Full text: Close-range imaging, long-range vision

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1, Honolulu, 
Guoqing Zhou 
Department of Civil Engineering an Technology 
Old Dominion University 
Kaufman Hall, Rm. 214, Norfolk, VA 23529 
Fax: (757) 683-5655; Tel; (757) 683-3619; E-mail: gzhou@odu.edu 
Commission V, WG V/IIT 
KEY WORDS: Urban 3D mapping, EPI technique, Image sequence analysis, DEM, Epipolar line, 3D GIS 
Urban three dimensional (3D) information extraction and urban 3D mapping and from aerial image sequences using epipolar-plane 
image (EPI) analysis technique requires the camera's operation to meet four conditions. In aerial photogrammetry, atmospheric 
turbulence, the aircraft's vibration, strong crosswinds, etc. make the actual operation of the camera considerably deviate from an 
ideal operation, resulting in distortion of the image. An approach to automatically rectify distorted image sequences is proposed, and 
the mathematical model was developed in this paper. In this model, an implicit relationship describing the rectified (normal) and the 
distorted (original) images is described. Three test fields are used for testing our algorithm. The experimental results demonstrated 
that the trajectories in the EPIs constructed by the rectified image sequences are apparently improved relative to the original 
trajectories constructed by the original image sequences. The accuracy of the DEM is improved over 34% by comparison with the 
DEM generated from the original image sequence. 
Bolles and Baker (1985a, 1985b) first presented the epipolar 
plane image (EPI) analysis technique for 3D mapping, which is 
called EPI technique. According to the principle of EPI 
analysis, the camera's movement must meets the following four 
conditions (Zhou et al., 1999): 
1. The camera's movement is restricted along a straight linear 
2. Image capture is rapid enough with respect to camera's 
movement and scene scale to ensure that the data is 
temporally continuous. 
3. The velocity of the camera's movement is a constant. 
4. The camera's position and attitude at each imaging site are 
We used this technique to experiment its application in 
photogrammetry (Zhou et al., 1999). From previous work, we 
produced digital elevation models (DEM) for three test fields in 
Berlin, Germany. The accuracy of the DEMs was poor due to 
several sources of error. These sources of error, as well as their 
influence size and law, have been discussed in Zhou ef al. 
(1999). One of reasons is because the camera deviates 
considerably from the ideal one due to atmospheric turbulence, 
the aircraft's vibration, strong crosswind, and so on. 
This paper presents an algorithm for improving 3D urban 
mapping accuracy when using the EPI technique for urban 3D 
GIS. A mathematical model for improving mapping accuracy is 
derived. Implicit instead of explicit parameters are used for 
rectifying the distortions directly. 
The irregular motions of an aircraft causes unpredictable 
changes to a camera's altitude (translation parameter) and 
attitude (rotate angles). The result is deviation of image points 
in the image plane from their ideal position. We call this 
geometric distortion. The process of rectifying the geometric 
distortion is called geometric rectification. 
According to the principle of EPI analysis, all conjugate 
epipolar lines for any point P in the image sequences are co- 
planar when the camera's movement meets the four conditions 
(Zhou ef al, 1999). In other words, the four constraint 
conditions make that all coordinates along the y direction in the 
image sequence planes are equal. This theory can be used for a 
basis of developing our mathematical model and geometric 
rectification algorithm. The geometric distortion can be 
decomposed into x and y components along the x and y axes in 
the image plane. We first consider the y component. The:x 
component's rectification will be discussed in Section 2.2. 
In development of mathematical model, we define the 
following coordinate systems. All are right-handed coordinate 
systems (see Figure 1). 
(1) Image plane coordination system (o; — xy): Each 
image has an image plane coordinate system (0; — xy) 
i=1,2,---n where o, represents the principal point of the i-th 
image plan (i.e., the intersection of the image plane with the 
optical axis) and the x and y axes are chosen parallel and 
orthogonal to the flying direction. 
(2) Camera coordination system (s; -u'v'w): Each 
projective center of camera s,(i=1,2---n) is taken as the 
original points, and the w' axis is vertical to ground. The u' 
axis is chosen to parallel to x axis of ground coordinate system. 
(3) Rectification coordination system (S, —UVW): The 
first projective center S, is taken as the original points, the W 
axis is parallel to Z axis of ground coordinate system, the U 
axis is chosen along flying direction (for a stereo pair, air base 
direction is U axis direction). 
(4) Ground coordinate system (G— XYZ) : This is an 
object space coordinate system. 

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