Towards Closed Form Solutions to the MultiView Constraints of Curves and Surfaces

In this paper we present the theoretical setting for the closed form solutions to the multiview constraints of curves and surfaces observed by the motion of a camera in a scene. We £nd that knowledge of a curve or surface's structure can provide matching constraints and thus closed form solutions for the position of a camera in a scene over many images. This is advantageous for the process of Structure From Motion (SFM) as it may negate some of the need for non-linear optimisation (Bundle-Adjustment) of an initial linear solution to the motion of the camera and structure of the scene.

[1]  Anders Heyden,et al.  Using conic correspondences in two images to estimate the epipolar geometry , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[2]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[3]  B. Triggs.  The Geometry of Projective Reconstruction I: Matching Constraints and the Joint Image , 1995 .

[4]  Falai Chen,et al.  Implicitization using moving curves and surfaces , 1995, SIGGRAPH.

[5]  Christopher G. Harris,et al.  A Combined Corner and Edge Detector , 1988, Alvey Vision Conference.

[6]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[7]  Amnon Shashua,et al.  Multiple view geometry of non-planar algebraic curves , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[8]  Long Quan,et al.  Conic Reconstruction and Correspondence From Two Views , 1996, IEEE Trans. Pattern Anal. Mach. Intell..