An Efficient and Accurate Method for 3D-Point Reconstruction from Multiple Views

In this paper we consider the problem of finding the position of a point in space given its projections in multiple images taken by cameras with known calibration and pose. Ideally the 3D point can be obtained as the intersection of multiple known rays in space. However, with noise the rays do not meet at a single point generally. Therefore, it is necessary to find a best point of intersection. In this paper we propose a modification of the method (Ma et al., 2001. Journal of Communications in Information and Systems, (1):51-73) based on the multiple-view epipolar constraints. The solution is simple in concept and straightforward to implement. It includes generally two steps: first, image points are corrected through approximating the error model to the first order, and then the 3D point can be reconstructed from the corrected image points using any generic triangulation method. Experiments are conducted both on simulated data and on real data to test the proposed method against previous methods. It is shown that results obtained with the proposed method are consistently more accurate than those of other linear methods. When the measurement error of image points is relatively small, its results are comparable to those of maximum likelihood estimation using Newton-type optimizers; and when processing image-point correspondences cross a small number of views, the proposed method is by far more efficient than the Newton-type optimizers.