las2dem interpolation method?

[Martin Isenburg]

Hello Marek.

yes, las2dem uses standard linear interpolation within each of the
Delaunay TIN triangles that the corresponding sampled x and y raster
position falls into.

Regards,

Martin @rapidlasso

On Nov 28, 12:42 am, Marek <marekj...@gmail.com> wrote:
> Hi Martin,
>
> I know las2dem uses a TIN to "rasterize" the image surface. My question is:
> is the rasterization process simply a nearest neighbor (i.e. DEM_xy =
> TIN_linearly_interpolated_value(x,y)) or is there any other type of
> interpolation going on (e.g. IDW or bilinear interpolation)? I'm assuming
> it's the former but I wanted to double check with you.
>
> thanks,
>
> m

[Henri Riihimäki]

Follow up question to this, what if the output resolution contains multiple xy positions (and triangles)?

I was thinking how exactly does las2dem handle coarser scale output resolution, say 25 meters, where there might be large variation even within pixel (cliffs etc.).

Br.,
Henri

[Martin Isenburg]

Hello,

Follow up question to this, what if the output resolution contains multiple xy positions (and triangles)?

I was thinking how exactly does las2dem handle coarser scale output resolution, say 25 meters, where there might be large variation even within pixel (cliffs etc.).

When you have LiDAR with a pulse spacing of, for example, 0.5 meter and what to construct a DSM or DTM with a magnitude coarser resolution of, for example, 25 meter then simply applying las2dem is both inefficient and incorrect.

It is inefficient because you will construct a gigantic TIN (gigantic in comparison to the output) and then sample its elevation at only very few triangles. Quick math for an arid terrain without vegetation. A pulse density of 0.5 pulses gives you 4 returns per square meter. That is 2500 returns per 25 meter by 25 meter pixel. Those turn into 5000 triangles during a Delaunay TIN construction. And only one of those 5000 triangles will be used (the one that covers the exact center of the pixel) to then probe the elevation for this 25 meter by 25 meter pixel. Very inefficient.

But it also incorrect. Imagine some high frequency featured landscape that has has tiny ups and downs with a size of just a meter or so. Then what elevation is sampled at every 25 by 25 area may not at all be representative of the elevation of the 25 meter cell. I think that is what you mean with the sentence "there might be large variation even within pixel (cliffs etc.)".

It has to do with sampling theory (remember the Nyquist Theorem?). You need to remove the frequencies (steep 1 meter rock formations or holes) that are too fine of a detail to be represented by your coarse (25 meter) resolution. You can do this either in raster or in point space.

In raster space, simply raster the DSM at the resolution of the LiDAR,with las2dem (e.g. at a step size of 0.5 meters) and then read up on how to properly do the down-sampling step directly in raster space.

http://rapidlasso.com/lasthin

http://lastools.org/download/lasthin_README.txt

In point space, you should thin the data first in a manner that removes the high  frequency details that the target resolution cannot represent. For a DTM created with LAStools this could (and maybe some sampling theorists can chime in here) this could be realized by thinning to the median:

lasthin -i 50cm_res.laz ^

           -keep_class 2 ^

           -percentile 50 ^

           -step 25 ^

           -o 25m_res.laz

but this does not consider a nice x/y distribution of the points. Maybe a two stage approach is better where we first create remove the frequency with a median filter on a slightly finer grid and then keep the most central of the surviving samples on a 25 meter grid.

lasthin -i 50cm_res.laz ^

           -keep_class 2 ^

           -percentile 50 ^

           -step 10 ^

           -o temp.laz

lasthin -i temp.laz ^

           -central ^

           -step 25 ^

           -o 25m_res.laz

Regards.

Martin @rapidlasso

[Henri Riihimäki]

Thank you Martin,

This was exactly why I was asking. I was thinking whether the las2dem (/blast2dem) has some sort of in-built functionality to account these issues, but it is good to know that the data must be pre-processed.

Best,
Henri