Dr Vitaliy Kurlin: mathematics & computer science

Data Science theory and applications. Everything is possible!

E-mail: vitaliy.kurlin(at)gmail.com, University of Liverpool, UK

Project Persistent skeletons based on papers in

PR 2021 | TopoInVis 2019 | AAM 2019 | CGF 2015 | CAIP 2015

HoPeS : a Homologically Persistent Skeleton outperforms other algorithms on noisy data

HoPeS on 10 points 1D persistence of 10 points
  • Phil Smith, Vitaliy Kurlin.
  • Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise.
  • Pattern Recognition, v.115 (2021), 107902.
  • PDF [extended, 48 pages, 7.6M]   url [official link]

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ASk : Approximate Skeleton of a point cloud

micelle
  • Yury Elkin, Di Liu, Vitaliy Kurlin.
  • A fast approximate skeleton with guarantees for any cloud of points in a Euclidean space.
  • Proceedings of TopoInVis 2019 (Topology-based methods in Visualization), to appear as a chapter in the Springer book Topological Methods in Data Analysis and Visualization VI (2021)
  • PDF [19 pages, 6.8M]  

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Higher-dimensional skeleton HoPeS

2D HoPeS
  • Sara Kalisnik, Vitaliy Kurlin, Davorin Lesnik.
  • A higher-dimensional Homologically Persistent Skeleton.
  • Advances in Applied Mathematics, v.102 (2019), p.113-142.
  • PDF [30 pages, 1M]   url [official link]

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HoPeS : a Homologically Persistent Skeleton

cloud   skeleton
  • Vitaliy Kurlin.
  • A one-dimensional Homologically Persistent Skeleton of a point cloud in any metric space.
  • Computer Graphics Forum, v. 34, no. 5 (2015), p. 253-262.
    A special issue devoted to SGP 2015: Eurographics Symposium on Geometry Processing.
  • PDF [10 pages, 3.2M]   Slides [pdf, 32 pages, 4.8M]   bib [code: beta-version]

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HePeS applications to image skeletonisation

hieroglyph reconstruction hieroglyph reconstruction
  • Vitaliy Kurlin.
  • A Homologically Persistent Skeleton is a fast and robust descriptor of interest points in 2D images.
  • Lecture Notes in Computer Science, v. 9265 (2015), p. 606-617.
  • Proceedings of CAIP 2015: Computer Analysis of Images and Patterns.
  • PDF [extended: 26 pages, 3M]   Poster [pdf, 1.1M]   bib [code: beta]  

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