**Author details**

*Infrastructure Management and Construction*

ent from that by lower buildings [25].

*<sup>ρ</sup>* <sup>=</sup> <sup>∑</sup>*i*=1

and *xj* belong to the same class.

tions is defined as

are spatial autocorrelation statistics [14, 21, 22] and nonparametric density estimation [23]. However, the potential of these SDM methods to explore urban height patterns using airborne lidar data has yet to be actively investigated. While a spatial autocorrelation statistic known as local Moran's I (LMI) is used to find the distribution pattern of building heights, the elevations of buildings were aggregated into large-sized cells using the mean elevation value of the included buildings [3, 22, 24]. Detection of the distribution pattern of clusters of relatively higher (CRH) buildings in a city with varying or heterogeneous heights is crucial for the spatial and temporal change analysis of vertical developments and for trend analysis of vertical urban compactness over time [15]. Detection of the CRH buildings in a city of heterogeneous heights is also essential for thermal urban modelling and urban heat island analyses because the level of heat produced by higher buildings is differ-

Geostatistics is a useful technique for spatial analysis. It refers to statistics used

*<sup>n</sup>* (*xi* <sup>−</sup> *<sup>x</sup>*¯) (*yi* <sup>−</sup> ¯*y*) \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

∑*i*=1 *<sup>n</sup>* (*yi* <sup>−</sup> ¯*y*)<sup>2</sup>

]

1/2 (6)

[∑*i*=1

series, say x, MI will estimate the correlation between *xi* and *xj*.

*<sup>n</sup>* (*xi* <sup>−</sup> *<sup>x</sup>*¯)<sup>2</sup>

where *x*´ and *y*´ are the mean values of x and y, respectively. For a univariate

For infrastructure monitoring, autocorrelation statistics can be applied to the variable describing the elevation of airborne lidar points in order to determine if *xi*

to analyse spatial data and spatiotemporal data sets. Shirowzhan and Lim [22] utilised a spatial analysis procedure using temporal point clouds in advanced GIS. In this analysis a novel method examined ground elevation extraction in slant areas and building classifications. A relevant technique for measuring compactness in three-dimensional environment is Moran's *I* (MI) and *G* indices. Moran's I and *G* are global autocorrelation statistics, which computes the correlation between pairs of data points [14]. Autocorrelation can be calculated for a variable that changes over time, for linear spatial series and for two-dimensional spatial series. MI is an extended version of Pearson's product-moment correlation coefficient for a single variable [14]. Pearson's correlation between two variables x and y from n observa-

**8**

Samad M.E. Sepasgozar1 \*, Sara Shirowzhan1 and Faham Tahmasebinia2

1 Faculty of Built Environment, The University of New South Wales, Sydney, NSW, Australia

2 School of Minerals and Energy Resources Engineering, The University of New South Wales, Sydney, NSW, Australia

\*Address all correspondence to: samad.sepasgozar@gmail.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
