This presentation will provide an update on the Lidar Division's work to produce an ASPRS document providing valuable information on airborne lidar density measuring and reporting. The scope of this document is: • To clarify various definitions of density and related terms • To document various methods for quantifying density • To develop and document various methods for representation of density • To document various tradeoffs among the methods of representation and quantification of density • To provide recommendations on the use of density

1. ASPRS LiDAR Division Update
With a focus on
Quantifying horizontal sampling density of
aerial lidar point cloud data
2023 ASPRS Conference at GeoWeek
February 15, 2023
Matt Bethel
Assistant Lidar Division Director for ASPRS
Director of Operations and Technology
Merrick & Company

2. ASPRS LiDAR Division Update Working Groups
• Best Practices and Guidelines Working Group
• Control points
• Data acquisition
• Data processing
• Standards
• LAS Working Group
• Update to LAS Domain Profile (LDP) Description:
Topobathy Lidar Version 2.0
• Bathy Working Group
• Created December 2022
• Initial focus is to complete and release the draft of the
Bathy Lidar Specification being worked on by federal
partners for community feedback

3. ASPRS Lidar Division Update
The airborne lidar calibration and validation working group has been
focused almost entirely on the completion of a new document titled:
“Quantifying horizontal sampling density of aerial lidar point cloud data”.
This includes the following:
• Requirements for lidar point density measurement and reporting
• Review the needs for visualizing density and violations
• Description of the methods typically used for estimating and
reporting lidar point density
• Comparisons of methods and identification of issues/limitations
• Recommendations
Why is change needed?

4. Lidar Density Testing
Methodology Comparisons
Using 8 ppsm linear mode lidar
data collected over the
Lakewood, CO Federal Center

5. Density Per Swath
Points per square meter
Line number 100% of swath 95% of swath 75% of swath 50% of swath
1 14.76 13.02 11.72 11.40
2 13.85 12.33 11.10 10.77
3 14.14 12.55 11.33 11.06
4 12.96 11.83 10.53 10.30
0
2
4
6
8
10
12
14
16
Line 1 Line 2 Line 3 Line 4
Points
per
square
meter
Chart of Single Swath Densities by Edge Clipping
100% of swath 95% of swath 75% of swath 50% of 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 in pitch.
• Needs interpretation if flying >50%
sidelap or multiple passes to
achieve planned density
• Results from lidar systems with
inconsistent scanner swath
densities can adversely affect the
reported density results. Edge
exclusion may need to be used.

6. Aggregate / Project Wide Point Density
Pros
• Considers all collected points (if linear mode, only first or
last return is used)
• 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.
Number of First
Return Points
Area of Polygon
(m2)
Point Density
(points/m2)
339,650,243 17,204,792 19.742

7. Grid / Point in Pixel Counting / Tile Based
Density Measurement Method
Typical grid analysis
Pros
• 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
• Integer rounding is inherent in this process, lacks decimal
precision compared to representative area density
calculation
• Different user defined processing cell size changes the
results
• Inherent with aliasing problems that invalidates the
results
Hybrid of swath and grid analysis using the
sweet spot of the swath
Pros
• Useful to compare against planned swath density
• Relatively easy to compute
• Reasonably batchable – one process per flightline
• Is not biased (inflated) by sidelap nor densification at the
edges of some scanners’ swaths
Cons
• Integer rounding is inherent in this process, lacks decimal
precision compared to representative area density
calculation
• Needs interpretation if flying >50% sidelap or multiple
passes to achieve planned density
• Does not show density everywhere
• Different user defined processing cell size changes the
results
• Inherent with aliasing problems that invalidates the
results

8. All Swaths Density Results
Using Point in Cell Counting Method

9. Binary Raster for Pass/Fail
Density Assessment
Typical grid analysis
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
• Integer rounding is inherent in this process, lacks decimal
precision compared to representative area density calculation
• The results are in pass/fail cell counts yet there are no establish
parameters for use or analysis (no passing thresholds)
• Results are severely misunderstood yet widely used and relied
upon by some in our industry
• Different user defined processing cell size changes the results
• Inherent with aliasing problems that invalidates the results
Hybrid of swath and grid analysis using the
sweet spot of the swath
Pros
• Useful to compare against planned swath density
• Relatively easy to compute
• Reasonably batchable – one process per flightline
• Is not biased (inflated) by sidelap nor densification at the
edges of some scanners’ swaths
Cons
• Integer rounding is inherent in this process, lacks decimal
precision compared to representative area density
calculation
• Needs interpretation if flying >50% sidelap or multiple
passes to achieve planned density
• Does not show density everywhere
• Different user defined processing cell size changes the
results
• Inherent with aliasing problems that invalidates the
results

10. All Swaths Binary Raster Pass/Fail (1m and 10m cell sizes)

11. What is Aliasing?
Aliasing is defined as the distortion or artifact that results when a signal reconstructed from samples is different from the original continuous signal.
Aliasing is defined as the distortion or artifact that results when measurements of evenly spaced samples are used to create a raster product from randomly spaced points.

13. Voronoi
Density
Point in Pixel
Binary Raster
Voronoi
Binary Raster
Voronoi
Pass/Fail
Aliasing / Moiré Pattern

14. Binary Raster
Results for
Synthesized
8ppsm data
8 points per square meter =
0.353553390593274 meter
point spacing

19. 65.71%
26.34%
64.81%
34.29%
73.66%
35.19%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1m x 1m 10m x 10m 100m x 100m
Synthisized QL2 Points - Pass/Fail Point Density Percentages by Varying Binary Raster Cell Sizes
% Fail
% Pass

20. Voronoi Density Measurement Method
Pros
• Most accurate representation of point density
• Measurement is an area of point influence. Density can be derived by 1/Voronoi area.
• Pass/fail is not biased by scanner type, sidelap, crosslines, or acquisition approach (e.g., >50% sidelap or
multiple sensors)
• Is not affected by aliasing or varying tile sizes
• Preserves decimal precision rather than being integer limited
Cons
• Generally, longer processing time than other methods but this can be mitigated with parallel and even
distributed processing

21. All Swaths Density Results
Using Voronoi Method
(Charts of 4X [default] and 8X Required Density)

22. All Swaths Voronoi Pass/Fail

23. Voronoi Results
for Synthesized
8ppsm data
8 points per square meter =
0.353553390593274 meter
point spacing

24. Passing Percentage Results by Testing Methodologies
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
Line 1 Line 2 Line 3 Line 4 All Lines with Overlap Synthesized 8ppsm
Binary Raster Pass (100% of swath)
Binary Raster Pass (50% of swath)
Voronoi Pass (100% of swath)
Binary Raster Pass (1m2 cells)
Binary Raster Pass (10m2 cells)
Binary Raster Pass (100m2 cells)
Binary Raster Pass (1000m2 cells)

25. 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
design
density
Project-wide
measurement
and
reporting
Is
scalable,
batchable,
and
distributable
Representative Sample Y N N Y Y N Y N N
Per Swath N N N Y Y Y N Y Y
Aggregate Y N N Y Y N Y Y Y
Point In Cell Raster Count Y N N N N Y Y Y Y
Compute Statistics for the
Sweet Spot of the Swath
N N N N N Y N Y Y
Binary Raster Y N N N N Y Y Y Y
Voronoi Y Y Y Y Y Y Y Y Y
Post-Conditioned Planar
Surface Density Assessment
Y Y Y Y Y Y Y Y Y

26. Thank You
• Matt Bethel
• Assistant Lidar Division Director for ASPRS
• matt.bethel@merrick.com
• (303) 353-3662