The purpose of this study is to prove the\nconvergence of the simultaneous estimation of the optical\nflow and object state (SEOS) method. The SEOS method\nutilizes dynamic object parameter information when\ncalculating optical flow in tracking a moving object within\na video stream. Optical flow estimation for the SEOS\nmethod requires the minimization of an error function\ncontaining the object�s physical parameter data. When\nthis function is discretized, the Euler-Lagrange equations\nform a system of linear equations. The system is arranged\nsuch that its property matrix is positive definite symmetric,\nproving the convergence of the Gauss-Seidel iterative\nmethods. The system of linear equations produced by\nSEOS can alternatively be resolved by Jacobi iterative\nschemes. The positive definite symmetric property is not\nsufficient for Jacobi convergence. The convergence of\nSEOS for a block diagonal Jacobi is proved by analysing\nthe Euclidean norm of the Jacobi matrix. In this paper,\nwe also investigate the use of SEOS for tracking individual\nobjects within a video sequence. The illustrations provided\nshow the effectiveness of SEOS for localizing objects\nwithin a video sequence and generating optical flow\nresults.
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