Calculate volume of a building using LiDAR data

Question

I would like to use 3D spatial metrics that introduced in the paper titled "Lidar and VHRS data for assessing living quality in cities - An approach based on 3D spatial indices". I have a lidar dataset including 14 las files and I have a shapefile including 416 buildings. I wanted to calculate cubic volume of each building using LiDAR data. As I understand,I need to clip las catalog for each object in the shapefile and then run voxels on every clipped las file. I tried to do that but I could not understand how to get the volume calculation for each building. Is there any way to write volume value into the shapefile?

Answer 1

Assuming that your shapefile contains polygons you could loop through each polygon and extract the points within the polygons.

For each point cloud, it is expected to contain only one building if your shapefile is well build. Also you have the area of the building with the polygon.

Thus, you can analyses each point cloud to find the elevation of your building. If we assume that the buildings are cuboid the highest point can do the job. Here what it could look like:

ctg = readLAScatalog(...)
buildings = shapefile(...)
buildings$Volume = 0

for (i in 1:length(buildings) {
  building = buildings[i,] # Get the polygon i
  las = clip_roi(ctg, building)
  hmax = max(las$Z) # Assuming a normalized dataset
  A = rgeos::gArea(building)
  V = A*hmax
  building$Volume[i] = V
}

shapefile(buildings, "/where/to/write/building.shp")

If building are not cuboid and you want something more accurate try to get only the surface points and average their heights

las = clip_roi(ctg, building)
las = filter_surfacepoints(las, 2)
hmean = mean(las$Z) # Assuming a normalized dataset
A = rgeos::gArea(building)
V = A*hmean

If you want something yet more accurate you have enough material to tweak these examples.