A clever elimination strategy for efficient minimal solvers

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.Comment: 13 pages, 7 figure

Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Gr\"obner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Gr\"obner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems

The Neutrino mass matrix after Kamland and SNO salt enhanced results

An updated analysis of all available neutrino oscillation evidence in Solar experiments including the latest SNO ES,CC and NC data (254d live time, NaCL enhanced efficiency) is presented. We obtain, for the fraction of active oscillating neutrinos: sin^2alpha=(\Phi_{NC}-\Phi_{CC})/(\Phi_{SSM}-\Phi_{CC})=0.94^{+0.0.065}_{-0.060} nearly 20\sigma from the pure sterile oscillation case. The fraction of oscillating sterile neutrinos cos^2\alpha \lsim 0.12 (1 sigma CL). At face value, these results might slightly favour the existence of a small sterile oscillating sector. In the framework of two active neutrino oscillations we determine individual neutrino mixing parameters and their errors we obtain Delta m^2= 7.01\pm 0.08 \times 10^{-5} eV^2, tan^2 theta=0.42^{+0.12}_{-0.07}. The main difference with previous analysis is a better resolution in parameter space. In particular the secondary region at larger mass differences (LMAII) is now excluded at 95% CL. The combined analysis of solar and Kamland data concludes that maximal mixing is not favoured at 4-5 sigma. This is not supported by the antineutrino reactor results alone. We estimate the individual elements of the two neutrino mass matrix, writing M^2=m^2 I+M_0^2, we obtain (1 sigma errors): M_0^2=10^{-5} eV^2\pmatrix{ 2.06^{+0.29}_{-0.31} & 3.15^{+0.29}_{-0.35} \cr 3.15^{+0.29}_{-0.35} & 4.60^{+0.56}_{-0.44} }

Testing Chern-Simons modified gravity with observations of extreme-mass-ratio binaries

Extreme-Mass-Ratio Inspirals (EMRIs) are one of the most promising sources of gravitational waves (GWs) for space-based detectors like the Laser Interferometer Space Antenna (LISA). EMRIs consist of a compact stellar object orbiting around a massive black hole (MBH). Since EMRI signals are expected to be long lasting (containing of the order of hundred thousand cycles), they will encode the structure of the MBH gravitational potential in a precise way such that features depending on the theory of gravity governing the system may be distinguished. That is, EMRI signals may be used to test gravity and the geometry of black holes. However, the development of a practical methodology for computing the generation and propagation of GWs from EMRIs in theories of gravity different than General Relativity (GR) has only recently begun. In this paper, we present a parameter estimation study of EMRIs in a particular modification of GR, which is described by a four-dimensional Chern-Simons (CS) gravitational term. We focus on determining to what extent a space-based GW observatory like LISA could distinguish between GR and CS gravity through the detection of GWs from EMRIs.Comment: 10 pages, JPCS of the Amaldi 9 and NRDA 201

Modelling the Interfacial Flow of Two Immiscible Liquids in Mixing Processes

This paper presents an interface tracking method for modelling the flow of immiscible metallic liquids in mixing processes. The methodology can provide an insight into mixing processes for studying the fundamental morphology development mechanisms for immiscible interfaces. The volume-of-fluid (VOF) method is adopted in the present study, following a review of various modelling approaches for immiscible fluid systems. The VOF method employed here utilises the piecewise linear for interface construction scheme as well as the continuum surface force algorithm for surface force modelling. A model coupling numerical and experimental data is established. The main flow features in the mixing process are investigated. It is observed that the mixing of immiscible metallic liquids is strongly influenced by the viscosity of the system, shear forces and turbulence. The numerical results show good qualitative agreement with experimental results, and are useful for optimisating the design of mixing casting processes

ASTErIsM - Application of topometric clustering algorithms in automatic galaxy detection and classification

We present a study on galaxy detection and shape classification using topometric clustering algorithms. We first use the DBSCAN algorithm to extract, from CCD frames, groups of adjacent pixels with significant fluxes and we then apply the DENCLUE algorithm to separate the contributions of overlapping sources. The DENCLUE separation is based on the localization of pattern of local maxima, through an iterative algorithm which associates each pixel to the closest local maximum. Our main classification goal is to take apart elliptical from spiral galaxies. We introduce new sets of features derived from the computation of geometrical invariant moments of the pixel group shape and from the statistics of the spatial distribution of the DENCLUE local maxima patterns. Ellipticals are characterized by a single group of local maxima, related to the galaxy core, while spiral galaxies have additional ones related to segments of spiral arms. We use two different supervised ensemble classification algorithms, Random Forest, and Gradient Boosting. Using a sample of ~ 24000 galaxies taken from the Galaxy Zoo 2 main sample with spectroscopic redshifts, and we test our classification against the Galaxy Zoo 2 catalog. We find that features extracted from our pipeline give on average an accuracy of ~ 93%, when testing on a test set with a size of 20% of our full data set, with features deriving from the angular distribution of density attractor ranking at the top of the discrimination power.Comment: 20 pages, 13 Figures, 8 Tables, Accepted for publication in the Monthly Notices of the Royal Astronomical Societ