We compare the convergence performance of different numerical schemes for computing the fundamental matrix from point correspondences over two images. First, we state the problem and the associated KCR lower bound. Then, we describe the algorithms of three well-known methods: FNS, HEIV, and renormalization. We also introduce Gauss-Newton iterations as a new method for fundamental matrix computation. For initial values, we test random choice, least squares, and Taubin's method. Experiments using simulated and real images reveal different characteristics of each method. Overall, FNS exhibits the best convergence properties.

In this paper we propose a parallel composition based adaptive notch filter for eliminating sinusoidal signals whose frequencies are unknown. The proposed filter which is implemented using second order all-pass filter and a band-pass filter can achieve high convergence speed by using the output of an additional band-pass filter to update the coefficients of the notch filter. The high convergence speed of the proposed notch filter is obtained by reducing an effect that an updating term of coefficient for adaptation of a notch filter significantly increases when the notch frequency approaches the sinusoidal frequency. In this paper, we analyze such effect obtained by the additional band-pass filter. We also present an analysis of a convergence performance of cascaded system of the proposed notch filter for eliminating multiple sinusoids. Simulation results have shown the effectiveness of the proposed adaptive notch filter.