Photogrammetric solution for projective reconstruction

Jeffrey J. Shan

doi:10.1117/12.364105

23 September 1999 Photogrammetric solution for projective reconstruction

Jeffrey J. Shan

Proceedings Volume 3811, Vision Geometry VIII; (1999) https://doi.org/10.1117/12.364105
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

This article proposes a novel solution for projective reconstruction for computer vision with non-metric camera. After a brief introduction of projective transformation as well as projective invariant and coordinates, the fundamental matrix is expressed as a production of two matrices, the projective base line matrix and the projective rotation matrix. This derivation is based on photogrammetric concepts and thus close similarity is found to the decomposition of the essential matrix for metric camera. A projective coefficient, which is proven to be the cross ratio of lengths of two conjugate projective rays, is therefore derived to calculate the homogeneous coordinates and projective coordinates (cross ratio of volume elements) of the projective model. In order to reconstruct the object from its projective model, as an extension to the well-known 2-D direct linear transformation (2-D DLT) solution for metric camera in conventional photogrammetry, a 3-D DLT solution is proposed. The reconstruction is linearly completed with minimum five conjugate known object points. Test results and analyses verify the solution and methodology.

Citation Download Citation

Jeffrey J. Shan "Photogrammetric solution for projective reconstruction", Proc. SPIE 3811, Vision Geometry VIII, (23 September 1999); https://doi.org/10.1117/12.364105

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