Decomposing Three Fundamental Matrices for Initializing 3-D Reconstruction from Three Views

Abstract

This paper focuses on initializing 3-D reconstruction from scratch without any prior scene information. Traditionally, this has been done from two-view matching, which is prone to the degeneracy called “imaginary focal lengths.” We overcome this difficulty by using three images, but we do not require three-view matching; all we need is three fundamental matrices separately computed from pair-wise image matching. We exploit the redundancy of the three fundamental matrices to optimize the camera parameters and the 3-D structure. The main theme of this paper is to give an analytical procedure for computing the positions and orientations of the three cameras and their internal parameters from three fundamental matrices. The emphasis is on resolving the ambiguity of the solution resulting from the sign indeterminacy of the fundamental matrices. We do numerical simulation to show that imaginary focal lengths are less likely for our three view methods, resulting in higher accuracy than the conventional two-view method. We also test the degeneracy tolerance capability of our method by using endoscopic intestine tract images, for which the camera configuration is almost always nearly degenerate. We demonstrate that our method allows us to obtain more detailed intestine structures than two-view reconstruction and observe how our three-view reconstruction is refined by bundle adjustment. Our method is expected to broaden medical applications of endoscopic images.