Lab Meeting Novembel 24, 2008(ZhenYu): Reconstructing a 3D Line from a Single Catadioptric Image

Title: Reconstructing a 3D Line from a Single Catadioptric Image (3DPVT'06)

Authors: Lanman, Douglas; Wachs, Megan; Taubin, Gabriel; Cukierman, Fernando

Abstract:

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.

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