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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.