Using Multi-Modal Satellite Imagery

TL;DR

The paper tackles the challenge of rapidly assessing urban transport potential from satellite data. It proposes a multi-modal, density-gradient analysis framework that fuses optical and SAR imagery to segment urban areas, identify centers, and extract two key metrics, the density-gradient coefficient $α$ and the minimum effective distance $LD$, from density-distance profiles. A K-means-based region segmentation is applied to residuals to distinguish uniform from high-variability regions, enabling morphology-informed transport planning. The approach is demonstrated on two contrasting Polish cities, revealing how monocentric versus polycentric forms influence transport strategies, and is positioned as a cost-effective, globally applicable tool with an open-source MIT-licensed implementation.

Abstract

This paper presents a novel computational approach for evaluating urban metrics through density gradient analysis using multi-modal satellite imagery, with applications including public transport and other urban systems. By combining optical and Synthetic Aperture Radar (SAR) data, we develop a method to segment urban areas, identify urban centers, and quantify density gradients. Our approach calculates two key metrics: the density gradient coefficient ($α$) and the minimum effective distance (LD) at which density reaches a target threshold. We further employ machine learning techniques, specifically K-means clustering, to objectively identify uniform and high-variability regions within density gradient plots. We demonstrate that these metrics provide an effective screening tool for public transport analyses by revealing the underlying urban structure. Through comparative analysis of two representative cities with contrasting urban morphologies (monocentric vs polycentric), we establish relationships between density gradient characteristics and public transport network topologies. Cities with clear density peaks in their gradient plots indicate distinct urban centers requiring different transport strategies than those with more uniform density distributions. This methodology offers urban planners a cost-effective, globally applicable approach to preliminary public transport assessment using freely available satellite data. The complete implementation, with additional examples and documentation, is available in an open-source repository under the MIT license at https://github.com/nexri/Satellite-Imagery-Urban-Analysis.

Figures (6)

• Figure 1: Urban Density Gradient Analysis Methodology Pipeline. Flow diagram showing the processing sequence from Sentinel-1/2 imagery through multi-modal fusion, segmentation, and parallel analysis of urban centers and density gradients, yielding classification metrics $\alpha$ and LD for characterizing urban morphology.
• Figure 2: Input satellite data: (a) Malbork optical RGB image (left) and (b) Kłodzko optical RGB image (right) in the top row; (c) Malbork SAR backscatter intensity image (left) and (d) Kłodzko SAR backscatter intensity image (right) in the bottom row.
• Figure 3: Edge detection and fusion results: (a) Malbork edge detection result (left) and (b) Kłodzko edge detection result (right) in the top row; (c) Malbork combined optical-SAR urban density map (left) and (d) Kłodzko combined optical-SAR urban density map (right) in the bottom row.
• Figure 4: Histogram analysis and segmentation: (a) Malbork histogram decomposition (left) and (b) Kłodzko histogram decomposition (right) in the top row; (c) Malbork segmented urban area with identified urban centers (left) and (d) Kłodzko segmented urban area with identified urban centers (right) in the bottom row.
• Figure 5: Urban density gradient analysis: (a) Malbork density gradient plot (left) and (b) Kłodzko density gradient plot (right). Each figure consists of two connected plots: the upper portion shows gradient density and fitting (yielding $\alpha$ values), while the lower portion shows deviations from the fitted line, highlighting areas of varying uniformity.