How is airborne LiDAR point density measured? How is it reported? What constitutes point density acceptance? The varied answers may surprise you. LiDAR providers, data QC entities, and end users go about this many different ways. It is eye opening to learn how open ended this topic is and how data density can be masked to look good but actually be compromised and vice versa. So what method is best? Maybe the answer depends on the application. This presentation will address these topics and uncover how a simple concept can be much more complicated than one would ever think. A better understanding of LiDAR point density is needed so that everyone involved can have clear measurement and reporting expectations at the beginning of projects.

1. AIRBORNE LIDAR POINT DENSITY, MORE TO THE POINT
July 23, 2019
Matt Bethel
Director of Operations and Technology
Merrick & Company

2. How Is Airborne LiDAR Density Measured?
0.5
meter
0.5
meter
0.5 meter
ground sample
distance (GSD) or
nominal point
spacing (NPS)

3. How Is Airborne LiDAR Density Measured?
Type equation here.
1 meter
1 meter
4 points per
square meter
(PPSM)
=
𝐍𝐏𝐒 =
𝟏
𝑫𝒆𝒏𝒔𝒊𝒕𝒚
𝑫𝒆𝒏𝒔𝒊𝒕𝒚 =
𝟏
𝑵𝑷𝑺 𝟐0.5 meter
ground sample
distance (GSD) or
nominal point
spacing (NPS)
𝑫𝒆𝒏𝒔𝒊𝒕𝒚 =
𝐟𝐢𝐫𝐬𝐭 𝐨𝐫 𝐥𝐚𝐬𝐭 𝐫𝐞𝐭𝐮𝐫𝐧 𝐩𝐨𝐢𝐧𝐭 𝐜𝐨𝐮𝐧𝐭
𝒂𝒓𝒆𝒂

4. How Is Airborne LiDAR Density Measured?
1 meter
1 meter
9 or maybe 1
but not 4 PPSM
=
4 points per
square meter
(PPSM)
0.5 meter
ground sample
distance (GSD) or
nominal point
spacing (NPS)

5. How Is Airborne LiDAR Density Measured?
confusing=
Q: Are points on cell
boundaries shared for density
calculations?
A: No, they must be counted
within only one cell.
REMEMBER
THIS!!!
0.5 meter
ground sample
distance (GSD) or
nominal point
spacing (NPS)

6. Ways of Measuring Airborne LiDAR Density
• Representative samples
Pros
• Fast and easy to calculate
• Good for areas of interests
Cons
• Biased by many factors such
as sidelap, patches,
turbulence, etc.
• Very localized, not
representative of swaths or
project extents
• Cannot automatedly find
problem areas that could be
considered failures /
specification violations
• Difficult to use for reporting

7. Ways of Measuring Airborne LiDAR Density
• Representative samples
• Per swath
Pros
• Ideal to compare against
planned swath density
• Relatively easy to compute
• Reasonably batchable – one
process per flightline
• Good to use for reporting
• Is not biased (inflated) by sidelap
• No hidden problems with use or
reporting – very straightforward
Cons
• Needs interpretation if flying
>50% sidelap to achieve planned
density

8. Ways of Measuring Airborne LiDAR Density
• Representative samples
• Per swath
• Aggregate / project
wide
Pros
• Considers all collected points
• Good for reporting
• Straightforward approach
(number of first or last return
points / area of project boundary)
Cons
• 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 localized density failures.
Area of Project Boundary (m2)

9. Ways of Measuring Airborne LiDAR Density
• Representative samples
• Per swath
• Aggregate / project wide
• 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
• Unlike grids, polygons share
representative edges with neighboring
polygons. With grid cells, four of the
eight neighboring cells are connected
through only a point.
Cons
• Cumbersome to work with
• If used, typically only in representative
sample areas or around check points -
not project wide

10. Ways of Measuring Airborne LiDAR Density
• Representative samples
• Per swath
• Aggregate / project wide
• Voronoi / Thiessen
polygon
Square
meters
Pros
• Most accurate representation of point
density
• Measurement is an area of point
influence
• Density can be derived by 1/Voronoi
area
• Unlike grids, polygons share
representative edges with neighboring
polygons. With grid cells, four of the
eight neighboring cells are connected
through only a point.
Cons
• Cumbersome to work with
• If used, typically only in representative
sample areas or around check points -
not project wide

11. Ways of Measuring Airborne LiDAR Density
• Representative samples
• Per swath
• Aggregate / project wide
• Voronoi / Thiessen
polygon
PPSM
Pros
• Most accurate representation of point
density
• Measurement is an area of point
influence
• Density can be derived by 1/Voronoi
area
• Unlike grids, polygons share
representative edges with neighboring
polygons. With grid cells, four of the
eight neighboring cells are connected
through only a point.
Cons
• Cumbersome to work with
• If used, typically only in representative
sample areas or around check points -
not project wide

12. Ways of Measuring Airborne LiDAR Density
• Representative samples
• Per swath
• Aggregate / project wide
• Voronoi / Thiessen
polygon
• Grid / raster / tile
Pros
• Fast and easy to calculate
• Seemingly straightforward approach – use grid or tile scheme to count
points and report on lowest divisible points per grid/tile area
• 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)
• User selected processing cell size changes the results
• Inherent with major problems
• Results are severely misunderstood yet widely used and relied upon

17. There is a better way…
• In digital signal processing, the minimum sampling rate is limited to 2X the
maximum frequency. The purpose for this limit is to preserve important
information throughout the transformation. This is known as the Nyquist-
Shannon sampling theorem. This 2X law can be applied to LiDAR density
measurement and derivative grid creation. This is known as the Nyquist
sampling criteria.
• The Nyquist sampling criteria states that we must sample at no less than twice
the resolution of the smallest detail we intend to measure or model.
• This means that grids used for density calculation or raster product creation
must have a cell size no less than 2 x NPS.

21. Third Party Reports 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.

22. That was all real LiDAR data with
random point spacing.
Let’s test synthetically created,
perfectly spaced point data.

23. 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.

24. If we take three LiDAR swaths
Export to an LAS grid file at exactly 2
PPSM / 0.7071067811865470 meter GSD
Then test and report on density using the
grid method.
We expect 100% passing of all tests.

30. What is going on here?

31. Less than Ideal Scan Pattern
Cross track point spacing = 0.5 m
Along track point spacing = 1 m
Parallel scanline pattern (Riegl)
(Minimum required point count per cell = 2)
190 cells contain 2 points
10 cells contain only 1 point
95% pass / 5% fail this test
Assume each cell is 1 m X 1 m (1 m2)
40 points across by 10 scan lines = 400 points / 200 cells = 2 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: Data with poor point spacing geometry can yield a high passing percentage “grade” using the grid
density test method.

32. Less than Ideal Scan Pattern
Cross track point spacing = 0.5 m
Along track point spacing = 1 m
Zigzag scanline pattern (Optech)
(Minimum required point count per cell = 2)
190 cells contain 2 points
10 cells contain only 1 point
95% pass / 5% fail this test
Assume each cell is 1 m X 1 m (1 m2)
40 points across by 10 scan lines = 400 points / 200 cells = 2 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: Data with poor point spacing geometry can yield a high passing percentage “grade” using the grid
density test method. Zigzag scanline patterns result in the same “grade” as parallel line scanning patterns.

33. Ideal Scan Pattern
Cross track point spacing = 0.71 m
Along track point spacing = 0.71 m
Parallel scanline pattern (Riegl)
(Minimum required point count per cell = 2)
100 cells contain 2 points
60 cells contain only 1 point
40 Cells contain more than 2 points
70% pass / 30% fail this test using 20 more points than the previous
example and a much improved point spacing distribution
Assume each cell is 1 m X 1 m (1 m2)
28 points across by 15 scan lines = 420 points / 200 cells = 2.1 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: Data with ideal point spacing geometry results in a much lower passing percentage “grade” using the grid density test method.
This method is severely flawed for analyzing and reporting LiDAR point density, especially as a PASS/FAIL percentage “grade”.

34. Ideal Scan Pattern
Cross track point spacing = 0.71 m
Along track point spacing (at nadir) = 0.71 m
Zigzag scanline pattern (Optech)
(Minimum required point count per cell = 2)
98 cells contain 2 points
60 cells contain only 1 point
42 Cells contain more than 2 points
70% pass / 30% fail this test using 20 more points than the previous
example and a much improved point spacing distribution
Assume each cell is 1 m X 1 m (1 m2)
28 points across by 15 scan lines = 420 points / 200 cells = 2.1 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: Data with ideal point spacing geometry results in a much lower passing percentage “grade” using the grid density test method. Zigzag scanline patterns result in the same “grade” as
parallel line scanning patterns. This method is severely flawed for analyzing and reporting LiDAR point density, especially as a PASS/FAIL percentage “grade”.

35. What happens when we increase
the size of the testing tile?

36. Ideal Scan Pattern
Cross track point spacing = 0.71 m
Along track point spacing = 0.71 m
Parallel scanline pattern (Riegl)
Cell size increased to 2m x 2m (Minimum required point count per cell = 8)
0 cells contain 8 points
10 cells contain less than 8 points
40 Cells contain more than 8 points
80% pass / 20% fail this test using 20 more points than the previous
example and a much improved point spacing distribution
Assume each cell is 2 m X 2 m (4 m2)
28 points across by 15 scan lines = 420 points / 50 cells / 4 m2 = 2.1 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: When using the grid density test, increasing the cell size used to analyze point density CHANGES the passing percentage “grade” which
invalidates the results. This method is severely flawed for analyzing and reporting LiDAR point density, especially as a PASS/FAIL percentage “grade”.

37. Ideal Scan Pattern
Cross track point spacing = 0.71 m
Along track point spacing (at nadir) = 0.71 m
Zigzag scanline pattern (Optech)
Cell size increased to 2m x 2m (Minimum required point count per cell = 8)
0 cells contain 8 points
10 cells contain less than 8 points
40 Cells contain more than 8 points
80% pass / 20% fail this test using 20 more points than the previous
example and a much improved point spacing distribution
Assume each cell is 2 m X 2 m (4 m2)
28 points across by 15 scan lines = 420 points / 50 cells / 4 m2 = 2.1 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: When using the grid density test, increasing the cell size used to analyze point density CHANGES the passing percentage “grade” which invalidates the results. Zigzag
scanline patterns result in the same “grade” as parallel line scanning patterns. This method is severely flawed for analyzing and reporting LiDAR point density, especially as a
PASS/FAIL percentage “grade”.

38. Ideal Scan Pattern
Cross track point spacing = 0.71 m
Along track point spacing = 0.71 m
Parallel scanline pattern (Riegl)
Cell size increased to 5m x 5m (Minimum required point count per cell = 50)
0 cells contain 50 points
4 cells contain less than 50 points
4 Cells contain more than 50 points
50% pass / 50% fail this test using 20 more points than the previous
example and a much improved point spacing distribution
Assume each cell is 5 m X 5 m (25 m2)
28 points across by 15 scan lines = 420 points / 8 cells / 25 m2 = 2.1 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: When using the grid density test, increasing the cell size used to analyze point density CHANGES the passing percentage “grade” which
invalidates the results. This method is severely flawed for analyzing and reporting LiDAR point density, especially as a PASS/FAIL percentage “grade”.

39. Ideal Scan Pattern
Cross track point spacing = 0.71 m
Along track point spacing (at nadir) = 0.71 m
Zigzag scanline pattern (Optech)
Cell size increased 5m x 5m (Minimum required point count per cell = 50)
0 cells contain 50 points
3 cells contain less than 50 points
5 Cells contain more than 50 points
60% pass / 40% fail this test using 20 more points than the previous
example and a much improved point spacing distribution
Assume each cell is 5 m X 5 m (25 m2)
28 points across by 15 scan lines = 420 points / 8 cells / 25 m2 = 2.1 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: When using the grid density test, increasing the cell size used to analyze point density CHANGES the passing percentage “grade” which invalidates the results.
Zigzag scanline patterns result in a similar “grade” as parallel line scanning patterns. This method is severely flawed for analyzing and reporting LiDAR point density, especially as
a PASS/FAIL percentage “grade”.

40. Ideal Scan Pattern With Nyquist Sampling Criteria
Cross track point spacing = 0.71 m
Along track point spacing = 0.71 m
Parallel scanline pattern (Riegl)
(Minimum required point count per cell = 1)
420 Cells contain more than 1 point
100% pass / 0% fail this test using
Assume each cell is 1.42m X 1.42 m (2.02 m2)
28 points across by 15 scan lines = 420 points / 200 cells = 2.1 ppsm
This passes the USGS LBS v1.x NPS/density requirement
Takeaway: Data with ideal point spacing geometry results in a 100% passing percentage “grade” using the Nyquist sampling criteria grid
density test method.

41. Ideal Scan Pattern With Nyquist Sampling Criteria
Cross track point spacing = 0.71 m
Along track point spacing (at nadir) = 0.71 m
Zigzag scanline pattern (Optech)
(Minimum required point count per cell = 1)
Takeaway: Data with ideal point spacing geometry results in a 100% passing percentage “grade” using the Nyquist sampling criteria grid density
test method. Zigzag scanline patterns result in the same “grade” as parallel line scanning patterns.
420 Cells contain more than 1 point
100% pass / 0% fail this test using
Assume each cell is 1.42m X 1.42 m (2.02 m2)
28 points across by 15 scan lines = 420 points / 200 cells = 2.1 ppsm
This passes the USGS LBS v1.x NPS/density requirement

42. Test
Cross track
spacing (m)
Along track
spacing (m)
at nadir
Raster cell
size (m)
Minimum
required
point count
per cell
Number of
points in
test
Percentage
of passing
cells
Percentage
of failing
cells

43. Test
Cross track
spacing (m)
Along track
spacing (m)
at nadir
Raster cell
size (m)
Minimum
required
point count
per cell
Number of
points in
test
Percentage
of passing
cells
Percentage
of failing
cells
Parallel scan pattern 0.5 1 1 2 400 95% 5%
Zigzag scan pattern 0.5 1 1 2 400 95% 5%

44. Test
Cross track
spacing (m)
Along track
spacing (m)
at nadir
Raster cell
size (m)
Minimum
required
point count
per cell
Number of
points in
test
Percentage
of passing
cells
Percentage
of failing
cells
Parallel scan pattern 0.5 1 1 2 400 95% 5%
Zigzag scan pattern 0.5 1 1 2 400 95% 5%
Parallel scan pattern 0.71 0.71 1 2 420 70% 30%
Zigzag scan pattern 0.71 0.71 1 2 420 70% 30%

45. Test
Cross track
spacing (m)
Along track
spacing (m)
at nadir
Raster cell
size (m)
Minimum
required
point count
per cell
Number of
points in
test
Percentage
of passing
cells
Percentage
of failing
cells
Parallel scan pattern 0.5 1 1 2 400 95% 5%
Zigzag scan pattern 0.5 1 1 2 400 95% 5%
Parallel scan pattern 0.71 0.71 1 2 420 70% 30%
Zigzag scan pattern 0.71 0.71 1 2 420 70% 30%
Parallel scan pattern 0.71 0.71 2 8 420 80% 20%
Zigzag scan pattern 0.71 0.71 2 8 420 80% 20%

46. Test
Cross track
spacing (m)
Along track
spacing (m)
at nadir
Raster cell
size (m)
Minimum
required
point count
per cell
Number of
points in
test
Percentage
of passing
cells
Percentage
of failing
cells
Parallel scan pattern 0.5 1 1 2 400 95% 5%
Zigzag scan pattern 0.5 1 1 2 400 95% 5%
Parallel scan pattern 0.71 0.71 1 2 420 70% 30%
Zigzag scan pattern 0.71 0.71 1 2 420 70% 30%
Parallel scan pattern 0.71 0.71 2 8 420 80% 20%
Zigzag scan pattern 0.71 0.71 2 8 420 80% 20%
Parallel scan pattern 0.71 0.71 5 50 420 50% 50%
Zigzag scan pattern 0.71 0.71 5 50 420 60% 40%

47. Test
Cross track
spacing (m)
Along track
spacing (m)
at nadir
Raster cell
size (m)
Minimum
required
point count
per cell
Number of
points in
test
Percentage
of passing
cells
Percentage
of failing
cells
Parallel scan pattern 0.5 1 1 2 400 95% 5%
Zigzag scan pattern 0.5 1 1 2 400 95% 5%
Parallel scan pattern 0.71 0.71 1 2 420 70% 30%
Zigzag scan pattern 0.71 0.71 1 2 420 70% 30%
Parallel scan pattern 0.71 0.71 2 8 420 80% 20%
Zigzag scan pattern 0.71 0.71 2 8 420 80% 20%
Parallel scan pattern 0.71 0.71 5 50 420 50% 50%
Zigzag scan pattern 0.71 0.71 5 50 420 60% 40%
Parallel scan pattern 0.71 0.71 1.42 1 420 100% 0%
Zigzag scan pattern 0.71 0.71 1.42 1 420 100% 0%

48. Conclusions and Recommendations
• Representative samples are too limiting for project analysis and reporting.
• Swath density analysis is straightforward, reliable, well understood, and very representative.
• Aggregate is too generalizing. A supplemental raster is required to identify localized failures.
• Voronoi is the most accurate but too cumbersome to use for thorough project analysis.
• Grid/raster/tile density method is very effective only if using the Nyquist sampling criteria. A
qualifying pass/fail threshold is required. Also, the results of this method are consistent with
the results from the reliable swath density analysis.
• Never use the flawed grid method with a simple points per square area calculation.

49. Thank You
Matt Bethel
Director of Operations and Technology
Merrick & Company
http://www.merrick.com/Geospatial
matt.bethel@merrick.com
(303) 353-3662