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March 2018
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
The DQMs are not direct point-to-point comparisons because
it is nearly impossible for a lidar system to collect conjugate
points in different swaths. It is easier to identify and extract
conjugate surfaces and related features (e.g. roof edges) from
lidar. The DQMs over natural surfaces and over roof planes
assume that these conjugate surfaces are planar, and deter-
mine the measure of separation between a point and the sur-
face (plane). The DQM over roof edges extract break lines or
roof edges from two intersecting planes and measure their
discrepancy.
DQM Over Natural Surfaces: Point to (Tangential and
Vertical) Plane Distance
This measure is calculated by selecting a point from one
swath, figure 3, (say point ´p´ in swath # 1), and determining
the neighboring points (at least three) for the same coordi-
nates in swath # 2. Ideally, the point ´p´ (from swath # 1)
should lie on the surface defined by the points selected from
swath # 2. Therefore, any departure from this ideal situation
will provide a measure of discrepancy, and hence can
be used as a DQM. This departure is measured by fit-
ting a plane to the points selected from swath # 2, and
measuring the (perpendicular) distance of point ´p´ to
this plane.
DQM Over Roof Planes: Point to Conjugate
Plane Distance
In the case where human-made planar features (e.g.
roof planes) are present in the region of overlap, these
features can be extracted and used for measuring the
inter-swath goodness of fit. These planes can be ex-
tracted automatically, or with assistance from an oper-
ator. Assuming PL1 and PL2 to be conjugate planes in
swath # 1 and swath # 2 respectively, the perpendicular
distance of points used to define PL1 to the plane PL2
can be determined easily. Instead of selecting any ran-
dom point, the centroid of points may be used to define
PL1 can be determined. The centroid to Plane PL2 (in
swath # 2) distance can be used as a DQM to measure the
inter-swath goodness of fit (Habib et. al., 2010).
DQM Over Roof Break Lines: Point to Conjugate Line
Distance
If human-made linear features (e.g. roof edges) are present
in the overlapping regions, these can also be used for mea-
suring discrepancy between adjacent swaths. Roof edges can
be defined as the intersection of two adjacent roof planes and
can be accurately extracted. Conjugate roof edges (L1 and L2)
in swaths #1 and # 2 should be first extracted automatically
or using operator assistance. The perpendicular distance be-
tween the centroid of L1 (in swath # 1) to the roof edge L2 (in
swath # 2) is a measure of discrepancy and can be used as
DQM to the measure inter-swath goodness of fit (Habib et.
al., 2010).
DQM Natural Surfaces Implementation
The discussion below is the result of prototype software de-
signed and implemented by the US Geological Survey to re-
search methods to determine inter-swath accuracy and esti-
mate errors of calibration and data acquisition.
The US Geological Survey developed prototype research soft-
ware that implements the concept of point to plane DQM.
The software works on ASPRS’s LAS format files containing
swath data. If the swaths are termed Swath # 1 and Swath
# 2 (Figure 4), the software uniformly samples single return
points in swath # 1 and chooses ‘n’ (user input) points. The
neighbors of these ´n´ points (single return points) in swath
# 2 are determined. There are three options available for de-
termining neighbors: Nearest neighbors, Voronoi neighbors or
Voronoi-Voronoi neighbors. However, other nearest neighbor
methods such as “all neighbors within 3 m” are also acceptable.
Table 1: Data Quality Measures (DQMs) or inter-swath goodness of fit
measures.
Nature of
surface
Examples
Data Quality Measures
(DQMs)/Goodness of fit
measures
Units
Natural
surfaces:
No feature
extraction
Ground, Roof
etc. i.e. not trees,
chimneys etc.
Point to surface
(tangential plane to
surface) distance
Meters
Man-made
surfaces via
feature
extraction
Roof planes
Perpendicular distance
from the centroid
of one plane to the
conjugate plane
Meters
Roof edges
Perpendicular distance
of the centroid of one
line segment to the
conjugate line segment
Meters
Figure 3: Representation of DQM over natural surfaces. Point ´p´
(red dot) is from swath # 1 and the blue dots are from swath # 2.
Point to (tangen�al) plane
distance
Point ‘p’ in swath # 1
Tangen�al plane
Surface described by
points in swath # 2
Figure 3.pdf 1 2/16/2018 2:50:26 PM
