Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model

Given a 3D binary digital image I, we define and compute an edge-weighted tree, called Homological Region Tree (or Hom-Tree, for short). It coincides, as unweighted graph, with the classical Region Adjacency Tree of black 6-connected components (CCs) and white 26- connected components of I. In addition, we define the weight of an edge (R, S) as the number of tunnels that the CCs R and S “share”. The Hom-Tree structure is still an isotopic invariant of I. Thus, it provides information about how the different homology groups interact between them, while preserving the duality of black and white CCs. An experimentation with a set of synthetic images showing different shapes and different complexity of connected component nesting is performed for numerically validating the method.Ministerio de Economía y Competitividad MTM2016-81030-

Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores

Importance of low-angle grain boundaries in YBa2Cu3O7-delta coated conductors

Over the past ten years the perception of grain boundaries in YBa2Cu3O7-δ conductors has changed greatly. They are no longer a problem to be eliminated but an inevitable and potentially favourable part of the material. This change has arisen as a consequence of new manufacturing techniques which result in excellent grain alignment, reducing the spread of grain boundary misorientation angles. At the same time there is considerable recent evidence which indicates that the variation of properties of grain boundaries with mismatch angle is more complex than a simple exponential decrease in critical current. This is due to the fact that low-angle grain boundaries represent a qualitatively different system to high angle boundaries. The time is therefore right for a targetted review of research into low-angle YBa2Cu3O7-δ grain boundaries. This article does not purport to be a comprehensive review of the physics of grain boundaries as found in YBa2Cu3O7-δ in general; for a broader overview we would recommend that the reader consult the comprehensive review of Hilgenkamp and Mannhart (Rev. Mod. Phys., 74, 485, 2002). The purpose of this article is to review the origin and properties of the low-angle grain boundaries found in YBa2Cu3O7-δ coated conductors both individually and as a collective system.EPSR

Linearization of homogeneous, nearly-isotropic cosmological models

Homogeneous, nearly-isotropic Bianchi cosmological models are considered. Their time evolution is expressed as a complete set of non-interacting linear modes on top of a Friedmann-Robertson-Walker background model. This connects the extensive literature on Bianchi models with the more commonly-adopted perturbation approach to general relativistic cosmological evolution. Expressions for the relevant metric perturbations in familiar coordinate systems can be extracted straightforwardly. Amongst other possibilities, this allows for future analysis of anisotropic matter sources in a more general geometry than usually attempted. We discuss the geometric mechanisms by which maximal symmetry is broken in the context of these models, shedding light on the origin of different Bianchi types. When all relevant length-scales are super-horizon, the simplest Bianchi I models emerge (in which anisotropic quantities appear parallel transported). Finally we highlight the existence of arbitrarily long near-isotropic epochs in models of general Bianchi type (including those without an exact isotropic limit).Comment: 31 pages, 2 figures. Submitted to CQ

Network Centralities in Polycentric Urban Regions: Methods for the Measurement of Spatial Metrics

The primary aim of this thesis is to explain the complex spatial organisations of polycentric urban regions (PURs). PURs are a form of regional morphology that often evolves from post-industrial structures and describe a subnational area featuring a plurality of urban centres. As of today, the analysis of the spatial organisation of PURs constitutes a hitherto uncharted territory. This is due to PURs’ inherent complexity that poses challenges for their conceptualisation. In this context, this thesis reviews theories on the spatial organisation of regions and cities and seeks to make a foundational methodological contribution by joining space syntax and central place theory in the conceptualisation of polycentric urban regions. It takes into account human agency embedded in the physical space, as well as the reciprocal effect of the spatial organisation for the emergence of centralities and demonstrates how these concepts can give insights into the fundamental regional functioning. The thesis scrutinises the role that the spatial organisation plays in such regions, in terms of organising flows of goods and people, ordering locational occupation and fostering centres of commercial activity. It proposes a series of novel measurements and techniques to analyse large and messy datasets. This includes a method for the application of large-scale volunteered geographic information in street network analysis. This is done, in the context of two post-industrial regions: the German Ruhr Valley and the British Nottinghamshire, Derbyshire and Yorkshire region. The thesis’ contribution to the understanding of regional spatial organisation and the study of regional morphology lies in the identification of spatial structural features of socio-economic potentials of regions and particular areas within them. It constitutes the first comparative study of comprehensive large-scale regional spatial networks and presents a framework for the analysis of regions and the evaluation of the predictive potential of spatial networks for socio-economic patterns and the location of centres in regional contexts

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Contact volume based model and computational issues

The contact volume based energy-conserving contact model is presented in the current paper as a specialised version of the general energy-conserving contact model established in the first paper of this series (Feng, 2020). It is based on the assumption that the contact energy potential is taken to be a function of the contact volume between two contacting bodies with arbitrary (convex and concave) shapes in both 2D and 3D cases. By choosing such a contact energy function, the full normal contact features can be determined without the need to introduce any additional assumptions/parameters. By further exploiting the geometric properties of the contact surfaces concerned, more effective integration schemes are developed to reduce the evaluation costs involved. When a linear contact energy function of the contact volume is adopted, a linear contact model is derived in which only the intersection between two contact shapes is needed, thereby substantially improving both efficiency and applicability of the proposed contact model. A comparison of this linear energy-conserving contact model with some existing models for discs and spheres further reveals the nature of the proposed model, and provides insights into how to appropriately choose the stiffness parameter included in the energy function. For general non-spherical shapes, mesh representations are required. The corresponding computational aspects are described when shapes are discretised into volumetric meshes, while new developments are presented and recommended for shapes that are represented by surface triangular meshes. Owing to its additive property of the contact geometric features involved, the proposed contact model can be conducted locally in parallel using GPU or GPGPU computing without occurring much communication overhead for shapes represented as either a volumetric or surface triangular mesh. A set of examples considering the elastic impact of two shapes are presented to verify the energy-conserving property of the proposed model for a wide range of concave shapes and contact scenarios, followed by examples involving large numbers of arbitrarily shaped particles to demonstrate the robustness and applicability for more complex and realistic problems