1293 
EPIPOLAR LINE GENERATION FROM IKONOS IMAGERY 
BASED ON RATIONAL FUNCTION MODEL 
Dan Zhao 3 , Xiuxiao Yuan 3 , Xin Liu 3 
a School of Remote Sensing and Information Engineering, Wuhan University, 
129 Luoyu Road, Wuhan 430079, China - zhaodanpppp@163.com 
Commission IV, WG IV/9 
KEY WORDS: Remote Sensing, IKONOS, Space Photogrammetry, Accuracy, Geography 
ABSTRACT: 
High-resolution satellite imagery is expected to be a major source of 3D measurement of ground, especially automatic stereo 
plotting to generate DEM by stereo matching technology is highly required. Epipolarity is a very useful concept in processing stereo 
imagery, and it has been widely used in process images captured by frame cameras. Different from perspective image, every scan 
line of linear array scanner scene has different perspective centre and attitude; this has limited the use of epipolar theory in 
processing the linear array scanner scenes. The purpose of this paper is to develop a method which can be used to generate the 
approximate epipolar line of this kind of imagery. The paper firstly describes the epipolar geometry of linear array scanner scenes; 
then explains the rational function model (RFM) and proposes the use of RFM to generate the epipolar lines; finally, makes a 
accuracy assessment of the rational polynomial coefficients (RPCs) used in experiment and emphatically describes the procedure 
and experiment of the generation of epipolar lines and epipolar line pairs of IKONOS stereo imagery. 
1. INTRODUCTION 
1.1 General Instructions 
High-resolution satellite imagery captured from linear array 
scanner is valued for their great potential in stereo plotting. The 
linear scanner with up to one-meter resolution from commercial 
satellites could deliver more benefits and provide a challenge to 
traditional topographic mapping based on aerial image. It is 
expected to be a major source of 3D measurement of ground. 
Due to the complicated imaging geometry of high-resolution 
satellite imagery, many traditional theories of photogrammetry 
can not be applied to this kind of imagery directly, so the 
appearing of high resolution satellite imagery provide new 
research contents to the space photography. 
Epipolarity is an important concept in processing stereo images. 
A useful property of an epipolar line is that all corresponding 
image points lie on the corresponding epipolar line pairs. This 
property makes epipolar constraint as an important constraint 
condition for 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). For the aerial and perspective 
image, epipolar geometry has been well founded and widely 
used. But due to the complex imaging geometry of linear array 
scanner scene, this geometry of such imagery is not easy to 
obtain and it has not been used as widely as it used in 
processing perspective images. To resolve this problem, many 
scholars have made a lot of efforts. Some have assumed that 
epipolar geometry would be the same for push-broom imagery 
as perspective image, some do not use this geometry at all. This 
paper is aims at developing a method which can be used to 
generate the epipolar lines of the linear array scanner scenes. 
It is important to select an appropriate sensor model to be 
utilized before the study of the epipolar geometry. The rigorous 
and generalized sensor models are the two broad categories of 
sensor model in use (McGlone, 1996). The representative of 
rigorous model is the collinearity equations. The generalized 
models include RFM, two-dimensional affine model, direct 
linear transformation (DLT). The sensor model used in this 
paper is RFM. It is a generalized model which can be generated 
from the physical sensor model and substituted for all sensor 
models and it is capable of achieving high approximation 
accuracy. However, RFM has a complex mathematical 
expression. Therefore, it is difficult to generate the exact 
epipolar curve for linear array scanner scenes use RFM. In this 
paper epipolar lines are generated by approximate method. 
1.2 The Epipolar Geometry of Linear Push-Broom Scenes 
For perspective image, there is only one perspective centre for 
the entire image, so the epipolar curve can be defined as the 
intersection between the epipolar plane and the image plane. 
The epipolar curve of any perspective images can be always 
represented as straight line, which is a well-known property of 
the epipolar geometry of perspective image. Conjugate epipolar 
pairs are exist for perspective image, the conjugate points must 
lie on the conjugate epipolar lines. Different from perspective 
image, every scan line of linear array scanner scene has 
different perspective centre and attitude. It is impossible to 
define an epipolar plane as perspective image, so it is not easy 
to give a rigorous definition for epipolarity of linear array 
scanner scenes. 
There are two difficulties in deriving the epipolar geometry of 
linear push-broom scenes, the first difficulty is that a generally 
accepted mathematical method to describe the relationship 
between image and object space has not yet been established 
(McGlone, 1996), and the second difficulty comes from the 
complexity of such a geometric relationship and difficulty in 
expressing the relationship in mathematical forms.