Reconstruction of Cubic Curves from Two or More Images using Geometric Intersection

Abstract

Reconstruction of algebraic curves in 3-D space from its perspec-tive views has received huge attention by many researchers. In this paper, reconstruction of a cubic curve in 3-D space from its two or more arbitrary perspective views is described. Two different methods are proposed for the reconstruction process based on the geometrical intersection approach. The advantages of proposed methods are to avoid the matching problem that oc-curs in pair of images of the curve and the reconstruction of non-planar curve. Parameters of a curve in 2-D digitized image planes are determined using least-square curve fitting. The generalized conical surfaces are obtained by these pa-rameters and the center of focus of the respective cameras. Simulation studies have been conducted to observe the effect of noise on errors in the process of reconstruction. The proposed methods have been verified using synthetic as well as real world data.