Perspective Factorization Methods for Euclidean Reconstruction

In this paper we describe a factorization-based method for Euclidean reconstruction with a perspective camera model. It iteratively recovers shape and motion by weak perspective factorization method and converges to a perspective model. We discuss the approach of solving the reversal shape ambiguity and analyze its convergence. We also present a factorization-based method to recover Euclidean shape and camera focal lengths from multiple semi-calibrated perspective views. The focal lengths are the only unknown intrinsic camera parameters and they are not necessarily constant among different views. The method rst performs projective reconstruction by using iterative factorization, then converts the projective solution to the Euclidean one and generates the focal lengths by using normalization constraints. This method introduces a new way of camera self-calibration. Experiments of shape reconstruction and camera calibration are presented. We design a criterion called back projection compactness to quantify the calibration results. It measures the radius of the minimum sphere through which all back projection rays from the image positions of the same object point pass. We discuss the validity of this criterion and use it to compare the calibration results with other methods.