*4.2.1 Ratio of volume change (RVC)*

*Sustainability in Urban Planning and Design*

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**Table 1.**

**Figure 4.**

*collected in 2013.*

Density (points/m2

**2005 UNSW 2008 UNSW 2013 UNSW**

**Optech ALTM 3100, Optech ALTM 3025**

**Leica ALS50-II**

**Optech ALTM 1225**

*Detailed information of airborne lidar data sets used in this study.*

Vertical accuracy (m) 0.10 0.15 0.3 Horizontal accuracy (m) 0.5 0.5 0.8

*Time series airborne lidar data over the selected area of Sydney, Australia and demonstrated areas of changes in yellow and red rectangles: (a) lidar data collected in 2005; (b) lidar data collected in 2008 and (c) lidar data* 

) 1 1.3 1.57

For comparison of the changes of new and demolished buildings, a volumetric descriptor of ratio of volume change (*RVC*) is proposed in (1):

of new and demolished building, a volumetric \(g \(R\_{VC}\) is proposed in \(1\):

$$R\_{VC} = \frac{\sum\_{i=1}^{k} n\_{\times} h\_{in}}{\sum\_{i=1}^{l} d\_{\times} h\_{id}} \tag{1}$$

where *n* demonstrates the area of a pixel on detected new buildings and *hin* demonstrates the height of that pixel above ground, *d* represents the area of a pixel in demolished buildings and *hid* is its corresponding height value. This ratio can be calculated using the results of image differencing.

One of the limitations of DSM differencing method is the selection of the appropriate thresholds for the unchanged class. Lu et al. [27] proposed thresholds to be [*m* − ,*m* + ] in the histogram of the resultant difference image (i.e. *DSMd*), where *m* is the mean of the distribution and σ represents the standard deviation. Shirowzhan [28] tested different values between 2 and 4 for the thresholds of γ in this study area and found that = 3 is an appropriate value.

The next step for this 3D metric is a careful visual inspection to determine whether the areas of change belong to buildings because the result of image differencing includes both buildings and vegetation changes. If this ratio is more than 1, it means that the volume of new buildings is greater than the volume of demolished buildings. However, this metric cannot show whether the development is of vertical form. Therefore, complementary descriptors are necessary to recognize whether the urban form change is vertical growth. For example, if this ratio is greater than 1 and the new buildings are higher than the demolished ones, it can be concluded that an infill vertical development is occurring in a study area.

#### *4.2.2 Mass and space index*

Other volumetric descriptors for spatial and temporal 3D urban growth can be proposed which use improved concepts of 3D mass and space in urban planning. Examples of a 3D mass index and a 3D space index are defined in (2) and (3) as the ratio of the volume of buildings (or vacant space if applicable) to the total volume of an assumed cube, whose footprint is the ground surface area including all buildings, and its height equals the tallest building height in the study extent. For a study extent, after calculation of the volume of new and demolished buildings, an increase in the 3D mass index will represent a trend toward more compact 3D urban form. The assumption for the cube is that it only contains buildings. \_

$$\text{GDP MassInddex} = \frac{\text{Vb}}{\text{Vc}} = \frac{\sum\_{i=1}^{n} b\_{\text{X}} \cdot h\_{b}}{\text{Vc}} \tag{2}$$

$$\text{GSD\\_Space\\_Index} = \frac{V\mathfrak{s}}{V\mathfrak{c}} = \frac{V\mathfrak{c} - \sum\_{i=1}^{n} b\_i \times h\_b}{V\mathfrak{c}} \tag{3}$$

where *Vb* is the volume of buildings, *Vc* is the volume of the containing cube and *Vs* represents the volume of vacant space. In a pixel-based method, *b* is the area of a pixel representing built form and *hb* is the corresponding height of the pixel.

## **5. Results**

Temporal point clouds of the selected case study were analyzed based on the developed procedure (refer to **Figure 3**). The purpose of the analysis was vegetation and building classification, ground classification and creating a DSM. Each of these objectives is presented in the following sections:
