Oriented projective geometry
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Visual Control of Robots: High-Performance Visual Serving
Visual Control of Robots: High-Performance Visual Serving
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Oriented Projective Geometry for Computer Vision
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Epipolar Geometry of Panoramic Cameras
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
A Theory of Catadioptric Image Formation
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Ego-Motion and Omnidirectional Cameras
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Fitting conics to paracatadioptric projections of lines
Computer Vision and Image Understanding
Fitting conics to paracatadioptric projections of lines
Computer Vision and Image Understanding
Cyclorotation models for eyes and cameras
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Active stereo tracking of N ≤ 3 targets using line scan cameras
IEEE Transactions on Robotics
PTZ camera modeling and panoramic view generation via focal plane mapping
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
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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 ℜ3 to ℜ2, 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.