Least-squares 3D reconstruction from one or more views and geometric clues

We present a method to reconstruct from one or more images a scene that is rich in planes, alignments, symmetries, orthogonalities, and other forms of geometrical regularity. Given image points of interest and some geometric information, the method recovers least-squares estimates of the 3D points, camera position(s), orientation(s), and eventually calibration(s). Our contributions lie (i) in a novel way of exploiting some types of symmetry and of geometric regularity, (ii) in treating indifferently one or more images, (iii) in a geometric test that indicates whether the input data uniquely defines a reconstruction, and (iv) a parameterization method for collections of 3D points subject to geometric constraints. Moreover, the reconstruction algorithm lends itself to sensitivity analysis. The method is benchmarked on synthetic data and its effectiveness is shown on real-world data.