On Unique Solution of 3D Motion Parameters Estimation by Homogaphy Matrix Decomposition

摘要

This paper discusses the solution ambiguity problem of linear 3D motion parameter estimation, especially concerning homography matrix decomposition. By considering the geometric relations of the object before and after the 3D motion, we found the solution ambiguity is not inevitably. For the same 3D motion, it depends on the size of the object; also it depends on the 3D motion parameters for the same object size. The former is proposed for the first time in this paper. Even though, as the latter, there is an inference proposed by Longuet-Higgins and Faugeras in 1980s, the theoretic proof which is under much more common conditions is done for the first time in this paper.