Jaehoon Jeong is with the Korea Ocean Satellite Center, Korea
Institute of Ocean Science and Technology, 787 Haean-ro(st).
Sangnok-gu, Ansan-si 15627, Republic of Korea (jaehoon@
kiost.ac.kr).
Taejung Kim is with the Department of Geoinformatic
Engineering, Inha Univeristy, 100 Inharo, Nam-gu, Incheon
22212, Republic of Korea. (
Photogrammetric Engineering & Remote Sensing
Vol. 82, No. 8, August 2016, pp. 625–633.
0099-1112/16/625–633
© 2016 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.82.8.625
Quantitative Estimation and Validation of the
Effects of the Convergence, Bisector Elevation,
and Asymmetry Angles on the Positioning
Accuracies of Satellite Stereo Pairs
Jaehoon Jeong and Taejung Kim
Abstract
The convergence, bisector elevation (
BIE
), and asymmetry
angles are three angles that describe the geometric conditions
in stereo imaging. In this study, the effects of the angles on the
positioning accuracies of stereo pairs were investigated. First,
through careful observation of the stereo geometry that deter-
mines the ray-intersection in object space, the effects of the
angles were visualized and quantified. Second, formulas to es-
timate the positioning errors, including these quantified effects,
were proposed. Third, the formulas were validated using real
satellite data. Our experiment results confirmed the accuracy
variations due to the angles, both visually and quantitatively,
and that all angles may significantly affect both the horizontal
and vertical accuracies, particularly for dual-satellite stereo
with weak geometry. The primary contributions of this paper
are the provision of theoretical background of the effects of
the angles and experimental confirmations of the quantita-
tive effects of them on the stereo positioning accuracies.
Introduction
High-resolution satellite stereo images provide information
that is useful for topographic mapping and have been widely
employed for this purpose. They deliver position information
with absolute accuracies comparable to their ground sample
distances (
GSDs
). For example, very high resolution images
taken from Geoeye-1 and WorldView-1 and 2 now enable
sub-meter positioning accuracy (Fraser and Ravanbakhsh,
2009; Aguilar
et al
., 2012; Aguilar
et al
., 2013). To retrieve
such accurate position information, a precise sensor model
is a prerequisite since such a model is necessary to accu-
rately establish the geometric relationship between the image
coordinates and the corresponding ground coordinates, by
updating the biases of the initially provided rational poly-
nomial coefficients (RPCs) or ephemeris data. Already, many
research groups have investigated and applied precise sensor
models to various satellite images (Dial
et al
., 2003; Kim and
Dowman, 2006; Kim
et al
., 2007; Tong
et al
., 2010; Teo, 2011;
Zhang
et al
., 2012).
Stable imaging geometry, in addition to a precise sensor
model, is also necessary to achieve detailed mapping. The
stability of the imaging geometry can be expressed by the val-
ues of three angles: the convergence, bisector elevation (
BIE
),
and asymmetry angles. The convergence angle reflects the
base-to-height ratio; the
BIE
angle describes the obliqueness of
the epipolar plane; the asymmetry angle specifies the level of
symmetry between the left and right observation rays (Jeong
and Kim, 2014). In the ideal imaging geometry, the epipolar
plane would be orthogonal (90°
BIE
angle) and symmetric
(0° asymmetry angle) to the ground plane, to avoid accuracy
degradation. To achieve stable geometry, these angles must
be close to their ideal values. Angles that differ significantly
from the ideal values may generate geometric weakness and
result in decreased accuracy (Jeong and Kim, 2014). Thus, the
three aforementioned angles should be considered carefully
to achieve precise mapping.
However, despite the importance of these angles, they
have not yet been thoroughly investigated and reviewed. For
example, although the research groups listed above used sat-
ellite stereo pairs to achieve precise ground points, their pri-
mary concern was only on compensating for the biases of the
sensor model. Close observation of the imaging geometry was
rarely provided. One reason is that the stereo images used in
the aforementioned studies were primarily taken from single
satellites, and the stereo acquisition mechanisms of single-
satellite stereos confine the three angles within appropriate
ranges. However, we argue that thoroughly analyzing the
imaging geometry is as important as compensating for sensor
model bias. In particular, if two images taken from different
satellites are combined to form a stereo pair, close attention
should be paid to the imaging geometry, as geometric con-
sistency and stability cannot be guaranteed. Among several
studies on the use of dual-sensor image pairs for mapping
(Li
et al
., 2007; Li
et al
., 2009; Zhang
et al
., 2013), however,
effects of imaging geometry on mapping accuracy were not
investigated. Our earlier investigation (Jeong and Kim, 2014)
revealed that the three angles affect the positioning accuracies
and noted that they are important considerations, particularly
for analyzing dual-sensor stereo images. However, the report
also indicated that the
BIE
and asymmetry angles require
further investigation and that quantitative formulation of the
effects of the three angles on the positioning accuracies must
be developed.
This paper extends our earlier discussion of the conver-
gence,
BIE
, and asymmetry angle effects on the positioning
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
August 2016
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