Efficient nearly-optimal motion and structure from images via analysis of dimensional reduction: application to safety checking system

In computing 3D motion and structure from image correspondences, often called the structure from motion (SFM) problem, dimensions of the used variable set are very large because it contains both motion and structure parameters. As a result, to solve the problem incurs much computational burden. However, in on-line applications of the SFM problem, computational efficiency needs to be stressed as some accuracy of the solutions is sacrificed. In this respect, various dimensional reduction methods are often introduced to improve computational efficiency and this usually leads to various reduced-form SFM problems. The so-obtained reduced-form SFM problems depend on fewer unknowns than the original SFM problem, thus allowing, in principle, for a less computationally intensive estimation, albeit potentially sacrificing accuracy of the results. It is thus interesting to study how much accuracy is lost. This is done by analytically proving results on equivalence or proximity of solutions for some example cases of the so-obtained reduced-form SFM problems. And then, based on the analysis, the author also proposes how to reduce the loss of accuracy in the reduced-form SFM problems (in the meaning of adjusting those reduced-form SFM problems to better approximate the original optimal SFM problem; that is, an optimal SFM problem that does not use any dimensional reduction methods). Experimental results are given to show the effect in practice. Finally, as an example application, a safety checking system using vision is considered.