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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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Editorial collection (peer-reviewed)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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- Malmberg, Filip, 1980-, et al.
(author)
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Seeded Segmentation Based on Object Homogeneity
- 2012
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In: Proceedings of the 21st International Conference on Pattern Recognition (ICPR). - 9781467322164 ; , s. 21-24
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Conference paper (peer-reviewed)abstract
- Seeded segmentation methods attempt to solve the segmentation problem in the presence of prior knowledge in the form of a partial segmentation, where a small subset of the image elements (seed-points) have been assigned correct segmentation labels. Common for most of the leading methods in this area is that they seek to find a segmentation where the boundaries of the segmented regions coincide with sharp edges in the image. Here, we instead propose a method for seeded segmentation that seeks to divide the image into areas of homogeneous pixel values. The method is based on the computation of minimal cost paths in a discrete representation of the image, using a novel path-cost function. The utility of the proposed method is demonstrated in a case study on segmentation of white matter hyperintensitities in MR images of the human brain.
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- Malmberg, Filip, 1980-, et al.
(author)
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When Can lp-norm Objective Functions Be Minimized via Graph Cuts?
- 2018
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In: Combinatorial Image Analysis. - Cham : Springer. - 9783030052874 ; , s. 112-117
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Conference paper (peer-reviewed)abstract
- Techniques based on minimal graph cuts have become a standard tool for solving combinatorial optimization problems arising in image processing and computer vision applications. These techniques can be used to minimize objective functions written as the sum of a set of unary and pairwise terms, provided that the objective function is sub-modular. This can be interpreted as minimizing the l1-norm of the vector containing all pairwise and unary terms. By raising each term to a power p, the same technique can also be used to minimize the lp-norm of the vector. Unfortunately, the submodularity of an l1-norm objective function does not guarantee the submodularity of the corresponding lp-norm objective function. The contribution of this paper is to provide useful conditions under which an lp-norm objective function is submodular for all p>= 1, thereby identifying a large class of lp-norm objective functions that can be minimized via minimal graph cuts.Techniques based on minimal graph cuts have become a standard tool for solving combinatorial optimization problems arising in image processing and computer vision applications. These techniques can be used to minimize objective functions written as the sum of a set of unary and pairwise terms, provided that the objective function is submodular. This can be interpreted as minimizing the l1l1-norm of the vector containing all pairwise and unary terms. By raising each term to a power p, the same technique can also be used to minimize the lplp-norm of the vector. Unfortunately, the submodularity of an l1l1-norm objective function does not guarantee the submodularity of the corresponding lplp-norm objective function. The contribution of this paper is to provide useful conditions under which an lplp-norm objective function is submodular for all p≥1p≥1, thereby identifying a large class of lplp-norm objective functions that can be minimized via minimal graph cuts.
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- Strand, Robin, 1978-, et al.
(author)
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The Minimum Barrier Distance : A Summary of Recent Advances
- 2017
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In: Discrete Geometry for Computer Imagery. DGCI 2017. - Cham : Springer. - 9783319662725 - 9783319662718 ; , s. 57-68
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Conference paper (peer-reviewed)abstract
- In this paper we present an overview and summary of recent results of the minimum barrier distance (MBD), a distance operator that is a promising tool in several image processing applications. The theory constitutes of the continuous MBD in Rn, its discrete formulation in Zn (in two different natural formulations), and of the discussion of convergence of discrete MBDs to their continuous counterpart. We describe two algorithms that compute MBD, one very fast but returning only approximate MBD, the other a bit slower, but returning the exact MBD. Finally, some image processing applications of MBD are presented and the directions of potential future research in this area are indicated.
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