The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Jean Marc Gambaudo - One of the best experts on this subject based on the ideXlab platform.
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rapid convergence to frequency for substitution tilings of the plane
Communications in Mathematical Physics, 2011Co-Authors: Jose Alisteprieto, Daniel Coronel, Jean Marc GambaudoAbstract:This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan Curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan Curve.
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rapid convergence to frequency for substitution tilings of the plane
Communications in Mathematical Physics, 2011Co-Authors: Jose Alisteprieto, Daniel Coronel, Jean Marc GambaudoAbstract:This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan Curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan Curve.
Carlo Tomasi - One of the best experts on this subject based on the ideXlab platform.
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topological persistence on a Jordan Curve
International Conference on Acoustics Speech and Signal Processing, 2012Co-Authors: Ying Zheng, Carlo TomasiAbstract:Topological persistence measures the resilience of extrema of a function to perturbations, and has received increasing attention in computer graphics, visualization and computer vision. While the notion of topological persistence for piece-wise linear functions defined on a simplicial complex has been well studied, the time complexity of all the known algorithms are super-linear (e.g. O(n log n)) in the size n of the complex. We give an O(n) algorithm to compute topological persistence for a function defined on a Jordan Curve. To the best of our knowledge, our algorithm is the first to attain linear asymptotic complexity, and is asymptotically optimal. We demonstrate the usefulness of persistence in shape abstraction and compression.
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ICASSP - Topological persistence on a Jordan Curve
2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012Co-Authors: Ying Zheng, Carlo TomasiAbstract:Topological persistence measures the resilience of extrema of a function to perturbations, and has received increasing attention in computer graphics, visualization and computer vision. While the notion of topological persistence for piece-wise linear functions defined on a simplicial complex has been well studied, the time complexity of all the known algorithms are super-linear (e.g. O(n log n)) in the size n of the complex. We give an O(n) algorithm to compute topological persistence for a function defined on a Jordan Curve. To the best of our knowledge, our algorithm is the first to attain linear asymptotic complexity, and is asymptotically optimal. We demonstrate the usefulness of persistence in shape abstraction and compression.
Jose Alisteprieto - One of the best experts on this subject based on the ideXlab platform.
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rapid convergence to frequency for substitution tilings of the plane
Communications in Mathematical Physics, 2011Co-Authors: Jose Alisteprieto, Daniel Coronel, Jean Marc GambaudoAbstract:This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan Curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan Curve.
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rapid convergence to frequency for substitution tilings of the plane
Communications in Mathematical Physics, 2011Co-Authors: Jose Alisteprieto, Daniel Coronel, Jean Marc GambaudoAbstract:This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan Curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan Curve.
Josef Šlapal - One of the best experts on this subject based on the ideXlab platform.
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Topological structuring of the digital plane
Discrete Mathematics and Theoretical Computer Science, 2013Co-Authors: Josef ŠlapalAbstract:We discuss an Alexandroff topology on ℤ2 having the property that its quotient topologies include the Khalimsky and Marcus-Wyse topologies. We introduce a further quotient topology and prove a Jordan Curve theorem for it.
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A Jordan Curve theorem with respect to a pretopology on ℤ2
International Journal of Computer Mathematics, 2013Co-Authors: Josef ŠlapalAbstract:We study a pretopology on ℤ2 having the property that the Khalimsky topology is one of its quotient pretopologies. Using this fact, we prove an analogue of the Jordan Curve theorem for this pretopology, thus showing that such a pretopology provides a large variety of digital Jordan Curves. Some consequences of this result are discussed too.
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a Jordan Curve theorem in the digital plane
International Workshop on Combinatorial Image Analysis, 2011Co-Authors: Josef ŠlapalAbstract:We study a certain Alexandroff topology on Z2 and some of its quotient topologies including the Khalimsky one. By proving an analogue of the Jordan Curve theorem for this topology we show that it provides a large variety of digital Jordan Curves. Some consequences of this result are discussed, too.
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IWCIA - A Jordan Curve theorem in the digital plane
Lecture Notes in Computer Science, 2011Co-Authors: Josef ŠlapalAbstract:We study a certain Alexandroff topology on Z2 and some of its quotient topologies including the Khalimsky one. By proving an analogue of the Jordan Curve theorem for this topology we show that it provides a large variety of digital Jordan Curves. Some consequences of this result are discussed, too.
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Jordan Curve theorems with respect to certain pretopologies on Z
2009Co-Authors: Josef ŠlapalAbstract:We discuss four quotient pretopologies of a certain basic topology on Z2. Three of them are even topologies and include the wellknown Khalimsky and Marcus-Wyse topologies. Some known Jordan Curves in the basic topology are used to prove Jordan Curve theorems that identify Jordan Curves among simple closed ones in each of the four quotient pretopologies.
Daniel Coronel - One of the best experts on this subject based on the ideXlab platform.
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rapid convergence to frequency for substitution tilings of the plane
Communications in Mathematical Physics, 2011Co-Authors: Jose Alisteprieto, Daniel Coronel, Jean Marc GambaudoAbstract:This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan Curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan Curve.
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rapid convergence to frequency for substitution tilings of the plane
Communications in Mathematical Physics, 2011Co-Authors: Jose Alisteprieto, Daniel Coronel, Jean Marc GambaudoAbstract:This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan Curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan Curve.
