1,937 research outputs found

    Continuum Percolation in the Relative Neighborhood Graph

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    In the present study, we establish the existence of nontrivial site percolation threshold in the Relative Neighborhood Graph (RNG) for Poisson stationary point process with unit intensity in the plane

    Clique descriptor of affine invariant regions for robust wide baseline image matching

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    Assuming that the image distortion between corresponding regions of a stereo pair of images with wide baseline can be approximated as an affine transformation if the regions are reasonably small, recent image matching algorithms have focused on affine invariant region (IR) detection and its description to increase the robustness in matching. However, the distinctiveness of an intensity-based region descriptor tends to deteriorate when an image includes homogeneous texture or repetitive pattern. To address this problem, we investigated the geometry of a local IR cluster (also called a clique) and propose a new clique-based image matching method. In the proposed method, the clique of an IR is estimated by Delaunay triangulation in a local affine frame and the Hausdorff distance is adopted for matching an inexact number of multiple descriptor vectors. We also introduce two adaptively weighted clique distances, where the neighbour distance in a clique is appropriately weighted according to characteristics of the local feature distribution. Experimental results show the clique-based matching method produces more tentative correspondences than variants of the SIFT-based method

    Dimension reduction for linear separation with curvilinear distances

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    Any high dimensional data in its original raw form may contain obviously classifiable clusters which are difficult to identify given the high-dimension representation. In reducing the dimensions it may be possible to perform a simple classification technique to extract this cluster information whilst retaining the overall topology of the data set. The supervised method presented here takes a high dimension data set consisting of multiple clusters and employs curvilinear distance as a relation between points, projecting in a lower dimension according to this relationship. This representation allows for linear separation of the non-separable high dimensional cluster data and the classification to a cluster of any successive unseen data point extracted from the same higher dimension

    A geometric network model of intrinsic grey-matter connectivity of the human brain

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    Network science provides a general framework for analysing the large-scale brain networks that naturally arise from modern neuroimaging studies, and a key goal in theoretical neuro- science is to understand the extent to which these neural architectures influence the dynamical processes they sustain. To date, brain network modelling has largely been conducted at the macroscale level (i.e. white-matter tracts), despite growing evidence of the role that local grey matter architecture plays in a variety of brain disorders. Here, we present a new model of intrinsic grey matter connectivity of the human connectome. Importantly, the new model incorporates detailed information on cortical geometry to construct ‘shortcuts’ through the thickness of the cortex, thus enabling spatially distant brain regions, as measured along the cortical surface, to communicate. Our study indicates that structures based on human brain surface information differ significantly, both in terms of their topological network characteristics and activity propagation properties, when compared against a variety of alternative geometries and generative algorithms. In particular, this might help explain histological patterns of grey matter connectivity, highlighting that observed connection distances may have arisen to maximise information processing ability, and that such gains are consistent with (and enhanced by) the presence of short-cut connections

    Structural Analysis Algorithms for Nanomaterials

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    Phase transitions in Delaunay Potts models

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    We establish phase transitions for classes of continuum Delaunay multi-type particle systems (continuum Potts models) with infinite range repulsive interaction between particles of different type. In one class of the Delaunay Potts models studied the repulsive interaction is a triangle (multi-body) interaction whereas in the second class the interaction is between pairs (edges) of the Delaunay graph. The result for the edge model is an extension of finite range results in \cite{BBD04} for the Delaunay graph and in \cite{GH96} for continuum Potts models to an infinite range repulsion decaying with the edge length. This is a proof of an old conjecture of Lebowitz and Lieb. The repulsive triangle interactions have infinite range as well and depend on the underlying geometry and thus are a first step towards studying phase transitions for geometry-dependent multi-body systems. Our approach involves a Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn representation of the Potts model. The phase transitions manifest themselves in the percolation of the corresponding random-cluster model. Our proofs rely on recent studies \cite{DDG12} of Gibbs measures for geometry-dependent interactions

    Reconstructing triangulated surfaces from unorganized points through local skeletal stars

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    Surface reconstruction from unorganized points arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from twodimensional slices, and interactive surface sketching. [...]Reconstrução da superfície de pontos desorganizados surge em uma variedade de situações práticas, tais como rastreamento de um objeto a partir de vários pontos de vista, a recuperação de formas biológicas de fatias bi-dimensionais, e esboçar superfícies interativas. [...
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