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Mapping without the sun
Zhang, Jixian

Jiaying Liu l ’ ,Guo Zhang 2 ’ ,Deren Li 3
1 School of Information Engineering and Remote Sensing ,Wuhan University ,129 Luoyu Road ,Wuhan ,430079,
China ,j iaying 1311 @ 163 .com
2 State key Library of Information Engineering in Surveying,Mapping and Remote Sensing,Wuhan
University,Wuhan,430079,China, guozhang@whu.edu.cn
3 State key Library of Information Engineering in Surveying,Mapping and Remote Sensing,Wuhan
KEY WORDS: epipolar resampling , projection track method , rational function model
This paper presents a practical method of epipolar resampling of imagery collected from various airborne and satellite sensors. With
increasing amount of data from various sensors, more information about an object or a study area can be obtained than from single
sensor data alone by means of integration of complementary data sets. It is meaningful to make full use of different types of imagery,
and epipolar resampling of imagery is an important prerequisite. Resampled imagery according to epipolar geometry is characterized
by having conjugate points along the same row (or column). Such a characteristic makes resampled imagery an important
prerequisite for many photogrammetric activities such as stereo viewing, image matching, fusion techniques, and orthophoto
generation.Firstly, this paper introduces the characteristics of the extended epipolarity model based on the projection track
method .Then how the model is suitably applicable to epipolar resampling is shown. Secondly, the paper proposes the rational
function model (RFM) to describe the object-to-image space transformation. RFMs are divided into forward RFM and inverse RFM
according to the relationship between object space and image space. Finally several experiments validate the proposed method with
data from various satellite sensors then the RMS value of vertical parallaxes between a pair of stereo epipolar images is calculated.
1.1 General Instructions
Epipolar geometry plays a very important role in stereo
viewing stereo measurement and image matching of satellite
imagery. Normalized imagery resampled according to epipolar
geometry guarantees that conjugate points in stereo-images
have zero y parallax. In addition to improving the stereo
viewing capabilities, the epipolar constraint is very helpful in
solving correspondence problems in image matching. Many
existing stereo matching algorithms use this constraint to
confine search dimensions, reduce processing time, and achieve
reliable match estimates (Zhang et al., 1995; Kim, 2000). With
increasing amount of data collected from various airborne and
satellite sensors, this paper attempts to generate epipolar
images to make full use of different types of imagery.
However, the theory and practice of epipolar geometry about
Linear Array Push-broom Imagery is not yet ripe. Every scan
line at each different exposure station has a different
perspective centre and attitude. Hence, the epipolar lines should
be clearly defined in such scenes before studying their
geometry. The epipolar line of CCD images is defined as the
locus of all possible conjugate points of one point in the other
scene based on the orientation parameter. The epipolar
geometry in the case of satellite imagery is defined as a curve,
not as a line, and unlike aerial photographs, it has complex
To establish the epipolar geometry of linear CCD push-broom
Imagery, scholars have put forward several extended
epipolarity models. One is based around the polynomial fitting
of conjugate points. Another model based on changing the
height of the corresponding object point along the light ray is
named as projection track method. The former scholars
conducted a lot of studies about the polynomial fits for CCD
images’ epipolar geometry, and pointed out the existence of
some shortcomings. This paper based on another theory-
projection track method.
1.2 Definition of projection track method
Changing the height of the corresponding object point along the
light ray connecting the perspective centre and projecting the
object points onto the other image, the track of a series of
pixels obtained is the epipolar curve. If a straight line can be
used to approximate the epipolar curve, it can be similar to the
epipolar line of traditional definition.
Firstly, the authors summarizes the literatures on the epipolar
geometry of linear CCD push-broom imagery and get the
conclusions as follows:
1. The epipolar line is similar to the hyperbolic curve
in the ordinary way , but in a small area or within
the image can be seen as the straight line to handle.
2. For a point q on a epipolar line of the image and an
adjacent point within limits, the conjugate points
of them all locate on the conjugate epipolar line of
point g.The conclusion is positive in the local area.
According to the conclusion 1 and 2, the search process of
stereo matching can be simplified from the two-dimensional to
3. A pair of conjugate epipolar lines is exist. If two
points are conjugate points, the epipolar lines are
conjugate lines, and the points on these two lines
are one-to-one correspondences.
This conclusion is positive in the local area the same as the
above two conclusions, that is to say, a pair of conjugate
epipolar lines exist in the local area.