Differential optical flow methods are widely used within the computer vision community. They are classified as being either local, as in the Lucas-Kanade method, or global, such as in the Horn-Schunck technique. Local differential techniques are known to have robustness under noise, whilst global techniques are able to produce dense optical flow fields. We will show that the Horn-Schunck Technique, when combined with Lucas-Kanade, can yield the advantage of having both robust and dense optical flow fields. Selection of neighborhood size is an important tuning parameter for the combined Lucas-Kanade/Horn-Schunck technique. Choosing the optimal neighborhood is a difficult task and greatly effects the performance of optical flow results. We outline a method for the automatic selection of neighborhood size based on Stein's Unbiased Risk Estimator (SURE). Algorithms are derived for a combined Lucas-Kanade/Horn-Schunck technique with automatic neighborhood selection. The performance of SURE neighborhood selection for the combined optical flow technique is simulated via Matlab, providing an illustration of the performance that is attainable.

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The framework of differential optical flow has been built upon to enhance the performance of motion estimation from optical flow. By coupling optical flow and object state parameters, an effective procedure for object tracking is implemented with the 'Simultaneous Estimation of Optical Flow and Object State' (SEOS) technique. The SEOS method utilizes dynamic object parameter information when calculating optical flow for tracking a moving object within a video stream. Optical flow estimation for the SEOS method requires minimization of an error functional containing object physical parameter data. The convergence of an energy functional to a feasible or optimal solution set is not guaranteed. Convergence criteria is often assumed and not shown explicitly. Convergence of the SEOS method for both the Jacobi and Gauss-Seidel numerical resolution methods is evaluated.

The purpose of this study is to prove the convergence of the simultaneous estimation of the optical flow and object state (SEOS) method. The SEOS method utilizes dynamic object parameter information when calculating optical flow in tracking a moving object within a video stream. Optical flow estimation for the SEOS method requires the minimization of an error function containing the object's physical parameter data. When this function is discretized, the Euler-Lagrange equations form a system of linear equations. The system is arranged such that its property matrix is positive definite symmetric, proving the convergence of the Gauss-Seidel iterative methods. The system of linear equations produced by SEOS can alternatively be resolved by Jacobi iterative schemes. The positive definite symmetric property is not sufficient for Jacobi convergence. The convergence of SEOS for a block diagonal Jacobi is proved by analysing the Euclidean norm of the Jacobi matrix. In this paper, we also investigate the use of SEOS for tracking individual objects within a video sequence. The illustrations provided show the effectiveness of SEOS for localizing objects within a video sequence and generating optical flow results.

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