A RANSAC based procedure is described for detecting inliers corresponding to multiple models in a given set of data points. The algorithm we present in this paper (called mul-tiRANSAC) on average performs better than traditional approaches based on the sequential application of a standard RANSAC algorithm followed by the removal of the detected set of inliers. We illustrate the effectiveness of our approach on a synthetic example and apply it to the problem of identifying multiple world planes in pairs of images containing dominant planar structures.

In this paper an analysis of rational iterations for the matrix sign function is presented. This analysis is based on Pad6 approximations of a certain hypergeometric function and it is shown that local convergence results for "multiplication-rich" polynomial iterations also apply to these rational methods. Multiplication-rich methods are of particular interest for many parallel and vector computing environments. The main diagonal Pad6 recursions, which include Newton's and Halley's methods as special cases, are globally convergent and can be implemented in a multiplication-rich fashion which is computationally competitive with the polynomial recursions (which are not globally convergent). Other rational iteration schemes are also discussed, including Laurent approximations, Cayley power methods, and globally convergent eigenvalue assignment methods.

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A new condition estimation procedure for general matrix functions is presented that accurately gauges sensitivity by measuring the effect of random perturbations at the point of evaluation. In this procedure the number of extra function evaluations used to evaluate the condition estimate determines the order of the estimate. That is, the probability that the estimate is off by a given factor is inversely proportional to the factor raised to the order of the method. The "transpose-free" nature of this new method allows it to be applied to a broad range of problems in which the function maps between spaces of different dimensions. This is in sharp contrast to the more common power method condition estimation procedure that is limited, in the usual case where the Fr6chet derivative is known only implicitly, to maps between spaces of equal dimension. A group of examples illustrates the flexibility of the new estimation procedure in handling a variety of problems and types of sensitivity estimates, such as mixed and componentwise condition estimates.

The standard inverse scaling and squaring algorithm for computing the matrix logarithm begins by transforming the matrix to Schur triangular form in order to facilitate subsequent matrix square root and Padé approximation computations. A transformation-free form of this method that exploits incomplete Denman-Beavers square root iterations and aims for a specified accuracy (ignoring roundoff) is presented. The error introduced by using approximate square roots is accounted for by a novel splitting lemma for logarithms of matrix products. The number of square root stages and the degree of the final Padé approximation are chosen to minimize the computational work. This new method is attractive for high-performance computation since it uses only the basic building blocks of matrix multiplication, LU factorization and matrix inversion.