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Analysis of Dual-Sensor Stereo Geometry
and Its Positioning Accuracy
Jaehoon Jeong and Taejung Kim
Abstract
This research investigated the positioning accuracy and
imaging geometry of dual-sensor stereo pairs in comparison
with those of conventional single-sensor stereo pairs. First, we
discuss the difference between single- and dual-sensor stereo
geometry and suggest that bisector elevation (BIE) and asym-
metry angle, in addition to convergence angle, are important
considerations for interpreting dual-sensor stereo geometry.
We point out that for single-sensor BIE angles and asymmetry
angles are close to ideal values, and their importance has
not been highlighted. We show that dual-sensor stereo may
produce small BIE angles and large asymmetry angles, and
such angles may lead to weak geometry and accuracy degra-
dation of dual-sensor stereo. Second, we compare rigorous
sensor models (RSMs) with rational function models (RFMs) for
handling dual-sensor stereo. For stable dual-sensor stereo,
both models show similar performance. However, for dual-sen-
sor stereo with weak geometry, RSMs produce better positioning
accuracies than RFM s.
Introduction
After high-resolution satellite images were introduced for civil-
ian users, their potential for topographic mapping and the lev-
el of accuracy achieved from them were studied. From SPOT5
stereo pairs,Büyüksalih e t al. (2005) reported 2 to 3 m errors
horizontally and 4 to 5 m errors vertically. From Ikonos pairs,
accuracy within 1 m to 2 m both horizontally and vertically
was achieved (Dial et al., 2003). From QuickBird pairs, similar
accuracy was also reported (Noguchi et al., 2004). Accuracy at
the sub-meter level was achieved with pairs from more recent
satellites, such as GeoEye-1 (Fraser and Ravanbakhsh, 2009;
Aguilar et al., 2012), Worldview-1 (Eckert, 2009; Dolloff and
Settergren, 2010) and WorldView-2 (Aguilar et al., 2013).
Previous studies revealed continual accuracy improvement
and higher potential in satellite images for topographic map-
ping. However, for real mapping applications, the bottleneck
has been availability of recently acquired stereo pairs of good
quality. So far, stereo pairs have been acquired from the same
satellite, and often from the same orbital segment. Such stereo
pairs, however, may not be available for an entire region of
interest. To handle this problem, one must form stereo pairs
from images taken by different sensors. Herein, we refer to
stereo pairs acquired from the same sensor as “single-sensor”
stereo pairs; we refer to stereo pairs from two different sensors
as “dual-sensor” stereo pairs.
Research into the possibility of using dual-sensor stereo
pairs was also conducted previously. Integration of Ikonos and
QuickBird was attempted with a positioning accuracy of 1 m
or less in X, Y, and Z (Li et al. 2007). Zhu et al. (2008) evalu-
ated the accuracy of the digital surface model obtained by the
Ikonos-QuickBird stereo pair. The combination of satellite and
aerial images was attempted (Tong et al. 2010). While these
studies demonstrated the potential of dual-sensor stereo pairs
for accurate mapping, their limitations and problems were not
investigated in detail. It may be misleading to accept the use
of dual-sensor stereo pairs without identifying constraints and
limitations associated with them. For example, arbitrary com-
binations of dual-sensor stereo pairs may produce weak stereo
geometry, which can diminish positioning accuracy.
The purpose of this paper is to investigate stereo geometry
from dual-sensor stereo pairs and its effects on positioning
accuracy. We compare stereo geometry of single-sensor and
dual-sensor stereo pairs and highlight differences. We show
that dual-sensor stereo pairs require additional geometric
parameters, bisector elevation (BIE) angle and asymmetry
angle, to avoid weak stereo geometry, in addition to base-to-
height ratio (B/H), or convergence angle. We also investigate
whether there is any accuracy difference between rigorous
sensor models (RSMs) and rational function models (RFMs) for
handling dual-sensor stereo pairs.
Single- and Dual-Sensor Stereo Geometry
Within a stereo pair, we can explain stereo geometry by the
layout of three vectors: the baseline, the left and the right ray,
and their relation with respect to the ground plane1 (see Fig-
ure 1). In the figure, the epipolar plane is the plane containing
the three vectors. B/H is the ratio of the length of the baseline
and the flying height of the platform. Equivalently, B/H can be
expressed by convergence angle, the angle between the two
rays. B/H or convergence angle has been widely known as a
critical factor for determining positioning accuracy of stereo
pairs (Gugan and Dowman 1988; Li et al. , 2009; Dolloff and
Theiss, 2010). The effects of convergence angle for dual-sen-
sor stereo pairs were also investigated by Li et al. (2007).
In Figure 1, there are two additional parameters explaining
stereo geometry. BIE angle represents the angle between an
epipolar plane and the ground plane and indicates obliqueness
of an epipolar plane. Bisector represents the line within an
Department of Geoinformatic Engineering, Inha University,
253 Yonghyun-Dong, Namgu, Incheon, Republic of Korea
(jaehoon@inha.edu).
Photogrammetric Engineering & Remote Sensing
Vol. 80, No. 7, July 2014, pp. 000–000.
0099-1112/14/8007–000
© 2014 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.80.7.000
1. For simplicity, we used elevation angles for a flat surface.
To include the effect of Earth curvature, we need to convert
elevation angles, for example, according to Wertz and Larson
(2003).
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