The Critical Sets of Lines for Camera Displacement Estimation: A Mixed Euclidean-Projective and Constructive Approach

摘要

The problem of the recovery of the motion, and the structure from motion is relevant to many computer vision applications. Many algorithms have been proposed to solve this problem. Some of these use line correspondences. For obvious practical reasons, it is important to study the limitation of such algorithms. In this paper, we are concerned with the problem of recovering the relative displacements of a camera by using line matches in three views. In particular, we want to know whether there exist sets of 3D lines such that no matter how many lines we observe there will always be several solutions to the relative displacement estimation problem. Such sets of lines may be called critical in the sense that they defeat the corresponding algorithm. This question has been studied in detail in the case of point matches by early-century Austrian photogrammeters and, independently, in the mid-seventies and early-eighties by computer vision scientists. The answer lies in the idea of a critical surface.