93,715 research outputs found

    Expanding the Angle of Incidence Tolerance of Unclonable Anticounterfeiting Labels Based on Microlens Arrays and Luminescent Microparticles

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    Unclonable anticounterfeiting labels can be based on micrometer-scale randomness created by stochastic processes like the distribution of luminescent microparticles in a transparent layer. Adding a microlens array to the layer can simplify the hardware needed for authentication in that magnification is no longer required. The bright point-pattern generated under light-emitting diode illumination can be captured by a standard digital camera. Shifting the angle of incidence (AOI) relocates the microlens foci changing the bright point-pattern. This provides unclonability, as several distinct bright point patterns at different AOI can be required for authentication. However, it also imposes technical requirements for the authentication setup in terms of the tolerance with which the AOI must be controlled. Herein, the AOI tolerance, the deviation of angle between reference and test image for which sufficiently similar bright point patterns are recorded that they are considered matching by the authentication algorithm, is investigated. Using microlens arrays with a focal length of 550 μm, the average size of the phosphor particle was varied from 9 ± 1 to 32.5 ± 2 μm, resulting in a relaxation of tolerance from 0.8° to 3.6°. Methods to further increase the AOI tolerance and facilitate the practical implementation of these labels are discussed

    Many-to-Many Graph Matching: a Continuous Relaxation Approach

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    Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a graph matching problem where one seeks a mapping between vertices of two graphs which optimally aligns their structure. In the classical formulation of graph matching, only one-to-one correspondences between vertices are considered. However, in many applications, graphs cannot be matched perfectly and it is more interesting to consider many-to-many correspondences where clusters of vertices in one graph are matched to clusters of vertices in the other graph. In this paper, we formulate the many-to-many graph matching problem as a discrete optimization problem and propose an approximate algorithm based on a continuous relaxation of the combinatorial problem. We compare our method with other existing methods on several benchmark computer vision datasets.Comment: 1

    Graph matching: relax or not?

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    We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly-stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n^2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic

    Structural graph matching using the EM algorithm and singular value decomposition

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    This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method

    A path following algorithm for the graph matching problem

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    We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four datasets: simulated graphs, QAPLib, retina vessel images and handwritten chinese characters. In all cases, the results are competitive with the state-of-the-art.Comment: 23 pages, 13 figures,typo correction, new results in sections 4,5,
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