Visiting European Cities from the WorldView Satellite
Seen from space, a city is way more than a collection of buildings: it is a tapestry of shapes, colours and geometries that reveal how the urban environment grows and changes. This is explained in the study “Built-up index and fractal dimension clustering of multispectral satellite urban images”, published on 13 August in the International Journal of Digital Earth, the result of a collaboration between Politecnico and Universidad Politécnica de Tulancingo in Mexico.
This work is part of an international joint PhD programme involving the two universities and featuring PhD students Armando Delgadillo-Jimenez and Aldo Aguilar-Vallejo, who are conducting research at both institutions under the supervision of Professor Anna Carbone, PhD supervisor at Politecnico, and Professor Carina Toxqui-Quitl, PhD supervisor at Universidad Politécnica de Tulancingo.
Using multispectral satellite images of 28 European cities, including Turin, the study analyses the urban environment using two indicators: built-up density and fractal dimension. The first measures the amount of a given area that is occupied by built structures; the second describes its geometric and spatial complexity, allowing more compact and homogeneous configurations to be distinguished from more fragmented and irregular ones.
Reality is complex, and this is confirmed by fractal geometry – whose name derives from the Latin fractus, meaning ‘broken’ or ‘fragmented’. Coastlines, mountains, the branches of trees and, likewise, the cities we inhabit cannot be described by Euclidean geometry, which represents space through whole dimensions and defined shapes. The urban fabric is, indeed, composed of structures that are distributed and interwoven throughout space in an articulated and fragmented pattern. Fractal geometry enables us to translate this complexity into a quantitative measure, thereby indicating how the built environment is organised in space.
To obtain this information, the researchers analysed multispectral images from various satellite systems, including WorldView-2 and Copernicus Sentinel-2, interpreting the acquired data to derive the two indicators. A key aspect of the methodological soundness of this approach is that built-up density and fractal dimension can be obtained from the same satellite image, without the need to integrate external GIS databases or census data.
By combining these two parameters, the study enables us to go beyond the question “How much of the territory is built up?” and to ask a second question: “How is the built environment organised in space?”. Two areas may, in fact, present a similar amount of built-up area whilst, at the same time, having very different structures: one more compact and uniform, the other more fragmented and complex. Analyzing 112 urban and suburban areas, the research has highlighted a significant relationship between density and morphological complexity: as the density of the built environment increases, so too does its spatial complexity. Urbanisation, therefore, does not merely entail an increase in the number of buildings within an area, but also progressively alters the geometry with which they occupy space.
This work is part of a wider research programme dedicated to the use of satellite imagery and quantitative tools to interpret the structure of cities. In parallel, the research team has developed an approach based on deep learning to estimate the fractal dimension directly from satellite imagery. This research has led to the development of RegFractNet, an artificial intelligence platform presented in the paper “Deep learning approach to fractal surfaces: application to satellite images of urban areas”, published in May in EPJ Data Science. The system uses an algorithm to analyse the images and obtain a quantitative value that describes the geometric complexity of the observed surface.
With this partnership, Politecnico reinforces its international commitment and its efforts to nurture young talent. The collaboration with the Universidad Politécnica de Tulancingo, expected to expand with new activities and initiatives, promotes the sharing of expertise and knowledge, the training and mobility of researchers and lecturers, and the development of joint research projects.
“Understanding a city’s morphology enables us to gain a better understanding of how the built environment develops and changes over time. The availability of statistical indicators on the density and complexity of the built environment is particularly relevant today, as this information can be useful in spatial planning and demographic studies, as well as for analysing energy-related issues, heat dissipation and urban ecology”, says Professor Anna Carbone.