Journal of Geographical Systems

, Volume 18, Issue 3, pp 183–204 | Cite as

Spatial indices for measuring three-dimensional patterns in a voxel-based space

Original Article


Spatial indices are used to quantitatively describe the spatial arrangements of the features within a study region. However, most of the indices used are two-dimensional in their representation of the surface characteristics, and this is insufficient to quantify the three-dimensional properties of an area or geospatial features. With the increased availability of 3D data from laser scanning and other collection methods, a voxel-based representation of space is an important methodology that allows for an intuitive visualization of geospatial features and their analysis with 3D GIS techniques. The objective of this study is to conceptualize, develop, and implement indices that can characterize three-dimensional space and can be used to analyze the structure of spatial features in a landscape. The indices for three-dimensional space that are implemented are, namely, surface area volume, fractal dimension, lacunarity, and Moran’s I which are all useful in the quantification of spatial organization found in ecological landscapes. In addition to providing the quantitative descriptors, the results indicate that a voxel-based representation provides a straightforward means of characterizing the form and composition of the spatial features using 3D indices.


Spatial indices Voxel-based space 3D Spatial pattern in 3D Geographic surface structure GIS 

JEL Classification

C6 C63 C39 Q5 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Spatial Analysis and Modelling Research Laboratory, Department of GeographySimon Fraser UniversityBurnabyCanada

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