Density and Spacing of LiDAR

Recently I worked with LiDAR from an Optech Gemini scanner in the Philippines and with LiDAR from a RIEGL Q680i scanner in Thailand. The two devices scan the terrain below with a very different pattern: the Optech uses an oscillating mirror producing zig-zag scan lines, whereas the RIEGL uses a rotating polygon producing parallel scan lines. In the following we investigate the point distribution in a small piece cut from each flightline.

First we compute an estimate for the average point density and the average point spacing with lasinfo:

D:\lastools\bin>lasinfo -i optech.laz ^
                        -nh -nv -nmm -cd
number of last returns: 2330671
covered area in square units/kilounits: 1280956/1.28
point density: all returns 2.25 last only 1.82 (per unit^2)
      spacing: all returns 0.67 last only 0.74 (in units)

The option ‘-nh’ asks lasinfo not to print the header (aka ‘no header’), the option ‘-nv’ means not to print the variable length records (aka ‘no vlr’), the option ‘-nmm’ supresses the output of minimum and maximum point values (aka ‘no min max’), and the option ‘-cd’ requests that an average point density is computed (aka ‘compute density’) from which the average point spacing is derived.

D:\lastools\bin>lasinfo -i riegl.laz ^
                        -nh -nv -nmm -cd
number of last returns: 3707217
covered area in square units/kilounits: 889816/0.89
point density: all returns 4.58 last only 4.17 (per unit^2)
      spacing: all returns 0.47 last only 0.49 (in units)

What we really want to know are pulse density and pulse spacing which we get by only counting one return from every pulse. Commonly one uses the last return, which is reported as ‘last only’ values by lasinfo. According to lasinfo the Optech and the RIEGL scan have an average pulse density of 1.82 and 4.17 [pulses per square meter] and an average pulse spacing of 0.74 and 0.49 [meters] respectively.

Single number averages do not capture anything about the actual distribution of the last returns in the swath of the scan. Let us compute density rasters with lasgrid. Because the density of the two scans is different we use 3 by 3 meter cells for the Optech, which should average 3 * 3 * 1.82 = 16.38 points per cell, and 2 by 2 meter cells for the RIEGL, which should average 2 * 2 * 4.17 = 16.68 points per cell.

lasgrid -i optech.laz -last_only ^
        -density -step 3 ^
        -odix _density3x3 -obil
lasview -i optech_density3x3.bil

lasgrid -i riegl.laz -last_only ^
        -density -step 2 ^
        -odix _density2x2 -obil
lasview -i riegl_density2x2.bil

A visual comparison of the two resulting density rasters in BIL format with lasview shows first differences in pulse distribution for the two scanners.

Using 'lasview' to inspect a BIL density raster: Elevation and colors show number of points per 3 by 3 meter cell for Optech (top) and per 2 by 2 meter cell for RIEGL (bottom).

Using ‘lasview’ to inspect a BIL density raster: Elevations and colors illustrate the number of last returns per 3 by 3 meter cell for Optech (top) and per 2 by 2 meter cell for RIEGL (bottom). The images use differently scaled color ramps.

It is noticable that the number of last returns per cell increases at the edges of the swath for the Optech whereas it decreases for the RIEGL. For the Optech it is higher due to the slowing down of the oscillating mirror and the reversing of scan direction when reaching either side of the scanline. This decreases the distances between pulses at the edges of the zig-zag scan and increases the number of last returns falling into cells there. For the rotating polygon scan of the RIEGL these pulse distances are more uniform. Here the numbers are lower because many cells along the edges of the swath are only partly covered by the scan and therefore receive fewer last returns.

lasgrid -i optech.laz -last_only ^
        -density -step 3 ^
        -false -set_min_max 0 20 ^
        -odix _density3x3 -opng

lasgrid -i riegl.laz -last_only ^
        -density -step 2 ^
        -false -set_min_max 0 20 ^
        -odix _density2x2 -opng

Here another visualization of the pulse distribution by letting lasgrid false-color density rasters to a fixed range of 0 to 20. This range is based on the near identical expected values of around 16.38 and 16.68 last returns per cell based on the average densities that lasinfo reported and the cell sized used here.

A more quantitative check of how well distributed the pulse are is to generate histograms. You can use lasinfo with the ‘-histo z 1’ option to print a histogram of the z values of the BIL rasters and import these statistics into your favorite software to create a chart.

lasinfo -i optech_density3x3.bil ^
        -nh -nv -nmm -histo z 1
lasinfo -i riegl_density2x2.bil ^
        -nh -nv -nmm -histo z 1

Both distributions have their peaks at the expected 16 to 17 last returns per cell although the Optech distribution has a significantly wider spead. The odd two-peak distribution of the Optech scan seems puzzling at first but looking at the density image shows that this is an aliasing artifact of putting a fixed 3 by 3 meter grid over zig-zagging scanlines.

The next experiments uses the new ‘-edge_shortest’ and ‘-edge_longest’ options available in las2dem that compute for each point the length of its shortest or longest edge in a Delaunay triangulation and then rasters these lengths. Below you see the command lines to do this and generate histograms of the rastered edge lengths.

las2dem -i optech.laz -last_only ^
        -step 1.5 ^
        -edge_longest ^
        -odix _edge_longest -obil
lasinfo -i optech_edge_longest.bil ^
        -nh -nv -nmm -histo z 0.1 ^
        -o optech_edge_shortest_0_10.txt
las2dem -i optech.laz -last_only ^
        -step 1.5 ^
        -edge_shortest ^
        -odix _edge_shortest -obil
lasinfo -i optech_edge_shortest.bil ^
        -nh -nv -nmm -histo z 0.05 ^
        -o optech_edge_shortest_0_05.txt
las2dem -i riegl.laz -last_only ^
        -edge_longest ^
        -odix _edge_longest -obil
lasinfo -i riegl_edge_longest.bil ^
        -nh -nv -nmm -histo z 0.05 ^
        -o riegl_edge_longest_0_05.txt
las2dem -i riegl.laz -last_only ^
        -edge_shortest ^
        -odix _edge_shortest -obil
lasinfo -i riegl_edge_shortest.bil ^
        -nh -nv -nmm -histo z 0.05 ^
        -o riegl_edge_shortest_0_05.txt

These resulting histograms do look quite different.

The more important histograms are those of longest edge lengths. They illustrate the observed spacing between pulses showing us the maximal distance of each pulse from its surrounding pulses. A perfect pulse distribution that samples the ground evenly in all directions would have one narrow peak. The Optech scan is far from this ideal with a wide and flat peak that tells us that pulses are spaced apart anywhere from 1.2 to 2.2 meters. Visualizing the scan pattern shows that the 2.2 meter spacings happen at the tips of zig-zag and the 1.2 meter spacings at nadir. The RIEGL scan has much narrower peak with most pulses spaced apart at most 60 to 80 centimeters.

The histograms of shortest edge lengths illustrate how close pulses are spaced. Again, it helps to visualize the zig-zag scan pattern to explain the odd distribution of shortest edge lengths in the Optech scan: as we get closer to the edges of the flightline the pulse spacing along the scanline becomes increasingly dense. This is represented on the left side in the histogram that is slowly leveling off to zero. Again, the RIEGL scan has a narrower peak with most pulses spaced no closer than 35 to 55 centimeters.

To confirm our findings we illustrate where the scanners produce longest or shortest edges using ranges that we find in the histograms above and create false-colored rasters:

las2dem -i optech.laz -last_only ^
        -step 1.5 -edge_longest ^
        -false -set_min_max 1 2.5 ^
        -odix _edge_longest -opng
las2dem -i optech.laz -last_only ^
        -step 1.5 -edge_shortest ^
        -false -set_min_max 0 0.7 ^
        -odix _edge_shortest -opng
las2dem -i riegl.laz -last_only ^
        -edge_longest ^
        -false -set_min_max 0.5 1.0 ^
        -odix _edge_longest -opng
las2dem -i riegl.laz -last_only ^
        -edge_shortest ^
        -false -set_min_max 0.1 0.7 ^
        -odix _edge_shortest -opng

The color-codings clearly illustrate that the Optech has a much wider pulse spacing on both edges of the flightline but also a much narrower pulse spacing. That reads contradictory but one are the “within-zig-zag” spacings and the other are the “between-zig-zag” spacings. The RIEGL has an overall much more even distribution in pulse spacings.

As a final confirmation to what causes the pulse spacings to be both widest and narrowest at the edges of the flightline for the Optech scan we scrutinizing the distribution of last returns and their triangulation visually.

Now it should be clear. At the edge of the flightline the Optech scanner has increasingly close-spaced pulses within each zig-zagging scan line but also increasingly distant-spaced pulses between subsequent pairs of zig-zagging scanlines. At the very edge of the flightline the scanner is almost sampling a “linear area” twice but leaves unsampled gaps that are twice as wide as in the center of the flightline. I believe this is one of the reasons why people “cut off” the edges of the flightlines based on the scan angle when using oscillating mirror systems. Now let’s took at the RIEGL.

There is no obvious difference in pulse distribution at the edges and the center of the flightline. The entire width of the swath seems more or less evenly sampled.

The above results show that “average point density” and “average point spacing” do not capture the whole picture. A quality check that properly verifies that a scan has the desired point / pulse density and spacing should measure the actual spacings – especially when operating a scanner with oscillating mirrors. We have done it here by computing for each last return its longest surrounding edge in the Delaunay triangulation, rasterizing these edge length, and then generating a histogram of the raster values.

 

Good follow-up reads are Dr. Ullrich’s “Impact of point distribution on information content of point clouds of airborne LiDAR” presented at ELMF 2013 and “Assessing the Information Content of LiDAR Point Clouds” from PhoWo 2013.