3D Data Processing Visualization and Transmission, International Symposium on (2006)
University of North Carolina, Chapel Hill, USA
June 14, 2006 to June 16, 2006
Douglas Lanman , Brown University, USA
Megan Wachs , Stanford University, USA
Gabriel Taubin , Brown University, USA
Fernando Cukierman , University of Buenos Aires, Argentina
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.
M. Wachs, F. Cukierman, D. Lanman and G. Taubin, "Reconstructing a 3D Line from a Single Catadioptric Image," 3D Data Processing Visualization and Transmission, International Symposium on(3DPVT), University of North Carolina, Chapel Hill, USA, 2006, pp. 89-96.