Scrutinizing LiDAR Pulse Density and Spacing: Two specific questions

[Floris Groesz]

See this link:

http://rapidlasso.com/2014/03/20/density-and-spacing-of-lidar/

This has been a topic before in the forum, but I have two new questions:

1) 3D or 2D distances in spacing analysis?

All analysis seems to be done on 3D points so all distances reflect 3D distance. This will influence the results in a way that distances and spacing statistics reported will always larger than in a 2D situation (only looking at X and Y). Sloping areas and buildings especially will have an effect. Does anyone has an opinion about this? One could remove z-values from the dataset and run point spacing analysis. Alternatively one could pick out representative flat areas without any other objects for analysis. I am not sure how large these effects can be and maybe they are not so relevant, but I would be good to have a 100% correct solution.

2) Point spacing versus point density

The normal relationship between point spacing and point density is point spacing = 1/(point density)^0.5. A 1 point per m2 dataset has a point spacing of 1, a 4 points per m2 dataset has a spacing of 0.5 meter. At least this is the formula that I see everywhere. However, If you take a regular 1x1 grid as example the average spacing is larger than 1 ( I think). In two directions it is exactly 1 meter, but in all directions the average distance is larger. If you would Martins method than the average distance of all Delaunay triangle edges would be something like  1.14 (each triangle has 2 sides of 1m and 1 side of 2^0.5 m) The max distance in an area would always be 2^0.5= 1.41. If you take another example in which all distances between points are 1 meter, the area for each point would be a hexagon. http://gregegan.customer.netspace.net.au/APPLETS/12/A2cells.gif

The hexagon has an area of 0.866. This means the point density is 1.15 points per m2. Correct me if I am wrong. So at best, if all point-spacings are even a 1.15 points per m2 dataset has an average point distance of 1 meter. Until now I always used the simple formula and never really thought about it…

By the way, a typical way of describing point spacing when planning LiDAR data capture is to split it into 2 directions: along-track and across-track. However, I think that this way is not correct when documenting accomplished results.

 Floris

[Heidemann, Hans]

Lidar Spacing/Density has traditionally been expressed in the context of a grid/lattice, largely because it is familiar to and readily understood by users, and also because lidar developed primarily as a means to produce raster DEMs.  Yes, the metric is a 2D assessment.

Whether or not this is the "best" or most accurate means of expressing this spatial characteristics of the point cloud can be, and has been, debated ad nauseum.   Along/cross-track, Delauney, Voronoi ... these methods all produce arguably valid values as well.

At some point in time, the geospatial community at large will start regarding the lidar point cloud as a data type unto its own, with its own intrinsic value well in excess of that of the derivative DEM, and the fundamental metrics used to describe the point cloud will evolve to describe it appropriately. I wouldn't hold my breath for a "100% correct solution"; there's always somebody who knows better.

Karl

H. Karl Heidemann, GISP

Physical Scientist, Lidar Science

U.S. Geological Survey

Mundt Federal Building

47914 252nd Street

Sioux Falls, SD  57110

605-594-2861

kheid...@usgs.gov

"Nothing matters very much, and very few things ... matter at all."

- Arthur James Balfour

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