MultiviewTriangulation

Abstract

In Chap. 4, we showed how we can reconstruct the 3D point positions from their two-view images using knowledge of the camera matrices. Here, we extend it, reconstructing the 3D point positions from multiple images. The basic principle is the same as the two-view case: we optimally correct the observed point positions such that the lines of sight they define intersect at a single point in the scene. We begin with the three-view case and describe the optimal triangulation procedure based on the fact that three rays intersect in the scene if and only if the trilinear constraint is satisfied, just in the same way that two rays intersect if and only if the epipolar constraint is satisfied. We then extend this to general M views, imposing the trilinear constraint on all three consecutive images.