85,161 research outputs found

    Detecting and localizing edges composed of steps, peaks and roofs

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    It is well known that the projection of depth or orientation discontinuities in a physical scene results in image intensity edges which are not ideal step edges but are more typically a combination of steps, peak and roof profiles. However most edge detection schemes ignore the composite nature of these edges, resulting in systematic errors in detection and localization. We address the problem of detecting and localizing these edges, while at the same time also solving the problem of false responses in smoothly shaded regions with constant gradient of the image brightness. We show that a class of nonlinear filters, known as quadratic filters, are appropriate for this task, while linear filters are not. A series of performance criteria are derived for characterizing the SNR, localization and multiple responses of these filters in a manner analogous to Canny's criteria for linear filters. A two-dimensional version of the approach is developed which has the property of being able to represent multiple edges at the same location and determine the orientation of each to any desired precision. This permits junctions to be localized without rounding. Experimental results are presented

    A framework for community detection in heterogeneous multi-relational networks

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    There has been a surge of interest in community detection in homogeneous single-relational networks which contain only one type of nodes and edges. However, many real-world systems are naturally described as heterogeneous multi-relational networks which contain multiple types of nodes and edges. In this paper, we propose a new method for detecting communities in such networks. Our method is based on optimizing the composite modularity, which is a new modularity proposed for evaluating partitions of a heterogeneous multi-relational network into communities. Our method is parameter-free, scalable, and suitable for various networks with general structure. We demonstrate that it outperforms the state-of-the-art techniques in detecting pre-planted communities in synthetic networks. Applied to a real-world Digg network, it successfully detects meaningful communities.Comment: 27 pages, 10 figure

    Composite Fermions, Edge Currents and the Fractional Quantum Hall Effect

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    We present a theory of composite fermion edge states and their transport properties in the fractional and integer quantum Hall regimes. We show that the effective electro-chemical potentials of composite fermions at the edges of a Hall bar differ, in general, from those of electrons. An expression for the difference is given. Composite fermion edge states of three different types are identified. Two of the three types have no analog in previous theories of the integer or fractional quantum Hall effect. The third type includes the usual integer edge states. The direction of propagation of the edge states agrees with experiment. The present theory yields the observed quantized Hall conductances at Landau level filling fractions p/(mp+-1), for m=0,2,4, p= 1,2,3,... It explains the results of experiments that involve conduction across smooth potential barriers and through adiabatic constrictions, and of experiments that involve selective population and detection of fractional edge channels. The relationship between the present work and Hartree theories of composite fermion edge structure is discussed.Comment: 19 pages + 6 figures. Self-unpacking uuencoded postscript. To appear in Physical Review B. Revised version has more details in the Appendix and a discussion of one more experiment in Section

    How Many Communities Are There?

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    Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called communities. The approach is inherently related to clustering with mixture models; and raises a similar model selection problem for the number of communities. The Bayesian information criterion (BIC) is a popular solution, however, for stochastic blockmodels, the conditional independence assumption given the communities of the endpoints among different edges is usually violated in practice. In this regard, we propose composite likelihood BIC (CL-BIC) to select the number of communities, and we show it is robust against possible misspecifications in the underlying stochastic blockmodel assumptions. We derive the requisite methodology and illustrate the approach using both simulated and real data. Supplementary materials containing the relevant computer code are available online.Comment: 26 pages, 3 figure

    Performance improvement of edge detection based on edge likelihood index

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    One of the problems of conventional edge detectors is the difficulty in distinguishing noise and true edges correctly using a simple measurement, such as gradient, local energy, or phase congruency. This paper proposes a performance improvement algorithm for edge detection based on a composite measurement called Edge Likelihood Index (ELI). In principle, given a raw edge map obtained from any edge detectors, edge contours can be extracted where gradient, continuity and smoothness of each contour are measured. The ELI of an edge contour is defined as directly proportional to its gradient and length, and inversely proportional to its smoothness, which offers a more flexible representation of true edges, such as those with low gradient, but continuous and smooth. The proposed method was tested on the South Florida data sets, using the Canny edge operator for edge detection, and evaluated using the Receiver Operator Characteristic curves. It can be shown that the proposed method reduces Bayes risk of ROC curves by over 10% in the aggregate test results.published_or_final_versio
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