3-D Reconstruction Using Mirror Images Based on a Plane Symmetry Recovering Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Geometric invariance in computer vision
Geometric invariance in computer vision
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
3D motion recovery via affine epipolar geometry
International Journal of Computer Vision
Affine Structure from Line Correspondences With Uncalibrated Affine Cameras
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Theory and Practice of Projective Rectification
International Journal of Computer Vision
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Estimating the Fundamental Matrix via Constrained Least-Squares: A Convex Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Catadioptric Stereo Using Planar Mirrors
International Journal of Computer Vision
Catadioptric Projective Geometry
International Journal of Computer Vision
Epipolar Geometry for Central Catadioptric Cameras
International Journal of Computer Vision
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
3D Reconstruction from a Single View of an Object and Its Image in a Plane Mirror
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
Omnidirectional Stereo Vision with a Hiperbolic Double Lobed Mirror
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Correspondence-Free Determination of the Affine Fundamental Matrix
IEEE Transactions on Pattern Analysis and Machine Intelligence
A general expression of the fundamental matrix for both perspective and affine cameras
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
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In order to simplify the design and implementation of a stereo vision system, catadioptric instruments have been used to capture stereo images with a single camera. These catadioptric stereo systems not only provide radiometric advantages over traditional two-camera stereo, but also reduce the complexity and cost of acquiring stereoscopic video. Although much research has been done on the design of the catadioptric stereo system, little attention has been paid to analyze the planar catadioptric stereo (PCS) system based on the epipolar geometry. In this paper, we investigated characteristics of a selected PCS system and proved that it can be approximated by affine epipolar geometry. This affine model reduces the number of parameters in the fundamental matrix from seven in the conventional stereo system to only four in the PCS system. Experimental results verify that estimation of the fundamental matrix for a PCS system can be more robust, precise, and much easier to implement with the affine model. Furthermore, rectification of the image pair based on the affine fundamental matrix can achieve better performance with much less geometric distortion. These significant advantages confirm the usefulness of an affine fundamental matrix model for the selected PCS system.