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3DPVT
2006
IEEE

Reconstructing a 3D Line from a Single Catadioptric Image

8 years 11 months ago
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.
Douglas Lanman, Megan Wachs, Gabriel Taubin, Ferna
Added 10 Jun 2010
Updated 10 Jun 2010
Type Conference
Year 2006
Where 3DPVT
Authors Douglas Lanman, Megan Wachs, Gabriel Taubin, Fernando Cukierman
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