This document discusses various methods for measuring airborne LiDAR point density and recommends an ideal methodology. It analyzes common density measurement approaches like using representative sample areas, analyzing densities per swath, and using grid/tile-based binary rasters. It finds that Voronoi polygon-based density calculations provide the most accurate representation while avoiding issues like aliasing. The recommended approach uses Voronoi polygons to calculate densities, rasterizes the results, and summarizes passing/failing percentages in tiles to both quantify and locate any density failures. Sample outputs applying this methodology to test data are provided.
3. Type equation here.
1 meter
1 meter
4 points per
square meter
(PPSM)
=
𝐍𝐏𝐒 =
𝟏
𝑫𝒆𝒏𝒔𝒊𝒕𝒚
𝑫𝒆𝒏𝒔𝒊𝒕𝒚 =
𝟏
𝑵𝑷𝑺𝟐
0.5 meter
ground sample
distance (GSD)
or nominal point
spacing (NPS)
𝑫𝒆𝒏𝒔𝒊𝒕𝒚 =
𝐟𝐢𝐫𝐬𝐭 𝐨𝐫 𝐥𝐚𝐬𝐭 𝐫𝐞𝐭𝐮𝐫𝐧 𝐩𝐨𝐢𝐧𝐭 𝐜𝐨𝐮𝐧𝐭
𝒂𝒓𝒆𝒂
LiDAR Density Basics
4. 1 meter
1 meter
9, 4, 1 PPSM
or other?
=
4 points per
square meter
(PPSM)
0.5 meter
ground sample
distance (GSD)
or nominal point
spacing (NPS)
LiDAR Density Basics
7. Airborne LiDAR Density Measurement Methodologies
• Representative
sample areas
Pros
• Fast and easy to calculate
• Good for specific areas of
interests
Cons
• Biased by many factors such as
sidelap, cross lines, patches,
location in scan, etc.
• Very localized - not
representative of average swath
density or overall project density
• Cannot effectively or
automatically find problem areas
that could be considered failures
/ specification violations
• Difficult to use for reporting
• Not usable for pass/fail
assessment
8. • Representative
sample areas
• Per swath
Pros
• Ideal to compare against planned
swath density
• Relatively easy to compute
• Reasonably batchable – one process
per flightline
• Decent to use for reporting
• Is not biased (inflated) by sidelap
• Very straightforward
Cons
• Does not adequately account for
localized density variations such as
changes in aircraft speed or sudden
variations it pitch.
• Needs interpretation if flying >50%
sidelap to achieve planned density.
• Results from LiDAR systems with
inconsistent scanner swath densities
can adversely affect the reported
density results. Edge clipping may
need to be used.
Airborne LiDAR Density Measurement Methods
10. 3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
0 10 20 30 40 50 60 70 80 90 100
Density
in
PPSM
Percent of Swath Width Used for Average Swath Density Calculation
Calculated Swath Density Using Clipped Swath
This shape varies by
sensor, field of view,
scan rate, AGL, etc.
11. • Representative
sample areas
• Per swath
• Aggregate / project
wide
Pros
• Considers all collected points
• Straightforward approach (number of
first or last return points / area of project
boundary)
Cons
• Swath edge densities, crosslines,
sidelap, collection block overlap, and
patches can inflate density results
• Tabular reporting only will not identify
localized density failures. A thematic
raster is needed for locating potential
density issues.
• Thematic density raster can be difficult
to interpret and unreliable to use due to
aliasing
Area of Project Boundary (m2)
Airborne LiDAR Density Measurement Methods
15. • Representative sample areas
• Per swath
• Aggregate / project wide
• Grid / tile / point in pixel /
“Binary Raster”
Pros
• Seemingly straightforward approach – use grid or tile
scheme to count points and report on normalized
point counts per grid/tile area
• Fast and easy to calculate
• Easy to use for reporting – pass fail percentage
results and graphic
Cons
• The results are in pass/fail cell counts yet there are
no establish parameters for use or analysis (no
passing thresholds)
• Different user defined processing cell size changes
the results.
• Inherent with aliasing problems that invalidates the
results
• Results are severely misunderstood yet widely used
and relied upon by some in our industry
Airborne LiDAR Density Measurement Methods
16.
17.
18.
19.
20. 74.50%
65.56%
71.12%
99.87%
65.32%
45.03% 45.64% 48.00%
25.50%
34.44%
28.88%
0.13%
34.68%
54.97% 54.36% 52.00%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1m x 1m including
overlap bit flag
10m x 10m including
overlap bit flag
100m x 100m including
overlap bit flag
1,000m x 1,000m
including overlap bit
flag
1m x 1m excluding
overlap bit flag
10m x 10m excluding
overlap bit flag
100m x 100m
excluding overlap bit
flag
1,000m x 1,000m
excluding overlap bit
flag
Pass/Fail Point Density Percentages by Varying Binary Raster Cell Sizes
% Fail
% Pass
21. That was all real LiDAR data
with random point spacing.
Let’s test synthetically created,
perfectly spaced point
data.
22. If we take three LiDAR swaths
Export to an LAS grid file at exactly 2
PPSM / 0.7071067811865470 GSD
Then test and report on density using
the grid method.
We expect 100% passing of all tests.
23. If we take three LiDAR swaths
Export to a synthisized LAS grid file at
exactly 2 PPSM /
0.7071067811865470 meter GSD
Then measure and report on density
using the binary raster method.
We expect 100% passing of all tests.
32. Free Third-Party COTS Software Showing
Varying Pass/Fail Percentage Results
These first return density reports were generated using third party software ran on two sample swaths using different cell sizes
(highlighted in each screenshot). Note the percentages widely vary with each cell size test.
33. 75.19%
58.48%
51.83% 53.97%
60.00% 57.81%
24.81%
41.52%
48.17% 46.03%
40.00% 42.19%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1.41m X 1.41m 2.24m X 2.24m 10m X 10m 31.62m X 10m 100m X 100m 316.23m X 316.23m
Free Third-Party COTS Software Pass/Fail Point Density Percentages by Varying Binary Raster Cell Sizes
% Fail
% Pass
39. • Representative sample
areas
• Per swath
• Aggregate / project
wide
• Grid / tile / point in
pixel / “Binary Raster”
• Voronoi / Thiessen
polygon
Pros
• Most accurate representation
of point density
• Measurement is an area of
point influence
• Density can be derived by
1/Voronoi area
• Is not affected by aliasing
Cons
• Historically considered time
consuming to create and
cumbersome to work with
Airborne LiDAR Density Measurement Methods
40. Square
meters
Airborne LiDAR Density Measurement Methods
Pros
• Most accurate representation
of point density
• Measurement is an area of
point influence
• Density can be derived by
1/Voronoi area
• Is not affected by aliasing
Cons
• Historically considered time
consuming to create and
cumbersome to work with
• Representative sample
areas
• Per swath
• Aggregate / project
wide
• Grid / tile / point in
pixel / “Binary Raster”
• Voronoi / Thiessen
polygon
41. PPSM
Airborne LiDAR Density Measurement Methods
Pros
• Most accurate representation
of point density
• Measurement is an area of
point influence
• Density can be derived by
1/Voronoi area
• Is not affected by aliasing
Cons
• Historically considered time
consuming to create and
cumbersome to work with
• Representative sample
areas
• Per swath
• Aggregate / project
wide
• Grid / tile / point in
pixel / “Binary Raster”
• Voronoi / Thiessen
polygon
43. Recommendations for an Ideal Density Testing and Reporting Methodology
• Sensor and scanner type agnostic
• Results are easy to interpret and reporting is meaningful with respect to
the entire project
• Quantitative (pass/fail) and qualitative (visual) results are required
• Pass/fail results cannot be biased (inflated) by sidelap, crosslines, patch
lines, or collection block overlap
• Need project wide measurement and reporting that can identify density
problems/failures anywhere
• Needs to be scalable, batchable, and distributable
• To be used as a post-collection data check tool and a pre-delivery QC tool
• Nice to haves:
o Ability to select classifications for density testing
o Ability to exclude water body (low density/void areas)
44. Proposed Voronoi Based Density Calculation and Reporting
Workflow:
1. Create Voronoi polygons.
2. Calculate area per Voronoi polygons.
3. Calculate and attribute density using 1/Area.
4. Rasterize the polygons using the density field
values setting the cell size to 0.5 X NPS to
preserve the density values derived from the
polygons.
5. Thematically color the Voronoi-based raster
for qualitative project wide review.
6. Create a tile scheme that is 100 X NPS
covering the extent of the Voronoi raster.
7. Attribute the tile scheme with the statistical
mode of the pixel values from step 4 falling
within the extent of each tile, ignoring No Data
values.
8. Thematically render this tile scheme green for
values that are greater than or equal to the
required density (passing) and red for values
that are less than the required density
(failing).
9. Summarize the percent of passing/failing tiles.
Recommendations:
• Process small, virtual, overlapping tiles that allow the software to manage
building TINs then Voronoi polygons in memory. This will likely be
machine dependent but virtual tiles containing ~1,000,000 points is a
good starting point.
• Disseminate processing using multi-threading and distributed computing.
Cloud computing is also possible and very helpful.
• No need to render or even store the Voronoi polygons, just the calculated
density arrays per virtual tile for statistical summarizations (txt, DB, etc.).
• Using last returns is better than using first returns to minimize lateral
displacement and avoid atmospheric points interfering with the density
calculations.
• Use a reasonable high density cutoff for the frequency distribution chart
so it does not plot the densities of interest compressed off to one side.
• Advanced options to consider providing:
62. Voronoi Density Testing Results for
Synthesized QL1 (=8 ppsm)
LAS grid GSD = 0.353553390593274 m
63.
64.
65.
66. Voronoi Density Testing Results for
Synthesized QL2 (=2 ppsm)
LAS grid GSD = 0.7071067811865470 m
67.
68.
69.
70. Sensor and
scanner type
agnostic
Results are
meaningful with
respect to the
entire project
Can be used to
easily identify
valid, reliable,
localized
problems
anywhere in the
project
Not flawed by
raster cell
aliasing
Not flawed by
varying tile sizes
for summary
reporting
Pass/fail results
are not
negatively biased
(inflated) by
sidelap,
crosslines, patch
lines, etc.
Easily used if
flying dual
channel, dual
sensor, or >50%
sidelap
configurations to
meet the
minimum
required density
Project wide
measurement
and reporting
Is scalable,
batchable, and
distributable
Representative
Sample
N N N Y Y N Y N N
Swath Analysis M M N Y Y Y N M Y
Aggregate /
Project Wide
N N N Y Y N Y Y Y
Grid / tile /
“Binary Raster”
M N N N N Y Y Y Y
Voronoi Polygon Y Y Y Y Y Y Y Y Y
Summary
71. Thank You
• Matt Bethel
• Director of Operations and Technology
• Merrick & Company
• http://www.merrick.com/Geospatial
• matt.bethel@merrick.com
• (303) 353-3662
