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Abstract : |
This paper presents a new framework for analyzing the geometry of multiple 3D scene points from multiple uncalibrated images, based on decomposing the projection of these points on the images into two stages: (i) the projection of the scene points onto a (real or virtual) physical reference planar surface in the scene; this creates a virtual "image " on the reference plane, and (ii) the re-projection of the virtual image onto the actual image plane of the camera. The positions of the virtual image points are directly related to the 3D locations of the scene points and the camera centers relative to the reference plane alone. All dependency on the internal camera calibration parameters and the orientation of the camera are folded into homographies relating each image plane to the reference plane. Bi-linear and tri-linear constraints involving multiple points and views are given a concrete physical interpretation in terms of geometric relations on the physical reference plane. In particular, the possible dualities in the relations between scene points and camera centers are shown to have simple and symmetric mathematical forms. These relations are directly related to physical points such as the epipole and the dual-epipole. In contrast to the plane+parallax (p+p) representation, which also uses a reference plane, the approach described here removes the dependency on a reference image plane and extends the analysis, |
