We present a method for reconstruction of structured scenes from one or more views, in which the user provides image points and geometric knowledge-coplanarity, ratios of distances, angles-about the corresponding 3D points. First, the geometric information is analyzed. Then vanishing points are estimated, from which camera calibration is obtained. Finally, an algebraic method gives the reconstruction.

Our algebraic reconstruction method improves the present state-of-the-art in many aspects: geometric knowledge includes not only planarity and alignment information, but also known ratios of lengths. The single and multipleview cases are treated in the same way and the method detects whether the input data is sufficient to define a rigid reconstruction. We benchmark, using synthetic data, the various steps of the estimation process and show reconstructions obtained from real-world situations in which other methods would fail.