Direct Solutions for Computing Cylinders from Minimal Sets of 3D Points

Efficient direct solutions for the determination of a cylinder from points are presented. The solutions range from the well known direct solution of a quadric to the minimal solution of a cylinder with five points. In contrast to the approach of G. Roth and M. D. Levine (1990), who used polynomial bases for representing the geometric entities, we use algebraic constraints on the quadric representing the cylinder. The solutions for six to eight points directly determine all the cylinder parameters in one step: (1) The eight-point-solution, similar to the estimation of the fundamental matrix, requires to solve for the roots of a 3rd-order-polynomial. (2) The seven-point-solution, similar to the sixpoint-solution for the relative orientation by J. Philip (1996), yields a linear equation system. (3) The six-point-solution, similar to the fivepoint-solution for the relative orientation by D. Nister (2003), yields a ten-by-ten eigenvalue problem. The new minimal five-point-solution first det...

• Type: Conference
• Year: 2006
• Where: ECCV
• Authors: Christian Beder, Wolfgang Förstner
• Keywords: Computer Vision, Cylinder Parallel, Cylinder Parameters, ECCV 2006, Efficient Direct Solutions, Linear Equation System, Relative Orientation