Inlier Clustering based on the Residuals of Random Hypotheses.

We present an approach for motion clustering based on a novel observation that a signature for putative pixel correspondences can be generated by collecting their residuals with respect to model hypotheses drawn randomly from the data. Inliers of the same motion cluster should have strongly correlated residuals, which are low when a hypothesis is consistent with the data in the cluster and high otherwise. After evaluating a number of hypotheses, members of the same cluster can be identified based on these correlations. Due to this property, we named our approach Inlier Clustering based on the Residuals of Random Hypotheses (ICR). An important advantage of ICR is that it does not require an inlier-outlier threshold or parameter tuning. In addition, we propose a supervised recursive formulation of ICR (r-ICR) that, unlike many motion clustering methods, does not require the number of clusters to be known a priori, as long as annotated data are available for training. We validate ICR and r-ICR on several publicly available datasets for robust geometric model fitting.

Ultra-long magnetization needle induced by focusing azimuthally polarized beams with a spherical mirror.

Based on extended Richards-Wolf theory for axisymmetric surfaces and the inverse Faraday effect, we propose the generation of a purely longitudinal magnetization needle by focusing Gaussian annular azimuthally polarized beams with a spherical mirror. The needle obtained has a longitudinal length varying hundreds to thousands of wavelengths while keeping the lateral size under 0.4λ, and the corresponding aspect ratio can easily reach more than 2000. It may be the first time that a magnetization needle whose aspect ratio is over 500 has been achieved. The approximate analytical expressions of the magnetization needle are given, and the longitudinal length is tunable by changing the value of the angular thickness and the position of the annular beams.