of conjugate points are identified across multiple images, the
principle of collinearity can be used to establish the relative
position and orientation of each photo by applying a bundle
block adjustment (
BBA
) to the image block. This procedure is
known as a relative orientation
.
Provided that the horizontal and vertical coordinates of at
least three
GCP
s are known, it is then possible to establish the
absolute positions and orientations of each photo in the block.
In practice, there are normally many more
GCP
s available than
the minimum required, and the optimal solution is arrived at
through a rigorous least-squares adjustment. Reconstruction of
the absolute position and orientation of each image in this man-
ner is known as an exterior orientation (
EO
). An alternative way
to carry out an
EO
is to use direct georeferencing, which uses
the information provided by the aircraft navigational sensors,
instead of
GCP
s. However, the results from direct georeferencing
are dependent on the accuracy of the navigation sensors: with a
low end
GPS
of the kind normally used in a small
UAS
typically
delivering horizontal accuracies in the 2 to 5 m range (Turner
et
al
., 2013). For most applications, the level of accuracy attainable
is generally too low to make direct georeferencing a practical
option for small
UAS
surveys, although that is likely to change
with improvements in positioning and navigation components..
The entire process of
GCP
collection and determination of the
EOP
s is known as aerial triangulation (
AT
). This is the method
of reconstruction used by traditional photogrammetric software
packages such as Inpho (e.g., Hugenholtz
et al
., 2013). However
the
AT
process is dependent on good camera calibration infor-
mation being available, and also imposes rigorous geometric
constraints on the imagery, which may be difficult to meet using
small
UASs
equipped with lightweight compact cameras
.
In recent years, SfM software packages have become wide-
ly used for processing image datasets acquired from small
UASs
. SfM software can make use of either semi-global or local
dense matching algorithms (Dall’Asta and Roncella, 2014).
The following discussion will focus on local dense match-
ing, which is the approach implemented by most commercial
SfM packages. Rather than attempting to identify conjugate
points across multiple images, local dense matching identifies
common features across multiple images, using a matching al-
gorithm such as a scale-invariant feature transform (
SIFT
) (e.g.,
Fonstad
et al
., 2013; Westoby
et al
., 2012). These algorithms
are fairly robust, and are often able to cope with variable im-
age overlaps, scale variations, and large image rotations more
successfully than traditional photogrammetric approaches.
SfM software is not dependent on precise camera calibration
information, and as such is well-suited to the compact cam-
eras normally used with small
UASs.
After completion of the
EO
process, the oriented photos can
be used to generate a
DEM
. The first step in
DEM
generation is to
produce a sparse point cloud through image matching. Point
cloud densification can then be carried out through a process
of hierarchical image matching between overlapping images.
The resulting
DEM
, produced through interpolation of the point
cloud, can then be used to orthorectify the source images, which
may then be combined to form a seamless orthoimage mosaic.
Mapping Standards
The most widely accepted standards used internationally for
mapping have been developed by the
ASPRS
, which in 1990
released its accuracy standards for large scale maps (US Army
Corps of Engineers, 1994;
ASPRS
, 1990), hereafter referred to
as
ASPRS
1990. This quickly became accepted as the
de facto
standard for the industry. However, the 1990 standards were
developed for printed maps, and are therefore inappropriate
for most modern day photogrammetric surveys, which are car-
ried out using digital imagery. In recognition of this, the
ASPRS
created the Map Accuracy Standards Working Group in 2011,
with the goal of developing standards appropriate for digital
mapping. In October 2013, the
ASPRS
released an initial draft
of the proposed new standard for discussion. Following input
from members, a revised draft was published in the December
2013 edition of
Photogrammetric Engineering and Remote
Sensing
(
ASPRS
, 2013). Through a process of consultation, the
standard subsequently underwent a number of revisions, with
Draft Revision-7 finally being approved by the
ASPRS
Board of
Directors on 17 November 2014. This standard was intro-
duced in the March 2015 edition of
Photogrammetric Engi-
neering and Remote Sensing
(
ASPRS
, 2015). The final version
of the new standard, hereafter referred to as
ASPRS
2015, is
fully designed for digital orthophotos and
DEM
s, and as such
is independent of both map scale and contour interval.
Both
ASPRS
1990 and
ASPRS
2015 have been designed to be
compatible with a number of US mapping standards, includ-
ing the National Map Accuracy Standard of 1947,
NMAS
(US
Bureau of the Budget, 1947), the National Standard for Spatial
Data Accuracy of 1998,
NSSDA
(Federal Geographic Data Com-
mittee, 1998), and the 2004 US National Digital Elevation Pro-
gram guidelines NDEP (National Digital Elevation Program,
2004). However these standards have been developed to meet
the requirements of US government agencies, and as such typ-
ically lack general applicability. Also, with the exception of
the
NMAS
, which is not appropriate for use with digital data,
none of these standards provide statistically testable accu-
racy thresholds that can be used to directly compare different
surveys carried out under different conditions. Descriptions
of both
ASPRS
1990 and
ASPRS
2015 are given in the following
section. Since this paper focuses on the application of
ASPRS
standards to surveys carried out using small
UASs
, only the
relevant aspects of both standards will be reviewed.
ASPRS 1990
ASPRS
1990 was developed following input from the photo-
grammetry community. The horizontal standard relates the
root-mean-square-error (
RMSE
) at a series of checkpoints to
the output map scale, while the vertical
RMSE
is related to
the contour interval chosen for the project. The error at each
checkpoint includes errors in the surveyed point position, as
well as map compilation and point measurement errors.
RMSE
is defined as the square root of the average of the squared dis-
crepancies, with the horizontal
RMSE
in the x-direction being
computed using the following formula (
ASPRS
, 1990):
RMSE D
x
=
( / )
2
n
(1)
where D
2
= d
1
2
+d
2
2
+d
3
2
+ …, d
n
2
; d is the discrepancy in the
x-direction defined by the field-measured x-coordinate
subtracted from the modeled x-coordinate, and
n
is the total
number of checkpoints. The same equation applies to
RMSE
in
the
y
- and
z
-directions. The horizontal radial
RMSE
(
RMSE
r
) is
calculated from:
RMSE RMSE RMSE
r
x
y
=
+
(
)
2
2
.
(2)
The highest level of accuracy defined under
ASPRS
1990 is
Class 1. Surveys carried out from
UASs
are normally appropri-
ate for mapping at the 1:500 to 1:1,000 scale range. For hori-
zontal mapping at a scale of 1:500, Class 1 accuracy permits a
maximum
RMSE
x
or
RMSE
y
of 0.125 m, whereas for horizontal
mapping at a scale of 1:1,000 the corresponding maximum
error is 0.25 m. Class 1 vertical accuracy requires the
RMSE
z
of all well-defined checkpoints to be less than one third the
specified contour interval. Thus, for a 0.5 m contour interval,
the maximum permitted
RMSE
z
is 0.167 m. For both horizontal
and vertical mapping, the allowable Class 2 error is twice the
allowable Class 1 error, the allowable Class 3 error is three
times the Class 1 error, and so on.
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