19,994 research outputs found

    For the Jubilee of Vladimir Mikhailovich Chernov

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    On April 25, 2019, Vladimir Chernov celebrated his 70th birthday, Doctor of Physics and Mathematics, Chief Researcher at the Laboratory of Mathematical Methods of Image Processing of the Image Processing Systems Institute of the Russian Academy of Sciences (IPSI RAS), a branch of the Federal Science Research Center "Crystallography and Photonics RAS and part-Time Professor at the Department of Geoinformatics and Information Security of the Samara National Research University named after academician S.P. Korolev (Samara University). The article briefly describes the scientific and pedagogical achievements of the hero of the day. © Published under licence by IOP Publishing Ltd

    A graph-based mathematical morphology reader

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    This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

    Symmetric measures via moments

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    Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection, namely, one between probabilistic models invariant under a finite group of (non-singular) linear transformations and polynomials invariant under the same group. Two specific aspects of the connection are discussed: generalization of the (uniqueness part of the multivariate) problem of moments and log-linear, or toric, modeling by expansion of invariant terms. A distribution of minuscule subimages extracted from a large database of natural images is analyzed to illustrate the above concepts.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6144 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

    Functional maps representation on product manifolds

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    We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices

    A Global Approach for Solving Edge-Matching Puzzles

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    We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this problem and provide conditions under which it exactly characterizes a puzzle. Using the new representation, we recast the combinatorial, discrete problem of solving puzzles as a global, polynomial system of equations with continuous variables. We further propose new algorithms for generating approximate solutions to the continuous problem by solving a sequence of convex relaxations
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