A constrained parameter estimation approach for some vision problems

Previous work of the authors developed a theoretically well-founded scheme (FNS) for finding the minimiser of a class of cost functions. Various problems in video analysis, stereo vision, ellipse-fitting, etc, may be expressed in terms of finding such a minimiser. However, in common with many other approaches, it is necessary to correct the minimiser as a post-process if an ancillary constraint is also to be satisfied. In this paper we develop the first integrated scheme (CFNS) for simultaneously minimising the cost function and satisfying the constraint. Preliminary experiments in the domain of fundamental-matrix estimation show that CFNS generates rank-2 estimates with smaller cost function values than rank-2 corrected FNS estimates. Furthermore, when compared with the HartleyZisserman Gold Standard method, CFNS is seen to generate results of comparable quality in a fraction of the time.