Epipolar parameterization for reconstructing a 3D rigid curve

This paper describes a new method for reconstructing a 3D rigid curve from a sequence of uncalibrated images using 3D epipolar parameterization of an object. The approach can be divided into the following two parts: First, a nonlinear discrete method is presented for point by point reconstruction of the curve instead of whole curve reconstruction. Projective and Euclidean geometric tools are used. Second the parametric representation of the curve is defined by 3D B-spline curves, a linear method is proposed to interpolate the reconstructed points to obtain a complete curve. Thus it is proved that the 3D curve interpolation is equivalent to determining a set of control points of 3D regularized B-spline curves. It is shown that the 3D epipolar parameterization is an efficient method for reconstructing a 3D curve from image sequences. Experimental results are presented for real data