Multiscale histograms: Summarizing topological relations in large spatial datasets

Summarizing topological relations is fundamental to many spatial applications including spatial query optimization. In this paper, we present several novel techniques to eectively construct cell density based spatial histograms for range (window) summarizations restricted to the four most important topological relations: contains, contained, overlap, and disjoint. We rst present a novel framework to construct a multiscale histogram composed of multiple Euler histograms with the guarantee of the exact summarization results for aligned windows in constant time. Then we present an approximate algorithm, with the approximate ratio 19/12, to minimize the storage spaces of such multiscale Euler histograms, although the problem is generally NP-hard. To conform to a limited storage space where only k Euler histograms are allowed, an effective algorithm is presented to construct multiscale histograms to achieve high accuracy. Finally, we present a new approximate algorithm to query an Euler histogram that cannot guarantee the exact answers; it runs in constant time. Our extensive experiments against both synthetic and real world datasets demonstrated that the approximate mul- tiscale histogram techniques may improve the accuracy of the existing techniques by several orders of magnitude while retaining the cost effciency, and the exact multiscale histogram technique requires only a storage space linearly proportional to the number of cells for the real datasets.

Seeing edge blur: receptive fields as multiscale neural templates

Edge blur is an important perceptual cue, but how does the visual system encode the degree of blur at edges? Blur could be measured by the width of the luminance gradient profile, peak ^ trough separation in the 2nd derivative profile, or the ratio of 1st-to-3rd derivative magnitudes. In template models, the system would store a set of templates of different sizes and find which one best fits the `signature' of the edge. The signature could be the luminance profile itself, or one of its spatial derivatives. I tested these possibilities in blur-matching experiments. In a 2AFC staircase procedure, observers adjusted the blur of Gaussian edges (30% contrast) to match the perceived blur of various non-Gaussian test edges. In experiment 1, test stimuli were mixtures of 2 Gaussian edges (eg 10 and 30 min of arc blur) at the same location, while in experiment 2, test stimuli were formed from a blurred edge sharpened to different extents by a compressive transformation. Predictions of the various models were tested against the blur-matching data, but only one model was strongly supported. This was the template model, in which the input signature is the 2nd derivative of the luminance profile, and the templates are applied to this signature at the zero-crossings. The templates are Gaussian derivative receptive fields that covary in width and length to form a self-similar set (ie same shape, different sizes). This naturally predicts that shorter edges should look sharper. As edge length gets shorter, responses of longer templates drop more than shorter ones, and so the response distribution shifts towards shorter (smaller) templates, signalling a sharper edge. The data confirmed this, including the scale-invariance implied by self-similarity, and a good fit was obtained from templates with a length-to-width ratio of about 1. The simultaneous analysis of edge blur and edge location may offer a new solution to the multiscale problem in edge detection.

Development of multiphase and multiscale mathematical models for thermal spray process

High velocity oxyfuel (HVOF) thermal spraying is one of the most significant developments in the thermal spray industry since the development of the original plasma spray technique. The first investigation deals with the combustion and discrete particle models within the general purpose commercial CFD code FLUENT to solve the combustion of kerosene and couple the motion of fuel droplets with the gas flow dynamics in a Lagrangian fashion. The effects of liquid fuel droplets on the thermodynamics of the combusting gas flow are examined thoroughly showing that combustion process of kerosene is independent on the initial fuel droplet sizes. The second analysis copes with the full water cooling numerical model, which can assist on thermal performance optimisation or to determine the best method for heat removal without the cost of building physical prototypes. The numerical results indicate that the water flow rate and direction has noticeable influence on the cooling efficiency but no noticeable effect on the gas flow dynamics within the thermal spraying gun. The third investigation deals with the development and implementation of discrete phase particle models. The results indicate that most powder particles are not melted upon hitting the substrate to be coated. The oxidation model confirms that HVOF guns can produce metallic coating with low oxidation within the typical standing-off distance about 30cm. Physical properties such as porosity, microstructure, surface roughness and adhesion strength of coatings produced by droplet deposition in a thermal spray process are determined to a large extent by the dynamics of deformation and solidification of the particles impinging on the substrate. Therefore, is one of the objectives of this study to present a complete numerical model of droplet impact and solidification. The modelling results show that solidification of droplets is significantly affected by the thermal contact resistance/substrate surface roughness.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

Application of finite element method and photo-elasticity to an lap welded connection

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Concurrent multiscale modelling of atomistic and hydrodynamic processes in liquids

Fluctuations of liquids at the scales where the hydrodynamic and atomistic descriptions overlap are considered. The importance of these fluctuations for atomistic motions is discussed and examples of their accurate modelling with a multi-space-time-scale fluctuating hydrodynamics scheme are provided. To resolve microscopic details of liquid systems, including biomolecular solutions, together with macroscopic fluctuations in space-time, a novel hybrid atomistic-fluctuating hydrodynamics approach is introduced. For a smooth transition between the atomistic and continuum representations, an analogy with two-phase hydrodynamics is used that leads to a strict preservation of macroscopic mass and momentum conservation laws. Examples of numerical implementation of the new hybrid approach for the multiscale simulation of liquid argon in equilibrium conditions are provided. © 2014 The Author(s) Published by the Royal Society.

Multiscale modelling of heterogeneously catalysed transesterification reaction process:an overview

Biodiesel is fast becoming one of the key transport fuels as the world endeavours to reduce its carbon footprint and find viable alternatives to oil derived fuels. Research in the field is currently focusing on more efficient ways to produce biodiesel, with the most promising avenue of research looking into the use of heterogeneous catalysis. This article presents a framework for kinetic reaction and diffusive transport modelling of the heterogeneously catalysed transesterification of triglycerides into fatty acid methyl esters (FAMEs), unveiled by a model system of tributyrin transesterification in the presence of MgO catalysts. In particular, the paper makes recommendations on multicomponent diffusion calculations such as the diffusion coefficients and molar fluxes from infinite dilution diffusion coefficients using the Wilke and Chang correlation, intrinsic reaction kinetic studies using the Eley-Rideal kinetic mechanism with methanol adsorption as the rate determining steps and multiscale reaction-diffusion process simulation between catalytic porous and bulk reactor scales. © 2013 The Royal Society of Chemistry.