Line reconstruction using prior knowledge in single non-central view

Line projections in non-central systems contain more geometric information than in central systems. The four degrees of freedom of the 3D line are mapped to the line-image and the 3D line can be theoretically recovered from 4 projecting rays (i.e. line-image points) from a single non-central view. In practice, extraction of line-images is consid- erably more difficult and the resulting reconstruction is imprecise and sensitive to noise. In this paper we present a minimal solution to recover the geometry of the 3D line from only three line-image points when the line is parallel to a given plane. A second minimal solution allows to recover the 3D line from two points when the direction of the 3D line is known. Both cases can exploit the prior knowledge of the vertical direction in man-made environments to reduce the complexity in line-image extraction and line reconstruction. The formulation based on Plucker lines is integrated in a line-extraction pipeline, which is tested with synthetic and real non-central circular panoramas. In addition, we evaluate the performance of the robust extractor and the accuracy of the proposal in comparison with the unconstrained method.

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