Reconstructing a 3D Line from a Single Catadioptric Image

This paper demonstrates that, for axial non-central optical systems, the equation of a 3D line can be estimated using only four points extracted from a single image of the line. This result, which is a direct consequence of the lack of vantage point, follows from a classic result in enumerative geometry: there are exactly two lines in 3-space which intersect four given lines in general position. We present a simple algorithm to reconstruct the equation of a 3D line from four image points. This algorithm is based on computing the Singular Value Decomposition (SVD) of the matrix of Pl¨ucker coordinates of the four corresponding rays. We evaluate the conditions for which the reconstruction fails, such as when the four rays are nearly coplanar. Preliminary experimental results using a spherical catadioptric camera are presented. We conclude by discussing the limitations imposed by poor calibration and numerical errors on the proposed reconstruction algorithm.

• Type: Conference
• Year: 2006
• Where: 3DPVT
• Authors: Douglas Lanman, Megan Wachs, Gabriel Taubin, Fernando Cukierman
• Keywords: 3DPVT 2006, Applied Computing, Non-central Optical Systems, Singular Value Decomposition, Spherical Catadioptric Camera