Dr Vitaliy Kurlin: mathematics & computer science

Current research: topological data analysis. Everything is possible!

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

Selected papers in top journals and conferences

Back to Top of this page | Back to Home page

Smaller research grants, see also larger awards

LMS logo Since 2017 the organiser of the LMS-funded network Applied Algebraic Topology with 3 meetings per year at the Universities of Liverpool, Queen Mary (G.Bianconi, M.Farber), Southampton (J.Brodzki, J.Grbić).
EPSRC logo EPSRC vacation bursaries (value 2×2.7K GBP) at the University of Liverpool for 2nd year undergraduates Simon Hirst (2017) and Gee Jack (2018).
LMS logo Summer bursary of the London Mathematical Society for Philip Smith (value 1.1K GBP) to work on our project Superpixel meshes for faster image and video processing in August - September 2016, closely related to the collaboration with Microsoft Research Cambridge.
IAS image Christopherson/Knott fellowship at Institute of Advanced Study (left after moving to Liverpool, UK). Title : Optimal meshes of superpixels for faster image processing (7.5K GBP for a 3-month teaching replacement).
Alan Turing Institute logo Conference grant (3K GBP, jointly with M.Grinfeld and M.Haw) to run the ATI strategic workshop on 14 March 2016 : Topological Data Analysis in Materials Science and Engineering.
LMS logo Travel grant of the London Mathematical Society to give the contributed 20-min talk Topological Computer Vision in the section Mathematical Image and Signal Processing at 7ECM (European Congress of Mathematicians) at TU Berlin on 18-22 July 2016.
ESF logo Travel grant (1.7K Euros) by the ACAT (Applied and Computational Algebraic Topology) network of ESF (European Science Foundation) to visit IST Austria (March 2015).
EC logo INTAS PhD Fellowship (10K Euros) at Moscow State University (Russia), March 2001 - February 2003, covered research collaboration at Universities of Montpellier II, Liverpool, Dijon, Toulouse III, Paris VII.

Back to Top of this page | Back to Home page

All papers in the reverse chronological order (Google scholar)

2017 : EMMCVPR   JEI   MathVis   arXiv:1701.08395

2016 : ISVC   PRL   CCIS

2015 : CGF   CAIP   CCCG   IVAPP

2014 : CVPR   CTIC   ICRoM

2013 : JAPS   Image-A

2012 : HHA

Earlier work in pure mathematics: 2008 - 2010 | 2005 - 2007 | 2001 - 2004 | 1999 - 2000

2017 : EMMCVPR   JEI   MathVis   arXiv:1701.08395

mesh reconstruction
  • V. Kurlin, D. Harvey.
  • Superpixels Optimized by Color and Shape (SOCS).
  • Proceedings of EMMCVPR 2017 (Energy Minimization Methods in Computer Vision and Pattern Recognition), 14 pages, LNCS 10746, Springer.
  • PDF [14 pages, 4.9M]   web [project page]   bib [reference]
Voronoi vs CCM
  • J. Forsythe, V. Kurlin.
  • Convex Constrained Meshes for superpixel segmentations of images.
  • Journal of Electronic Imaging, 26(6), 061609 (13 pages), 2017
    (substantially extended version of the conference paper at ISVC 2016).
  • PDF [30 pages, 6.5M]   web [project page]   bib [reference]
knotted protein

Back to Top of this page | Back to Home page

2016 : ISVC   PRL   CCIS

mesh reconstruction
  • J. Forsythe, V. Kurlin, A. Fitzgibbon.
  • Resolution-independent superpixels based on convex constrained meshes without small angles.
  • Proceedings of ISVC 2016: International Symposium on Visual Computing.
  • Lecture Notes in Computer Science, v. 10072, p. 223-233.
  • PDF [10 pages, 3.7M]   web [project page]   bib [reference]
original image noisy input segmentation
  • V. Kurlin.
  • A fast persistence-based segmentation of noisy 2D clouds with provable guarantees.
  • Pattern Recognition Letters, v. 83 (2016), p. 3-12.
  • PDF [full version: 16 pages, 4.2M]   web [project page]   bib [reference]   url [official]
knotted neuron

Back to Top of this page | Back to Home page

2015 : 4 papers in   CGF   CAIP   CCCG   IVAPP

cloud   skeleton
  • V. 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]   web [project page]   bib [reference]   url [official link]
hieroglyph reconstruction hieroglyph reconstruction
  • V. Kurlin.
  • A Homologically Persistent Skeleton is a fast and robust descriptor of interest points in 2D images.
  • Lecture Notes in Computer Science, v. 9256 (2015), p. 606-617.
  • (Proceedings of CAIP 2015: Computer Analysis of Images and Patterns).
  • PDF [12 pages, 1.2M]   web [project page]   bib [reference]   url [official link]
disk packing
  • H. Edelsbrunner, M. Iglesias-Ham, V. Kurlin.
  • Relaxed disk packing.
  • Proceedings of CCCG 2015: Canadian Conference on Computational Geometry, p.128-135.
  • PDF [8 pages, 390K]   web [arXiv:1505.03402]   url [proceedings in pdf, 30M]
  • @inproceedings{EIHK15CCCG,
    	author = {Edelsbrunner, E. and Iglesias-Ham, M. and  Kurlin, V.},
    	title = {Relaxed disk packing},
    	booktitle = {Proceedings of CCCG 2015: Canadian Conference on Computational Geometry}, 
       	year = {2015}
    }
a 3-page embedding of a Hopf graph
  • V. Kurlin.
  • A linear time algorithm for visualizing knotted structures in 3 pages.
  • Proceedings of IVAPP 2015: Information Visualization Theory and Applications, p. 5-16.
  • PDF [12 pages, 2.5M]   web [project page]   bib [reference]   url [official link]

Back to Top of this page | Back to Home page

2014 : 3 papers in   CVPR   CTIC   ICRoM

count holes in a cloud
  • V. Kurlin.
  • A fast and robust algorithm to count topologically persistent holes in noisy clouds.
  • Proceedings of CVPR 2014: Computer Vision and Pattern Recognition, p. 1458-1463
    (top 3 conference in Computer Science, the highest h-index conference in any field).
  • pdf [extended: 10 pages, 1.6M]   web [project page]   bib [reference]
noisy input automatic output
  • V. Kurlin.
  • Auto-completion of contours in sketches, maps and sparse 2D images based on topological persistence.
  • Proceedings of workshop CTIC (Computational Topology in Image Context) at SYNASC 2014
  • (Symposium on Symbolic and Numeric Algorithms for Scientific Computing), p. 594-601.
  • PDF [8 pages, 1.1M]   web [project page]   bib [reference]   bib [code: beta-version]
round robots in a metric graph
  • V. Kurlin, M. Safi-Samghabadi.
    Computing a skeleton of the configuration space of 2 round robots on a metric graph.
  • Proceedings of ICRoM 2014: International Conference on Robotics and Mechatronics, p. 723-729.
  • PDF [7 pages, 370K]   Slides [pdf, 32 pages, 1.6M]   url [official link]
  • @inproceedings{KS14ICRoM,
    	author = {Kurlin, V., Safi-Samghabadi, M.},
    	title = {Computing a skeleton of the configuration space of 2 round robots on a metric graph},
    	booktitle = {Proceedings of ICRoM 2014: International Conference on Robotics and Mechatronics},
    	pages = {723-729},
       	year = {2014}
    }
  • Input: a radius r of 2 robots and a metric graph G with fixed lengths of edges.
  • Output: connected components of the configuration space of 2 robots in G.
  • Running time: O(n4) for the number n of vertices in the given graph G.
  • Abstract. A connected metric graph G with n vertices and without loops and multiple edges can be represented as an n-by-n matrix whose entries are length of edges of G. A robot in the metric graph G is a metric ball with a centre x in G and a radius r>0. The configuration space OC(G,r) of 2 robots in G is the set of all centers (x,y) such that the centres x,y are at least 2r away from each other. We introduce the configuration skeleton CS(G,r) that captures all connectivity information of the space OC(G,r). As a consequence we get a polynomial time algorithm to find all connected components of OC(G,r) that are maximal subsets of all positions (x,y) connectable by collision-free motions.

Back to Top of this page | Back to Home page

2013 : 2 papers

Back to Top of this page | Back to Home page

2012 : 1 paper

Back to Top of this page | Back to Home page

2008 - 2010 : earlier work in pure mathematics

Back to Top of this page | Back to Home page

2005 - 2007 : postdoctoral work

Back to Top of this page | Back to Home page

2001 - 2004 : PhD studies

Back to Top of this page | Back to Home page

1999 - 2000 : MSc studies

Back to All papers | Back to Top of this page | Back to Home page

Invited lectures at international conferences

2017 | 2016 | 2015 | 2011-2014 | 2007-2010 | 2005-2006 | 1999-2004

Oral presentations given in 2017

Back to All lectures | Back to Top of this page | Back to Home page

Oral presentations given in 2016

Back to All lectures | Back to Top of this page | Back to Home page

Oral presentations given in 2015

Back to All lectures | Back to Top of this page | Back to Home page

Oral presentations given in 2011-2014

Back to All lectures | Back to Top of this page | Back to Home page

Oral presentations given in 2007-2010

Back to All lectures | Back to Top of this page | Back to Home page

Oral presentations given in 2005-2006

Back to All lectures | Back to Top of this page | Back to Home page

Oral presentations given in 1999-2004

Back to All lectures | Back to Top of this page | Back to Home page

Seminar of the Topological Data Analysis group

Back to Top of this page | Back to Home page

Co-authors in the alphabetical order

Back to Top of this page | Back to Home page