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Epipolar Geometry of Line Cameras Moving with Constant Velocity and Attitude

ETRI journal, v.27 no.2, 2005년, pp.172 - 180  

Habib, Ayman F. (Department of Geomatics Engineering, University of Calgary) ,  Morgan, Michel F. (Department of Geomatics Engineering, University of Calgary) ,  Jeong, Soo (Department of Civil Engineering, Andong National University) ,  Kim, Kyung-Ok (Telematics & USN Research Division,ETRI)

Abstract AI-Helper 아이콘AI-Helper

Image resampling according to epipolar geometry is an important prerequisite for a variety of photogrammetric tasks. Established procedures for resampling frame images according to epipolar geometry are not suitable for scenes captured by line cameras. In this paper, the mathematical model describin...

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문제 정의

  • In this research, we will be investigating the epipolar geometry of line cameras moving along their trajectory with constant velocity and attitude. Such a flight path is a subclass of the one investigated by Kim [4].
  • Such a flight path is a subclass of the one investigated by Kim [4]. The main objective of this investigation is to see whether such a simplification would lead to straight epipolar lines. Before going into the details of the epipolar geometry for such a trajectory, we will outline one principle that distinguishes the epipolar geometry of line cameras from that associated with frame cameras.
  • The paper proceeded by analyzing the deviation from straightness in the resulting epipolar lines from imaging situations beyond those ideal cases. This analysis is motivated by the fact that normalized image generation aims at manipulating the original scenes in such a way that the epipolar lines are transferred to coincide with corresponding rows or columns. Thus, having non-straight epipolar lines would yield distortions in the normalized images.
  • One of the main objectives of photogrammetry is to derive three-dimensional coordinates from two-dimensional images/scenes. This objective is achieved by intersecting conjugate light rays associated with corresponding points in overlapping views. Therefore, the availability of different views or stereo coverage of the area of interest is essential for deriving three-dimensional coordinates from two-dimensional imagery.
  • This paper outlined a comprehensive investigation of the epipolar geometry of line cameras moving with constant velocity and attitude. It has been shown that the epipolar geometry for such cameras is far more complicated than that of frame images.

가설 설정

  • For the ideal across-track stereo configuration, the thrse vectors (B, U, r2) are coplanar as shown in Fig. 5. Thejeo© the epipolar lines will coincide with the scene rows (i.e., they will become straight lines). Ideal along-track stereo configuration requires the collinearity of the velocity and air base vectors, as shown in Fig.
  • Ideal along-track stereo configuration requires the collinearity of the velocity and air base vectors, as shown in Fig. 6. Therefore, all epipolar planes (formed by the point of interest in the left scene, its perspective center, and the perspective centers of the right scene) will coincide, forming a unique epipolar plane. Thus, the intersection of such a plane with the scene plane results in a straight epipolar line.
  • Kim [4] investigated the epipolar geometry of scenes captured by line cameras moving in a trajectory, where the position and heading components are described by second - order polynomial functions, while the roll and pitch angles are represented by first-order polynomials. The author concluded that the epipolar lines in scenes captured from such a trajectory are not straight lines. The fact that the resulting epipolar lines are not straight makes the normalized image generation of such scenes extremely difficult if not impossible.
  • Kim [4] investigated the epipolar geometry of scenes captured by line cameras moving in a trajectory, where the position and heading components are described by second - order polynomial functions, while the roll and pitch angles are represented by first-order polynomials. The author concluded that the epipolar lines in scenes captured from such a trajectory are not straight lines. The fact that the resulting epipolar lines are not straight makes the normalized image generation of such scenes extremely difficult if not impossible.
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참고문헌 (2)

  1. Sohn, Hong-Gyoo, Yoo, Hwan-Hee, Kim, Seong-Sam. Evaluation of Geometric Modeling for KOMPSAT-1 EOC Imagery Using Ephemeris Data. ETRI journal, vol.26, no.3, 218-228.

  2. Gupta, R., Hartley, R.I.. Linear pushbroom cameras. IEEE transactions on pattern analysis and machine intelligence, vol.19, no.9, 963-975.

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