Between 2D and 3D: Studying Structural Complexity of Urban Fabric Using Voxels and LiDAR-Derived DSMs

Abstract

Cities are complex systems and their physical forms are the manifestation of cultural, social and economic processes shaped by the geometry of natural and man-made elements. Digital Surface Models (DSM) using LiDAR provide an efficient volumetric transformation of urban fabric including all built and natural elements which allows the study of urban complexity through the lens of fractal dimension (D). Founded on the “box-counting” method, we reveal a voxelization technique developed in GIS (Geographic Information System) to estimate D values of ten DSM samples across central Melbourne. Estimated D values of surface models (between 2 and 3) provide a measure to interpret the structural complexity of different urban characters defined by the pattern of developments and densities. The correlations between D values with other DSM properties such as elevation, volume, solar radiation and surface roughness, showed a strong relationship between DSM volume and mean elevation. Lower strength correlations were recorded with solar radiation and surface roughness. The proposed method provides opportunities for fractal research to study pressing issues in complex urban environments such as declining physical fitness, mental health and urban biodiversity.

Fractal Features in Terrain Restoration of Jiuzhai Valley, a World Natural Heritage Site in China

“…The present study focused only on the fractal analysis of two-dimensional planes. In future research, a combination of 2D and 3D fractal analysis could describe natural and non-natural environments by using LiDAR-derived DSM or Arc GIS for fractal analysis [45,73]. In summary, fractal theory quantifies the degree of space occupation in its unique geometric form, which may then be combined with various methods and widely applied in landscape design.…”

“…Fractal dimension characteristics can also be seen in artificial landscapes, such as terraces [29,30], artificial land use [31], building environments [32][33][34], traffic networks [35,36] and others. The practice of fractal geometry in landscape restoration of quarries, open-pit mines, and other damaged environments [37,38], as well as river shoreline restoration [39], urban skyline construction [40,41], urban spatial organization structure [42][43][44][45][46][47], and landscape restoration [11], has confirmed that the balance, congruence, and symmetry of fractal images enhance pleasure in perception and cognition. Therefore, any change in fractal dimensions may affect people's visual judgment and preference for a landscape [48][49][50].…”

Urban Texture Identification and Characteristic Analysis Based on Percolation Theory—A Case Study of the Second Ring Road Area in Wuhan City

“…Its physical form is a manifestation of cultural, social, and economic processes shaped by the geometry of the natural and man-made world [12]. The urban environment encompasses various elements, such as buildings, roads, plants, signage, lighting, and many other elements, all of which combine Land 2024, 13, 717 2 of 22 to shape the urban fabric or physical form of urbanized areas [13]. Under the influence of planning and management processes, cities were traditionally perceived as being organized in a top-down manner within the perspective of systems theory [14].…”

Measurement of 2D and 3D Fractal Features of Urban Morphology from an Architectural View and Its Influencing Factors

“…The box-counting method measures the spatial filling degree of fractal objects, in other words, it reveals how the space is occupied by complex patterns [13,14]. The conventional box-counting method is commonly employed in a 2D plane to describe the urban spatial structure and texture; further, a 3D voxel-counting method is developed to measure the building morphology embedded into a 3-dimensional space [15].…”