Point Density And Spacing

[Amir Haniff]

I'm currently having trouble understanding point density and spacing and how they relate to image resolution.

For my current project I have a point density of "all returns 2.86 last only 1.91 (/ m^2)" and a point spacing of "all returns 0.59 last only 0.72 (meters)

[Tobias K Kohoutek]

Spacing = (1/Density)^0,5

I'm quite sure it's actuall written in one of Martin's ReadMe.files

Cheers

[Martin Isenburg]

Hello,

it seems you have an *average* LiDAR densities of around 2 *pulses* per square meter in your project. By counting only the last return from each laser pulse fired we are essentially counting each pulse that was fired only once (in contrast to the all return density that is more of a measure of "how much fluffy stuff / vegetation / structures / wires / building edges / etc" is there on the terrain. In your case each pulse generated an average of 2.86 / 1.91 = 1.5 returns. An empty soccer field generates an average of 1 return per pulse. A tropical forest or a power station may generate up to average of 5 returns per pulse.

The image resolution for generating a DTM does not have to be much finer than the pulse spacing (i.e. the last return spacing) as the best you can hope for is that each pulse hit the ground and that therefore the ground was sampled with returns that are 0.72 meters apart. So an DTM resolution of 0.5 meters would probably capture all the elevation information that the laser pulses could have possibly captured. However, if your penetration rate is much much lower (e.g. the ground return density / spacing) then you could probably be okay with a 1 meter DTM.

However, some scanning systems / flight patterns / ... produce highly non-uniform pulse distributions on the ground so that the "average spacing" may be misleading. Have a look at this blog post:

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

To more exactly compute the spacing between your last return LiDAR samples run this:

E:\LAStools\bin>las2tin -i ..\data\fusa.laz ^

                                      -last_only ^

                                      -histo_only edge_length 0.1

edge length histogram histogram with bin size 0.1

  bin [0,0.1) has 663

  bin [0.1,0.2) has 3634

  bin [0.2,0.3) has 10288

  bin [0.3,0.4) has 247678

  bin [0.4,0.5) has 46179

  bin [0.5,0.6) has 108588

  bin [0.6,0.7) has 106505

  bin [0.7,0.8) has 122776

  bin [0.8,0.9) has 94903

  bin [0.9,1) has 31486

  bin [1,1.1) has 5721

  bin [1.1,1.2) has 2441

  bin [1.2,1.3) has 2755

  bin [1.3,1.4) has 2176

  bin [1.4,1.5) has 807

  bin [1.5,1.6) has 409

  bin [1.6,1.7) has 361

  bin [1.7,1.8) has 1175

  bin [1.8,1.9) has 239

[...]

The same is true for a DSM although off-nadir scan angles may in theory produce a sampling of the uppermost surface of vegetation / objects that is effectively higher than than of the bare terrain by hitting more than one "top surface object" (e.g. first glance the crown of a high tree and than that of a lower tree at a 20 degree angle in a manner such that both hits are not obscured when viewer from above. Computing the edge-length histogram of a spike-free *TIN* would probably a good way to capture the horizontal resolution for a DSM in a manner that accounts for that.

https://rapidlasso.com/2016/02/03/generating-spike-free-digital-surface-models-from-lidar/

Regards,

Martin @rapidlasso

On Tue, Oct 17, 2017 at 10:43 PM, Amir Haniff <amirhan...@gmail.com> wrote:

I'm currently having trouble understanding point density and spacing and how they relate to image resolution.

For my current project I have a point density of "all returns 2.86 last only 1.91 (/ m^2)" and a point spacing of "all returns 0.59 last only 0.72 (meters)

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