A Featureless Approach to 3D Polyhedral Building Modeling from Aerial Images

This paper presents a model-based approach for reconstructing 3D polyhedral building models from aerial images. The proposed approach exploits some geometric and photometric properties resulting from the perspective projection of planar structures. Data are provided by calibrated aerial images. The novelty of the approach lies in its featurelessness and in its use of direct optimization based on image rawbrightness. The proposed framework avoids feature extraction and matching. The 3D polyhedral model is directly estimated by optimizing an objective function that combines an image-based dissimilarity measure and a gradient score over several aerial images. The optimization process is carried out by the Differential Evolution algorithm. The proposed approach is intended to provide more accurate 3D reconstruction than feature-based approaches. Fast 3D model rectification and updating can take advantage of the proposed method. Several results and evaluations of performance from real and synthetic images show the feasibility and robustness of the proposed approach.

Geometric integration applied to moving mesh methods and degenerate Lagrangians

Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the simulation, but redistribute them over time to follow the areas where a higher mesh point density is required. There are a very limited number of moving mesh methods designed for solving field-theoretic partial differential equations, and the numerical analysis of the resulting schemes is challenging. In this thesis we present two ways to construct r-adaptive variational and multisymplectic integrators for (1+1)-dimensional Lagrangian field theories. The first method uses a variational discretization of the physical equations and the mesh equations are then coupled in a way typical of the existing r-adaptive schemes. The second method treats the mesh points as pseudo-particles and incorporates their dynamics directly into the variational principle. A user-specified adaptation strategy is then enforced through Lagrange multipliers as a constraint on the dynamics of both the physical field and the mesh points. We discuss the advantages and limitations of our methods. The proposed methods are readily applicable to (weakly) non-degenerate field theories---numerical results for the Sine-Gordon equation are presented.

In an attempt to extend our approach to degenerate field theories, in the last part of this thesis we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for variational integration. Our main observation is that the evolution takes place on the primary constraint and the 'Hamiltonian' equations of motion can be formulated as an index 1 differential-algebraic system. We then proceed to construct variational Runge-Kutta methods and analyze their properties. The general properties of Runge-Kutta methods depend on the 'velocity' part of the Lagrangian. If the 'velocity' part is also linear in the position coordinate, then we show that non-partitioned variational Runge-Kutta methods are equivalent to integration of the corresponding first-order Euler-Lagrange equations, which have the form of a Poisson system with a constant structure matrix, and the classical properties of the Runge-Kutta method are retained. If the 'velocity' part is nonlinear in the position coordinate, we observe a reduction of the order of convergence, which is typical of numerical integration of DAEs. We also apply our methods to several models and present the results of our numerical experiments.

Polarisation diversity of conformal arrays based on geometric algebra via convex optimisation

A simple and general design procedure is presented for the polarisation diversity of arbitrary conformal arrays; this procedure is based on the mathematical framework of geometric algebra and can be solved optimally using convex optimisation. Aside from being simpler and more direct than other derivations in the literature, this derivation is also entirely general in that it expresses the transformations in terms of rotors in geometric algebra which can easily be formulated for any arbitrary conformal array geometry. Convex optimisation has a number of advantages; solvers are widespread and freely available, the process generally requires a small number of iterations and a wide variety of constraints can be readily incorporated. The study outlines a two-step approach for addressing polarisation diversity in arbitrary conformal arrays: first, the authors obtain the array polarisation patterns using geometric algebra and secondly use a convex optimisation approach to find the optimal weights for the polarisation diversity problem. The versatility of this approach is illustrated via simulations of a 7×10 cylindrical conformal array. © 2012 The Institution of Engineering and Technology.

Innovative Stereo Vision-Based Approach to Generate Dense Depth Map of Transportation Infrastructure

Three-dimensional (3-D) spatial data of a transportation infrastructure contain useful information for civil engineering applications, including as-built documentation, on-site safety enhancements, and progress monitoring. Several techniques have been developed for acquiring 3-D point coordinates of infrastructure, such as laser scanning. Although the method yields accurate results, the high device costs and human effort required render the process infeasible for generic applications in the construction industry. A quick and reliable approach, which is based on the principles of stereo vision, is proposed for generating a depth map of an infrastructure. Initially, two images are captured by two similar stereo cameras at the scene of the infrastructure. A Harris feature detector is used to extract feature points from the first view, and an innovative adaptive window-matching technique is used to compute feature point correspondences in the second view. A robust algorithm computes the nonfeature point correspondences. Thus, the correspondences of all the points in the scene are obtained. After all correspondences have been obtained, the geometric principles of stereo vision are used to generate a dense depth map of the scene. The proposed algorithm has been tested on several data sets, and results illustrate its potential for stereo correspondence and depth map generation.

Innovative Stereo Vision-Based Approach to Generate Dense Depth Map of Transportation Infrastructure

Three-dimensional (3-D) spatial data of a transportation infrastructure contain useful information for civil engineering applications, including as-built documentation, on-site safety enhancements, and progress monitoring. Several techniques have been developed for acquiring 3-D point coordinates of infrastructure, such as laser scanning. Although the method yields accurate results, the high device costs and human effort required render the process infeasible for generic applications in the construction industry. A quick and reliable approach, which is based on the principles of stereo vision, is proposed for generating a depth map of an infrastructure. Initially, two images are captured by two similar stereo cameras at the scene of the infrastructure. A Harris feature detector is used to extract feature points from the first view, and an innovative adaptive window-matching technique is used to compute feature point correspondences in the second view. A robust algorithm computes the nonfeature point correspondences. Thus, the correspondences of all the points in the scene are obtained. After all correspondences have been obtained, the geometric principles of stereo vision are used to generate a dense depth map of the scene. The proposed algorithm has been tested on several data sets, and results illustrate its potential for stereo correspondence and depth map generation.

Novel applications of BEM based Poisson level set approach

Accurate and efficient computation of the distance function d for a given domain is important for many areas of numerical modeling. Partial differential (e.g. HamiltonJacobi type) equation based distance function algorithms have desirable computational efficiency and accuracy. In this study, as an alternative, a Poisson equation based level set (distance function) is considered and solved using the meshless boundary element method (BEM). The application of this for shape topology analysis, including the medial axis for domain decomposition, geometric de-featuring and other aspects of numerical modeling is assessed. © 2011 Elsevier Ltd. All rights reserved.

Linear regression under fixed-rank constraints: A Riemannian approach

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to high-dimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixed-rank matrices. Numerical experiments on benchmarks suggest that the proposed algorithms compete with the state-of-the-art, and that manifold optimization offers a versatile framework for the design of rank-constrained machine learning algorithms. Copyright 2011 by the author(s)/owner(s).

An approach to multi-fidelity optimization of aeroengine compression systems

The aerodynamic design of turbomachinery presents the design optimisation community with a number of exquisite challenges. Chief among these are the size of the design space and the extent of discontinuity therein. This discontinuity can serve to limit the full exploitation of high-fidelity computational fluid dynamics (CFD): such codes require detailed geometric information often available only sometime after the basic configuration of the machine has been set by other means. The premise of this paper is that it should be possible to produce higher performing designs in less time by exploiting multi-fidelity techniques to effectively harness CFD earlier in the design process, specifically by facilitating its participation in configuration selection. The adopted strategy of local multi-fidelity correction, generated on demand, combined with a global search algorithm via an adaptive trust region is first tested on a modest, smooth external aerodynamic problem. Speed-up of an order of magnitude is demonstrated, comparable to established techniques applied to smooth problems. A number of enhancements aimed principally at effectively evaluating a wide range of configurations quickly is then applied to the basic strategy, and the emerging technique is tested on a generic aeroengine core compression system. A similar order of magnitude speed-up is achieved on this relatively large and highly discontinuous problem. A five-fold increase in the number of configurations assessed with CFD is observed. As the technique places constraints neither on the underlying physical modelling of the constituent analysis codes nor on first-order agreement between those codes, it has potential applicability to a range of multidisciplinary design challenges. © 2012 by Jerome Jarrett and Tiziano Ghisu.

Ultrafast geometric manipulation of electron spin and detection of the geometric phase via Faraday rotation spectroscopy

Time-resolved Faraday rotation spectroscopy is currently exploited as a powerful technique to probe spin dynamics in semiconductors. We propose here an all-optical approach to geometrically manipulate electron spin and to detect the geometric phase by this type of extremely sensitive experiment. The global nature of the geometric phase can make the quantum manipulation more stable, which may find interesting applications in quantum devices.

Modelling raindrop impact and splash erosion processes within a spatial cell: a stochastic approach

A new approach is proposed to simulate splash erosion on local soil surfaces. Without the effect of wind and other raindrops, the impact of free-falling raindrops was considered as an independent event from the stochastic viewpoint. The erosivity of a single raindrop depending on its kinetic energy was computed by an empirical relationship in which the kinetic energy was expressed as a power function of the equivalent diameter of the raindrop. An empirical linear function combining the kinetic energy and soil shear strength was used to estimate the impacted amount of soil particles by a single raindrop. Considering an ideal local soil surface with size of I m x I m, the expected number of received free-failing raindrops with different diameters per unit time was described by the combination of the raindrop size distribution function and the terminal velocity of raindrops. The total splash amount was seen as the sum of the impact amount by all raindrops in the rainfall event. The total splash amount per unit time was subdivided into three different components, including net splash amount, single impact amount and re-detachment amount. The re-detachment amount was obtained by a spatial geometric probability derived using the Poisson function in which overlapped impacted areas were considered. The net splash amount was defined as the mass of soil particles collected outside the splash dish. It was estimated by another spatial geometric probability in which the average splashed distance related to the median grain size of soil and effects of other impacted soil particles and other free-falling raindrops were considered. Splash experiments in artificial rainfall were carried out to validate the availability and accuracy of the model. Our simulated results suggested that the net splash amount and re-detachment amount were small parts of the total splash amount. Their proportions were 0.15% and 2.6%, respectively. The comparison of simulated data with measured data showed that this model could be applied to simulate the soil-splash process successfully and needed information of the rainfall intensity and original soil properties including initial bulk intensity, water content, median grain size and some empirical constants related to the soil surface shear strength, the raindrop size distribution function and the average splashed distance. Copyright (c) 2007 John Wiley & Sons, Ltd.

Efficient FPGA Hardware Development: A Multi-Language Approach

This paper presents a multi-language framework to FPGA hardware development which aims to satisfy the dual requirement of high-level hardware design and efficient hardware implementation. The central idea of this framework is the integration of different hardware languages in a way that harnesses the best features of each language. This is illustrated in this paper by the integration of two hardware languages in the form of HIDE: a structured hardware language which provides more abstract and elegant hardware descriptions and compositions than are possible in traditional hardware description languages such as VHDL or Verilog, and Handel-C: an ANSI C-like hardware language which allows software and hardware engineers alike to target FPGAs from high-level algorithmic descriptions. On the one hand, HIDE has proven to be very successful in the description and generation of highly optimised parameterisable FPGA circuits from geometric descriptions. On the other hand, Handel-C has also proven to be very successful in the rapid design and prototyping of FPGA circuits from algorithmic application descriptions. The proposed integrated framework hence harnesses HIDE for the generation of highly optimised circuits for regular parts of algorithms, while Handel-C is used as a top-level design language from which HIDE functionality is dynamically invoked. The overall message of this paper posits that there need not be an exclusive choice between different hardware design flows. Rather, an integrated framework where different design flows can seamlessly interoperate should be adopted. Although the idea might seem simple prima facie, it could have serious implications on the design of future generations of hardware languages.

Geometric bonding effects in the X2A1, A2∑+u, and B2IIg states of Li2F

Published ab-initio and pseudopotential calculations for the dialkali halide systems suggest that the preferred co-linear geometry is for the metal to approach the metal end of the alkali halide. Here, ab-initio calculations on the Li2F system reveal that the well depth on the halide side in this radical is much deeper and is a local saddle-point associated with the ionic non-linear global minima. Although many features of the pseudopotential surfaces are confirmed, significant differences are apparent including the existence of a linear excited state instead of a triangular one, a considerably deeper global minimum some 50% lower in energy and a close approach between the X2A1 and the states, with the minimum 87 kJ mol-1 below the ground state asymptote. All the results can be rationalised as the avoided crossings between a long range, covalent potential dominant within the LiLiF geometry and an ionic state that forms the global minimum. Calculations on the 3rd 2A' potential indicate that even for Li + LiF collisions at ultracold temperatures the collision dynamics could involve as many as three electronic states.

Modeling the geometric characteristics of five-dimensionally woven composites

An analytical modeling approach for the prediction of the geometric characteristics of five-dimensional (5D) woven composites has been formulated. The model is driven by readily available data including the weaving parameters and constituent material properties. The new model calculates the individual proportions of fiber in each direction, areal density, overall fiber volume fraction, and laminate thickness. This information is useful for the engineer in the design and manufacture of 5D woven composites. In addition the present model outputs the mathematical definition of the 5D woven composite unit cell, which could be implemented as the geometric input for a downstream analytical model that is capable of predicting the elastic stiffness of 5D woven composites. Input parameters have been sourced from existing published work and the subsequent predictions made by the model are compared with the available experimental data on 5D woven composites.

Spontaneous spin polarization and charge localization in metal nanowires: the role of a geometric constriction

An idealized jellium model of conducting nanowires with a geometric constriction is investigated by density functional theory (DFT) in the local spin density (LSD) approximation. The results reveal a fascinating variety of spin and charge patterns arising in wires of sufficiently low (r(s) >= 15) average electron density, pinned at the indentation by an apparent attractive interaction with the constriction. The spin-resolved frequency-dependent conductivity shows a marked asymmetry in the two spin channels, reflecting the spontaneous spin polarization around the wire neck. The relevance of the computational results is discussed in relation to the so-called 0.7 anomaly found by experiments in the low-frequency conductivity of nanowires at near-breaking conditions (see 2008 J. Phys.: Condens Matter 20, special issue on the 0.7 anomaly). Although our mean-field approach cannot account for the intrinsic many-body effects underlying the 0.7 anomaly, it still provides a diagnostic tool to predict impending transitions in the electronic structure.

Validation of a passive stereophotogrammetry system for imaging of the breast: A geometric analysis

The overall aim of this study was to assess the accuracy, reproducibility and stability of a high resolution passive stereophotogrammetry system to image a female mannequin torso, to validate measurements made on the textured virtual surface compared with those obtained using manual techniques and to develop an approach to make objective measurements of the female breast. 3D surface imaging was carried out on a textured female torso and measurements made in accordance with the system of mammometrics. Linear errors in measurements were less than 0.5 mm, system calibration produced errors of less than 1.0 mm over 94% over the surface and intra-rater reliability measured by ICC = 0.999. The mean difference between manual and digital curved surface distances was 1.36 mm with maximum and minimum differences of 3.15 mm and 0.02 mm, respectively. The stereophotogrammetry system has been demonstrated to perform accurately and reliably with specific reference to breast assessment. (C) 2011 IPEM. Published by Elsevier Ltd. All rights reserved.