Reconstruction of General Curves, Using Factorization and Bundle Adjustment
International Journal of Computer Vision
Accelerated epipolar geometry computation for 3D reconstruction using projective texturing
Proceedings of the 20th spring conference on Computer graphics
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This paper presents algorithms for stereo reconstruction from uncalibrated binocular stereo views using correspondences of curves between the two images. We mainly consider curves which are projections of planar 3-D curves although some of our methods work without this restriction as well. First a brief description of reconstruction algorithms based on point correspondences is given. Then we introduce a coordinate system which is invariant to the unknown camera parameters. Compared to similar constructions reported in the literature our method has the advantage that no restrictions concerning the relative position of the cameras (e.g. parallel optical axes) are necessary. Using this coordinate system we show how to reduce the reconstruction from conic correspondences to the point based case. Next the case of general curves is considered. By applying a simple tangent construction we obtain for a given pair of corresponding curves at least two pairs of matching curve points. By fitting at these points an osculating conic we get pairs of matching conics which reduces the problem to conics based stereo reconstruction. All these algorithms rely on the assumption that the epipolar geometry (encoded in the fundamental matrix) is known. We discuss how to recover the epipolar geometry from conic correspondences. The appendix contains some useful results concerning normal forms of pairs of conics.