A Fast and Robust Scan-Line Search Algorithm
for Object-to-Image Projection of Airborne
Pushbroom Images
Xiang Shen, Guofeng Wu, Ke Sun, and Qingquan Li
Abstract
The projection of a 3
D
object point onto a 2
D
image plane
(i.e., the object-to-image projection) is one of the fundamental
operations in photogrammetric data processing. Unlike
that for a frame image, the object-to-image projection for a
pushbroom image is not a straightforward process because
each scan line is exposed at a distinct instant of time, and
a preliminary step is therefore required to determine the
corresponding scan-line coordinate of the ground point to
be projected. This paper presents a new scan-line search
algorithm for the object-to-image projection of airborne
pushbroom images, which employs a coarse-to-fine strategy
following four consecutive steps: affine transformation,
iterative search, sequential search, and sub-pixel inter-
polation. The experimental results with 255 pushbroom
images captured in various flight conditions show that the
proposed algorithm is robust and can save at least 15 percent
of the computational time when compared to the previous
methods, while the latter often cannot yield correct results in
strong turbulence scenarios.
Introduction
Pushbroom imaging sensors have been extensively used in
satellite photogrammetry and remote sensing (Green
et al
.,
2011; Aguilar
et al
., 2012; Bettemir, 2012; Pan
et al
., 2013;
Wang
et al
., 2014). In recent years, large-format line-scan cam-
eras, especially three-line scanners (Petrie and Walker, 2007;
Sandau, 2010; Jia
et al
., 2013), have become increasingly
popular in airborne photogrammetry as a result of their dis-
tinct characteristics (e.g., line perspective geometry and 100
percent forward overlap) when compared to traditional frame
cameras, and have shown promise for various topographic
mapping applications, such as orthophoto and true orthopho-
to production (Jacobsen, 2006; Petrie and Walker, 2007).
The projection of 3
D
object points onto a 2
D
image plane
(i.e., the object-to-image projection) plays a fundamental
role for a variety of photogrammetric tasks such as epipolar
resampling and orthorectification (Kim
et al
., 2001; Habib
et
al
., 2006; Wang
et al
., 2009). For a frame image, the object-to-
image projection process can be directly realized by the well-
known collinearity equations after the image is georeferenced.
As for a pushbroom image, however, the object-to-image
projection is not a straightforward process. Since the different
scan lines in a pushbroom image are exposed at different mo-
ments in time, the corresponding exterior orientation param-
eters of an arbitrary ground point are not explicitly known
and, accordingly, the collinearity equations cannot be applied
directly (Chen and Lee, 1993; Habib
et al.
, 2006).
The core problem of the object-to-image projection for a
pushbroom image is to determine the corresponding time
of the imaging or, equivalently, the corresponding scan-line
coordinate (because scan-line coordinates linearly vary with
sampling time) (Chen and Lee, 1993). To date, many scan-line
solving algorithms have been developed for the object-to-
image projection of satellite (Chen and Lee, 1993; Chen and
Rau, 1993; Kim
et al
., 2001; Habib
et al
., 2006) or aerial push-
broom images (Zhao and Li, 2006; Liu and Wang, 2007; Wang
et al
., 2009). Satellites are well known to have very stable
orbits, and, therefore, if their position and orientation data
are modeled by a second-order polynomial function of time,
the corresponding scan-line coordinate of a ground point
can be directly solved by the Newton-Raphson method from
a high-order polynomial equation (Chen and Lee, 1993) or
by an iterative algorithm from an approximate second-order
equation (Kim
et al
., 2001). These methods, however, cannot
be applied to airborne pushbroom image processing because
orientation data in aerial scenarios often suffer from abrupt
changes caused by atmospheric turbulence (Lee
et al
., 2000;
Wohlfeil, 2012) and, accordingly, cannot be simply modeled
by a low-order polynomial over a long period of time. Instead,
a search algorithm is required to indirectly find the corre-
sponding scan-line coordinate of a ground point to satisfy the
collinearity equations. The scan-line search process is very
often time-consuming, and an iterative search procedure has
been recommended by many researchers due to its relatively
low computational requirements (Zhao and Li, 2006; Wang
et
al
., 2009). However, to simplify the analysis, all the previous
iterative search algorithms were designed with the assump-
tion of meeting the ideal line imaging geometry condition
(i.e., the light rays captured by the same
CCD
detector from
different scan lines are strictly parallel to each other) (Wang
et
al
., 2009). In practice, although an airborne three-line scanner
Xiang Shen is with the College of Information Engineering;
the Shenzhen Key Laboratory of Spatial Smart Sensing
and Services; and the Key Laboratory for Geo-Environment
Monitoring of Coastal Zone of the National Administration
of Surveying, Mapping and GeoInformation, Shenzhen
University, Nanhai Road 3688, Nanshan District, Shenzhen,
Guangdong, China.
Guofeng Wu and Qingquan Li are with the Shenzhen Key
Laboratory of Spatial Smart Sensing and Services and the Key
Laboratory for Geo-Environment Monitoring of Coastal Zone
of the National Administration of Surveying, Mapping and
GeoInformation, Shenzhen University, Nanhai Road 3688,
Nanshan District, Shenzhen, Guangdong, China
(
).
Ke Sun is with the Wuda Geoinformatics Company, Ltd., East
Lake High-tech Development Zone, Wuhan, China.
Photogrammetric Engineering & Remote Sensing
Vol. 81, No. 7, July 2015, pp. 565–572.
0099-1112/15/565–572
© 2015 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.81.7.565
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
July 2015
565
