A Study on the Epipolarity of Linear Pushbroom Images
Taejung Kim · Photogrammetric Engineering & Remote Sensing · 2000
for such images are not as available as those for images Although epipolar geometry is a very useful clue in processing obtained from perspective cameras (McGlone, 1996). Some stereo images, it has not been thoroughly examined previously published methods for retrieving 3D information from such for linear pushbroom images. Some have assumed that epi- images a~mme that the e~i~olarit~ of linear pushbroom polar geometry would be the same for pushbroom images as images is the same as that for perspective images with or with- for perspective images. Some do not use this geometry at all Out acknowledging the difference between the two (Al-Rousan because it is not fully understood. The purpose of this paper eta)., 1997; Tateishi and Akutsu, 1992). Some do not use the is to provide a theoretical basis for the epipolar geometry of e~i~olar constraint at all due to the possible complexity of the linear pushbroom images and to discuss the practical impli- difference (Ottomd Chaul 1989). cations of this geometry in processing such images. We show These approaches are, however, misleading because there that epipolarity for linear pushbroom images is different from exists a unique e~i~olar geometry for linear pushbroom images that for perspective images. We also derive an equation for and it is different from that for perspective images. The purpose epipolar curves of linear pushbroom images, which are not of this paper is to derive the epipolar geometry of linear push- lines but hyperbola-like non-linear curves. Through analyses broom images in a mathematical form and to discuss the Prop- of the properties of these curves, we conclude that these curves erties of such a geometry incom~arisonwiththatfor Perspec- can be approximated as piece-wise linear segments and that tive images. First, the e~i~olar geometry for perspective images any closely located points on one epipolar curve are mapped and its known ~ro~e*ies will be explained. We will point out onto a common epipolar curve. that epipolar curves for perspective images are represented by straight lines. Second, the epipolar geometry of linear push-