A Factorization Method for Projective and Euclidean Reconstruction from Multiple Perspective Views via Iterative Depth Estimation

Abstract

A factorization method is proposed for recovering camera motion and object shapes from point correspondences observed in multiple images with perspective projection. For any factorization-based approaches for perspective images, scaling parameters called projective depths must be estimated in order to obtain a measurement matrix that could be decomposed into motion and shape. One possible approach, proposed by Sturm and Triggs[11], is to compute projective depths from fundamental matrices and epipoles. The estimation process of the fundamental matrices, however, might be unstable if the measurement noise is large or the cameras and the object points are nearly in critical configurations. In this paper, the authors propose an algorithm by which the projective depths are iteratively estimated so that the measurement matrix is made to be as close as possible to rank 4. This estimation process requires no fundamental matrix computation and is therefore robust against measurement noise. Camera motion and shape in 3D projective space are then recovered by factoring the measurement matrix computed from the obtained projective depths. The authors also derive metric constraints for a perspective camera model in the case where the intrinsic camera parameters are available and show that these constraints can be linearly solved for a projective transformation which relates projective and Euclidean descriptions of the scene structure. Using this transformation, the projective motion and shape obtained in the previous factorization step is upgraded to metric descriptions, that is, represented with respect to the Euclidean coordinate frame. The validity of the proposed method is confirmed by experiments with real images.