Hexagonal structure for intelligent vision

Using hexagonal grids to represent digital images have been studied for more than 40 years. Increased processing capabilities of graphic devices and recent improvements in CCD technology have made hexagonal sampling attractive for practical applications and brought new interests on this topic. The hexagonal structure is considered to be preferable to the rectangular structure due to its higher sampling efficiency, consistent connectivity and higher angular resolution and is even proved to be superior to square structure in many applications. Since there is no mature hardware for hexagonal-based image capture and display, square to hexagonal image conversion has to be done before hexagonal-based image processing. Although hexagonal image representation and storage has not yet come to a standard, experiments based on existing hexagonal coordinate systems have never ceased. In this paper, we firstly introduced general reasons that hexagonally sampled images are chosen for research. Then, typical hexagonal coordinates and addressing schemes, as well as hexagonal based image processing and applications, are fully reviewed. © 2005 IEEE

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Numerical simulation of Faraday waves

We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier-Stokes equations are solved using a finite-difference projection method coupled with a front-tracking method for the interface between the two fluids. The domain of calculation is periodic in the horizontal directions and bounded in the vertical direction by two rigid horizontal plates. The critical accelerations and wavenumbers, as well as the temporal behaviour at onset are compared with the results of the linear Floquet analysis of Kumar and Tuckerman [J. Fluid Mech. 279, 49-68 (1994)]. The finite amplitude results are compared with the experiments of Kityk et al. [Phys. Rev. E 72, 036209 (2005)]. In particular we reproduce the detailed spatiotemporal spectrum of both square and hexagonal patterns within experimental uncertainty

Elastostatics of star-polygon tile-based architectured planar lattices

We showed a panoptic view of architectured planar lattices based on star-polygon tilings. Four star-polygon-based lattice sub-families were investigated numerically and experimentally. Finite element-based homogenization allowed computation of Poisson's ratio, elastic modulus, shear modulus, and planar bulk modulus. A comprehensive understanding of the range of properties and micromechanical deformation mechanisms was developed. By adjusting the star angle from $0^\circ$ to the uniqueness limit ($120^\circ$ to $150^\circ$), our results showed an over 250-fold range in elastic modulus, over a 10-fold range in density, and a range of $-0.919$ to $+0.988$ for Poisson's ratio. Additively manufactured lattices showed good agreement in properties. The additive manufacturing procedure for each lattice is available on www.fullcontrol.xyz/#/models/1d3528. Three of the four sub-families exhibited in-plane elastic isotropy. One showed high stiffness with auxeticity at low density with a primarily axial deformation mode as opposed to bending deformation for the other three lattices. The range of achievable properties, demonstrated with property maps, proves the extension of the conventional material-property space. Lattice metamaterials with Triangle-Triangle, Kagome, Hexagonal, Square, Truncated Archimedean, Triangular, and Truncated Hexagonal topologies have been studied in the literature individually. We show that all these structures belong to the presented overarching lattices

CORNER DETECTION ON HEXAGONAL PIXEL BASED IMAGES

ABSTRAC

Structure and magnetism of Cr2BP3O12: Towards the quantum-classical crossover in a spin-3/2 alternating chain

Magnetic properties of the spin-3/2 Heisenberg system Cr2BP3O12 are investigated by magnetic susceptibility chi(T) measurements, electron spin resonance, neutron diffraction, and density functional theory (DFT) calculations, as well as classical and quantum Monte Carlo (MC) simulations. The broad maximum of chi(T) at 85K and the antiferromagnetic Weiss temperature of 139 K indicate low-dimensional magnetic behavior. Below TN = 28 K, Cr2BP3O12 is antiferromagnetically ordered with the k = 0 propagation vector and an ordered moment of 2.5 muB/Cr. DFT calculations, including DFT+U and hybrid functionals, yield a microscopic model of spin chains with alternating nearest-neighbor couplings J1 and J1' . The chains are coupled by two inequivalent interchain exchanges of similar strength (~1-2 K), but different sign (antiferromagnetic and ferromagnetic). The resulting spin lattice is quasi-one-dimensional and not frustrated. Quantum MC simulations show excellent agreement with the experimental data for the parameters J1 ~= 50 K and J1'/J1 ~= 0.5. Therefore, Cr2BP3O12 is close to the gapless critical point (J1'/J1 = 0.41) of the spin-3/2 bond-alternating Heisenberg chain. The applicability limits of the classical approximation are addressed by quantum and classical MC simulations. Implications for a wide range of low-dimensional S = 3/2 materials are discussed.Comment: Published version: 13 pages, 7 figures, 5 tables + Supplementary informatio