Camera distortion self-calibration using the plumb-line constraint and minimal Hough entropy

In this paper we present a simple and robust method for self-correction of camera distortion using single images of scenes which contain straight lines. Since the most common distortion can be modelled as radial distortion, we illustrate the method using the Harris radial distortion model, but the method is applicable to any distortion model. The method is based on transforming the edgels of the distorted image to a 1-D angular Hough space, and optimizing the distortion correction parameters which minimize the entropy of the corresponding normalized histogram. Properly corrected imagery will have fewer curved lines, and therefore less spread in Hough space. Since the method does not rely on any image structure beyond the existence of edgels sharing some common orientations and does not use edge fitting, it is applicable to a wide variety of image types. For instance, it can be applied equally well to images of texture with weak but dominant orientations, or images with strong vanishing points. Finally, the method is performed on both synthetic and real data revealing that it is particularly robust to noise.Comment: 9 pages, 5 figures Corrected errors in equation 1

Reducing the Size Distortion of the KPSS Test

This paper proposes a new stationarity test based on the KPSS test with less size distortion. We extend the boundary rule proposed by Sul, Phillips and Choi (2005) to the autoregressive spectral density estimator and parametrically estimate the long-run variance. We also derive the finite sample bias of the numerator of the test statistic up to the 1/T order and propose a correction to the bias term in the numerator. Finite sample simulations show that the correction term effectively reduces the bias in the numerator and that the finite sample size of our test is close to the nominal one as long as the long-run parameter in the model satisfies the boundary condition.Stationary test, size distortion, boundary rule, bias correction

Baseline correction for NMR spectroscopic metabolomics data analysis.

BackgroundWe propose a statistically principled baseline correction method, derived from a parametric smoothing model. It uses a score function to describe the key features of baseline distortion and constructs an optimal baseline curve to maximize it. The parameters are determined automatically by using LOWESS (locally weighted scatterplot smoothing) regression to estimate the noise variance.ResultsWe tested this method on 1D NMR spectra with different forms of baseline distortions, and demonstrated that it is effective for both regular 1D NMR spectra and metabolomics spectra with over-crowded peaks.ConclusionCompared with the automatic baseline correction function in XWINNMR 3.5, the penalized smoothing method provides more accurate baseline correction for high-signal density metabolomics spectra

Compensation for phase distortions in nonlinear media by phase conjugation

We demonstrate theoretically that the distortion-correction property of phase-conjugate beams propagating in reverse through aberrating media is also operative when the indices of refraction of the media depend on the intensity. A necessary condition is that the phase-conjugate mirror that generates the reflected beam possess a unity (magnitude) "reflection" coefficient

Correction Factors for Reactions involving Quark-Antiquark Annihilation or Production

In reactions with $q \bar q$ production or $q\bar q$ annihilation, initial- and final-state interactions give rise to large corrections to the lowest-order cross sections. We evaluate the correction factor first for low relative kinetic energies by studying the distortion of the relative wave function. We then follow the procedure of Schwinger to interpolate this result with the well-known perturbative QCD vertex correction factors at high energies, to obtain an explicit semi-empirical correction factor applicable to the whole range of energies. The correction factor predicts an enhancement for $q\bar q$ in color-singlet states and a suppression for color-octet states, the effect increasing as the relative velocity decreases. Consequences on dilepton production in the quark-gluon plasma, the Drell-Yan process, and heavy quark production processes are discussed.Comment: 25 pages (REVTeX), includes 2 uuencoded compressed postscript figure

Diversities and the Geometry of Hypergraphs

The embedding of finite metrics in $\ell_1$ has become a fundamental tool for both combinatorial optimization and large-scale data analysis. One important application is to network flow problems in which there is close relation between max-flow min-cut theorems and the minimal distortion embeddings of metrics into $\ell_1$. Here we show that this theory can be generalized considerably to encompass Steiner tree packing problems in both graphs and hypergraphs. Instead of the theory of $\ell_1$ metrics and minimal distortion embeddings, the parallel is the theory of diversities recently introduced by Bryant and Tupper, and the corresponding theory of $\ell_1$ diversities and embeddings which we develop here.Comment: 19 pages, no figures. This version: further small correction

Lens distortion correction by analysing the shape of patterns in Hough transform space : a thesis presented in partial fulfilment of the requirements for the degree of Master of Engineering in Electronics and Computer Engineering at Massey University, Manawatu, New Zealand

Many low cost, wide angle lenses suffer from lens distortion, resulting from a radial variation in the lens magnification. As a result, straight lines, particularly those in the periphery, appear curved. The Hough transform is a commonly used linear feature detection technique within an image. In Hough transform space, straight lines and curved lines have different shapes of peaks. This thesis proposes a lens distortion correction method named SLDC based on analysing the shape of patterns in the Hough transform space. It works by reconstructing the distorted line from significant points on the smile-shaped Hough pattern. It then optimises the distortion parameter by mapping the reconstructed curved line into a straight line and minimising the RMSE. From both simulation and correcting real world images, the SLDC provides encouraging results