This paper presents a multi-resolution optical flow estimation method that is robust against large variation in the estimation parameter. For each level solution of the multi-grid estimation, a nonlinear iteration is proposed differently from the existing method, where the incremental displacement from the coarser level optical flow is calculated by linear iteration. The experimental results show that the proposed scheme has better error-performance in a much wider range of regularization parameters.

This paper presents a fast inversion method for electromagnetic imaging of cylindrical dielectric objects with the optimal regularization parameter used in the Levenberg-Marquardt method. A novel procedure for choosing the optimal regularization parameter is proposed. The method of moments with pulse-basis functions and point matching is applied to discretize the equations for the scattered electric field and the total electric field inside the object. Then the inverse scattering problem is reduced to solving the matrix equation for the unknown expansion coefficients of a contrast function, which is represented as a function of the relative permittivity of the object. The matrix equation may be solved in the least-squares sense with the Levenberg-Marquardt method. Thus the contrast function can be reconstructed by the minimization of a functional, which is expressed as the sum of a standard error term on the scattered electric field and an additional regularization term. While a regularization parameter is usually chosen according to the generalized cross-validation (GCV) method, the optimal one is now determined by minimizing the absolute value of the radius of curvature of the GCV function. This scheme is quite different from the GCV method. Numerical results are presented for a circular cylinder and a stratified circular cylinder consisting of two concentric homogeneous layers. The convergence behaviors of the proposed method and the GCV method are compared with each other. It is confirmed from the numerical results that the proposed method provides successful reconstructions with the property of much faster convergence than the conventional GCV method.