Full text: Mapping without the sun

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.

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