| 1. |
- Holroyd, Alexander E., et al.
(författare)
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Minimal matchings of point processes
- 2022
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Ingår i: Probability Theory and Related Fields. - : Springer Science and Business Media LLC. - 0178-8051 .- 1432-2064. ; 184:1-2, s. 571-611
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Tidskriftsartikel (refereegranskat)abstract
- Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in R-d. For a positive (respectively, negative) parameter gamma we consider red-blue matchings that locally minimize (respectively, maximize) the sum of gamma th powers of the edge lengths, subject to locally minimizing the number of unmatched points. The parameter can be viewed as a measure of fairness. The limit gamma -> -infinity is equivalent to Gale-Shapley stable matching. We also consider limits as gamma approaches 0, 1-, 1+ and infinity. We focus on dimension d = 1. We prove that almost surely no such matching has unmatched points. (This question is open for higher d). For each gamma < 1 we establish that there is almost surely a unique such matching, and that it can be expressed as a finitary factor of the points. Moreover, its typical edge length has finite rth moment if and only if r < 1 /2. In contrast, for gamma = 1 there are uncountably many matchings, while for gamma > 1 there are countably many, but it is impossible to choose one in a translation-invariant way. We obtain existence results in higher dimensions (covering many but not all cases). We address analogous questions for one-colour matchings also.
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| 2. |
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Discrete Geometry and Mathematical Morphology : First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24–27, 2021, Proceedings
- 2021
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Samlingsverk (redaktörskap) (refereegranskat)abstract
- This book constitutes the proceedings of the First IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2021, which was held during May 24-27, 2021, in Uppsala, Sweden.The conference was created by joining the International Conference on Discrete Geometry for computer Imagery, DGCI, with the International Symposium on Mathematical Morphology, ISMM.The 36 papers included in this volume were carefully reviewed and selected from 59 submissions. They were organized in topical sections as follows: applications in image processing, computer vision, and pattern recognition; discrete and combinatorial topology; discrete geometry - models, transforms, visualization; discrete tomography and inverse problems; hierarchical and graph-based models, analysis and segmentation; learning-based approaches to mathematical morphology; multivariate and PDE-based mathematical morphology, morphological filtering.The book also contains 3 invited keynote papers.
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| 3. |
- Malmberg, Filip, et al.
(författare)
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An efficient algorithm for exact evaluation of stochastic watersheds
- 2014
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Ingår i: Pattern Recognition Letters. - : Elsevier BV. - 0167-8655 .- 1872-7344. ; 47, s. 80-84
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Tidskriftsartikel (refereegranskat)abstract
- The stochastic watershed is a method for unsupervised image segmentation proposed by Angulo and Jeulin (2007). The method first computes a probability density function (PDF), assigning to each piece of contour in the image the probability to appear as a segmentation boundary in seeded watershed segmentation with randomly selected seeds. Contours that appear with high probability are assumed to be more important. This PDF is then post-processed to obtain a final segmentation. The main computational hurdle with the stochastic watershed method is the calculation of the PDF. In the original publication by Angulo and Jeulin, the PDF was estimated by Monte Carlo simulation, i.e., repeatedly selecting random markers and performing seeded watershed segmentation. Meyer and Stawiaski (2010) showed that the PDF can be calculated exactly, without performing any Monte Carlo simulations, but do not provide any implementation details. In a naive implementation, the computational cost of their method is too high to make it useful in practice. Here, we extend the work of Meyer and Stawiaski by presenting an efficient (quasi-linear) algorithm for exact computation of the PDF. We demonstrate that in practice, the proposed method is faster than any previously reported method by more than two orders of magnitude. The algorithm is formulated for general undirected graphs, and thus trivially generalizes to images with any number of dimensions.
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| 4. |
- Curic, Vladimir, et al.
(författare)
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Salience adaptive structuring elements
- 2012
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Ingår i: IEEE Journal on Selected Topics in Signal Processing. - 1932-4553 .- 1941-0484. ; 6:7, s. 809-819
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Tidskriftsartikel (refereegranskat)abstract
- Spatially adaptive structuring elements adjust their shape to the local structures in the image, and are often defined by a ball in a geodesic distance or gray-weighted distance metric space. This paper introduces salience adaptive structuring elements as spatially variant structuring elements that modify not only their shape, but also their size according to the salience of the edges in the image. Morphological operators with salience adaptive structuring elements shift edges with high salience to a less extent than those with low salience. Salience adaptive structuring elements are less flexible than morphological amoebas and their shape is less affected by noise in the image. Consequently, morphological operators using salience adaptive structuring elements have better properties.
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| 5. |
- Curic, Vladimir, et al.
(författare)
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Salience-Based Parabolic Structuring Functions
- 2013
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Ingår i: Mathematical Morphology and Its Applications to Signal and Image Processing. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642382932 ; 7883, s. 183-194
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Konferensbidrag (refereegranskat)abstract
- It has been shown that the use of the salience map based on the salience distance transform can be useful for the construction of spatially adaptive structuring elements. In this paper, we propose salience-based parabolic structuring functions that are defined for a fixed, predefined spatial support, and have low computational complexity. In addition, we discuss how to properly define adjunct morphological operators using the new spatially adaptive structuring functions. It is also possible to obtain flat adaptive structuring elements by thresholding the salience-based parabolic structuring functions.
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| 6. |
- Luengo, Cris, et al.
(författare)
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Adaptive structuring elements based on salience information
- 2012
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Ingår i: Lecture Notes in Computer Science. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 0302-9743 .- 1611-3349. ; 7594, s. 321-328, s. 321-328
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Konferensbidrag (refereegranskat)abstract
- Adaptive structuring elements modify their shape and size according to the image content and may outperform fixed structuring elements. Without any restrictions, they suffer from a high computational complexity, which is often higher than linear with respect to the number of pixels in the image. This paper introduces adaptive structuring elements that have predefined shape, but where the size is adjusted to the local image structures. The size of adaptive structuring elements is determined by the salience map that corresponds to the salience of the edges in the image, which can be computed in linear time. We illustrate the difference between the new adaptive structuring elements and morphological amoebas. As an example of its usefulness, we show how the new adaptive morphological operations can isolate the text in historical documents.
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| 7. |
- Fridenfalk, Mikael, 1971-
(författare)
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Application for Real-Time Generation of Mathematically Defined 3D Worlds
- 2016. - 1
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Ingår i: Transactions on Computational Science XXVIII: Special Issue on Cyberworlds and Cybersecurity. - Berlin Heidelberg : Springer Berlin/Heidelberg. - 9783662530894 - 9783662530900 ; , s. 45-68
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Konferensbidrag (refereegranskat)abstract
- This paper presents an application developed as a research platform for the real-time generation of 3D L- system structures, including rudimentary game physics and a freely scalable depth buffer that enables the user to interact with the L-system geometries, and in addition to render a mathematically defined world that is virtually unlimited in scope.
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| 8. |
- Fridenfalk, Mikael, 1971-
(författare)
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Cellular Automata in Modular Space : Rigid Systems – Volume I – Number I
- 2015. - 1
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book series presents a new type of cellular automata for 2D pattern generation, characterized by a high reproduction rate, in combination with the application of a small-sized 2D modular square lattice. The presented patterns are in the spirit of mathematical minimalism, generated from rudimentary kernels and a minimal set of rules. In similarity with fractals, this new concept could provide for the generation of patterns and geometries with applications in areas such as, visual arts, logo design, architecture, and game design.
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| 9. |
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| 10. |
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