NDLI: A General Framework for the Selection of World Coordinate Systems in Perspective and Catadioptric Imaging Applications

Content Provider	Springer Nature Link
Author	Barreto, João P. Araujo, Helder
Copyright Year	2004
Abstract	An imaging system with a single effective viewpoint is called a central projection system. The conventional perspective camera is an example of central projection system. A catadioptric realization of omnidirectional vision combines reflective surfaces with lenses. Catadioptric systems with an unique projection center are also examples of central projection systems. Whenever an image is acquired, points in 3D space are mapped into points in the 2D image plane. The image formation process represents a transformation from ℜ$^{3}$ to ℜ$^{2}$, and mathematical models can be used to describe it. This paper discusses the definition of world coordinate systems that simplify the modeling of general central projection imaging. We show that an adequate choice of the world coordinate reference system can be highly advantageous. Such a choice does not imply that new information will be available in the images. Instead the geometric transformations will be represented in a common and more compact framework, while simultaneously enabling newer insights. The first part of the paper focuses on static imaging systems that include both perspective cameras and catadioptric systems. A systematic approach to select the world reference frame is presented. In particular we derive coordinate systems that satisfy two differential constraints (the “compactness” and the “decoupling” constraints). These coordinate systems have several advantages for the representation of the transformations between the 3D world and the image plane. The second part of the paper applies the derived mathematical framework to active tracking of moving targets. In applications of visual control of motion the relationship between motion in the scene and image motion must be established. In the case of active tracking of moving targets these relationships become more complex due to camera motion. Suitable world coordinate reference systems are defined for three distinct situations: perspective camera with planar translation motion, perspective camera with pan and tilt rotation motion, and catadioptric imaging system rotating around an axis going through the effective viewpoint and the camera center. Position and velocity equations relating image motion, camera motion and target 3D motion are derived and discussed. Control laws to perform active tracking of moving targets using visual information are established.
Starting Page	23
Ending Page	47
Page Count	25
File Format	PDF
ISSN	09205691
Journal	International Journal of Computer Vision
Volume Number	57
Issue Number	1
e-ISSN	15731405
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2004-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Artificial Intelligence (incl. Robotics) Computer Imaging, Graphics and Computer Vision Image Processing Automation and Robotics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Vision and Pattern Recognition Software

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