Multiple View Geometry of Non-planar Algebraic Curves

We introduce a number of new results in the context of multi-view geometry from general algebraic curves. We start with the derivation of the extended Kruppa's equations which are responsible for describing the epipolar constraint of two projections of a general (non-planar) algebraic curve. As part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus. We then establish new results on the reconstruction of general algebraic curves from multiple views. We address three different representations of curves: (i) the regular point representation for which we show that the reconstruction from two views of a curve of degree admits two solutions, one of degree and the other of degree ? ??, (ii) the dual space representation (tangents) for which we derive a lower bound for the number of views necessary for ...

• Type: Conference
• Year: 2001
• Where: ICCV
• Authors: Jeremy Yermiyahou Kaminski, Michael Fryers, Amnon Shashua, Mina Teicher
• Keywords: Computer Vision, Curve Degree, Curve Fitting, Dual Space Representation, General Algebraic Curves, ICCV 2001, Regular Point Representation