
Selected papers in top journals and conferences
 V. Kurlin, A fast persistencebased segmentation of noisy 2D clouds with provable guarantees,
PRL : Pattern Recognition Letters, v. 83 (2016), p. 312.  V. Kurlin, A onedimensional Homologically Persistent Skeleton of an unstructured point cloud in any metric space,
CGF : Computer Graphics Forum, v. 34, no. 5 (2015), p. 253262.  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. 14581463
(top 3 conference in Computer Science, the highest hindex conference in any field).  C. Kearton, V. Kurlin,
All 2dimensional links live inside a universal 3dimensional polyhedron,
AGT : Algebraic and Geometric Topology, v. 8 (2008), no. 3, p. 12231247.  V. Kurlin, Compressed Drinfeld associators, Journal of Algebra, v. 292 (2005), no. 1, p. 184242.
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All papers in the reverse chronological order (Google scholar)
2017 : 1 paper in MathVis 2 preprints
2016 : 3 papers in ISVC PRL CCIS
2015 : 4 papers in CGF CAIP CCCG IVAPP
2014 : 3 papers in CVPR CTIC ICRoM
2013 : 2 papers in JAPS ImageA
2012 : 1 paper in HHA
Earlier work in pure mathematics: 2008  2010  2005  2007  2001  2004  1999  2000
2017 : 1 paper in MathVis (more papers are under review)

2016 : 3 papers in ISVC PRL CCIS

@inproceedings{FKF16ISVC, author = {Forsythe, J. and Kurlin, V. and Fitzgibbon, A.}, title = {Resolutionindependent superpixels based on convex constrained meshes without small angles}, booktitle = {Lecture Notes in Computer Science (Proceedings of ISVC 2016)}, volume = {10072}, pages = {223233}, year = {2016} }
 Abstract. The oversegmentation problem for images is studied in the new resolutionindependent formulation when a large image is approximated by a small number of convex polygons with straight edges at subpixel precision. These polygonal superpixels are obtained by refining and extending subpixel edge segments to a full mesh of convex polygons without small angles and with approximation guarantees. Another novelty is the objective error difference between an original pixelbased image and the reconstructed image with a best constant color over each superpixel, which does not need human segmentations. The experiments on images from the Berkeley Segmentation Database show that new meshes are smaller and provide better approximations than the stateoftheart.
 Benchmarks of CCM superpixels: (average number of superpixels, average benchmark in percentages)
 BR (Boundary Recall with the 2pixel offset) : (349.1, 63.95), (376.6, 65.15),(386.6, 65.58), (446.7, 67.1), (528.0, 68.0)
 CUE (Corrected Undersegmentation Error) : (349.1, 4.87), (376.6, 4.67), (386.6, 4.57), (446.7, 4.33), (528.0, 4.24)
 USE (Undersegmentation Symmetric Error) : (349.1, 9.64), (376.6, 9.34), (386.6, 9.14), (446.7, 8.66), (528.0, 8.48)
 If you use these benchmarks for comparison over 500 BSD images, please cite the paper above.
 

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2015 : 4 papers in CGF CAIP CCCG IVAPP
 
 

@inproceedings{EIHK15CCCG, author = {Edelsbrunner, E. and IglesiasHam, M. and Kurlin, V.}, title = {Relaxed disk packing}, booktitle = {Proceedings of CCCG 2015: Canadian Conference on Computational Geometry}, year = {2015} }

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2014 : 3 papers in CVPR CTIC ICRoM
 


@inproceedings{KS14ICRoM, author = {Kurlin, V., SafiSamghabadi, 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 = {723729}, 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(n^{4}) 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 nbyn 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 collisionfree motions.
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2013 : 2 papers
 V. Kurlin, L. Mihaylova.
How many wireless sensors are needed to guarantee connectivity of a 1dimensional network with random internode spacings?
J Applied Probability and Statistics, v. 8 (2013), no. 2, p. 2750.
(223K, 24 pages). 
A. Chernov, V. Kurlin.
Reconstructing persistent graph structures from noisy images.
ImageA, v. 3 (2013), no. 5, p. 1922.
(234K, 4 pages).
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2012 : 1 paper
 V. Kurlin.
Computing braid groups of graphs with applications to robot motion planning.
Homology, Homotopy and Applications, v. 14 (2012), no. 1, p. 159180.
(249K, 22 pages).
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2008  2010 : earlier work in pure mathematics
 T. Fiedler, V. Kurlin.
Recognizing trace graphs of closed braids.
Osaka J Mathematics, v. 47 (2010), no. 4, p. 885909.
(1M, 25 pages).  T. Fiedler, V. Kurlin.
A oneparameter approach to links in a solid torus.
J Math Society of Japan, v. 62 (2010), no. 1, p. 167211.
(1.5M, 45 pages).  T. Fiedler, V. Kurlin.
Fiber quadrisecants in knot isotopies.
J Knot Theory Ramifications, v. 17 (2008), no. 11, p. 14151428.
(846K, 14 pages).  C. Kearton, V. Kurlin.
All 2dimensional links live inside a universal 3dimensional polyhedron.
Algebraic & Geometric Topology, v. 8 (2008), no. 3, p. 12231247.
(913K, 25 pages).  V. Kurlin.
Gauss paragraphs of classical links and a characterization of virtual link groups.
Math. Proc. Cambridge Phil. Society, v. 145 (2008), no. 1, p. 129140.
(212K, 12 pages).
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2005  2007 : postdoctoral work
 V. Kurlin, D. Lines.
Peripherally specified homomorphs of link groups.
J Knot Theory Ramifications, v. 16 (2007), no. 6, p. 719740.
(435K, 22 pages).  V. Kurlin.
The BakerCampbellHausdorff formula in the free metabelian Lie algebra.
Journal of Lie Theory, v. 17 (2007), no. 3, p. 525538.
(192K, 14 pages).  V. Kurlin.
Threepage encoding and complexity theory for spatial graphs.
J Knot Theory Ramifications, v. 16 (2007), no. 1, p. 59102.
(786K, 44 pages).  V. Kurlin.
Compressed Drinfeld associators.
Journal of Algebra, v. 292 (2005), no. 1, p. 184242.
(1.3M, 59 pages).
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2001  2004 : PhD studies
 V. Kurlin, V. Vershinin.
Threepage embeddings of singular knots.
Functional Analysis and Its Applications, v. 38 (2004), no. 1, p. 1427.
(212K, 14 pages).  V. Kurlin.
Basic embeddings and 3page embeddings of graphs.
Russian Mathematical Surveys, v. 58 (2003), no. 2, p. 372374.
(116K, 3 pages).  V. Kurlin.
Threepage Dynnikov's diagrams of spatial 3valent graphs.
Functional Analysis and Its Applications, v. 35 (2001), no. 3, p. 230233.
(107K, 4 pages).
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1999  2000 : MSc studies
 V. Kurlin.
Basic embeddings into a product of graphs.
Topology and Its Applications, v. 102 (2000), no. 2, p. 113137.
(273K, 25 pages).  V. Kurlin.
Reduction of framed links to ordinary links.
Russian Mathematical Surveys, v. 54 (1999), no. 4, p. 845846.
(244K, 2 pages).  V. Kurlin.
Invariants of colored links.
Moscow University Math. Bulletin, v. 54 (1999), no. 3, p. 4244.
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Invited lectures at international conferences
2017  2016  2015  20112014  20072010  20052006  19992004
Oral presentations given in 2017
 June 2017 : Applied Topology conference, Bedlewo, Poland.
Title : "Topological methods for a faster materials discovery" (45min invited talk).  May 2017 : International workshop on machine learning and data analytics in advanced metals processing, Manchester.
Title : "Topological Data Analysis for Materials Science" (30min contributed talk).  May 2017 : ACAT
(Applied and Computational Algebraic Topology), HIM Bonn, Germany.
Title : "Line segment detector inspired by Topological Data Analysis" (20min software demo).
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Oral presentations given in 2016
 August 2016 : BTM 2016 (British Topology Meeting), Glasgow University, UK.
Title : "Graph reconstruction from noisy scans based on persistence" (1hour keynote lecture).  July 2016, ATMCS 8 (Applied Topology: Methods, Computation, Science), Turin, Italy.
Title : "Graph reconstruction from noisy point samples" (30min software demo).  July 2016, 7 ECM (European Congress of Mathematics), Berlin, Germany.
Title : "Topological Computer Vision" (20min contributed talk).  April 2016, symposium Today's Data Predicting Tomorrow, Loughborough, UK.
Title : "Applications of Topological Data Analysis" (25min invited talk).  April 2016, BAMC 2016: British Applied Mathematical Colloquium, Oxford, UK.
Title : "Convex constrained meshes of superpixels" (20min contributed talk).  January 2016, ATI workshop
Mathematical Foundations of Learning for nonEuclidean Objects, UK.
Title : "Topological Computer Vision" (20min invited talk).  January 2016, Prospects in Data Science, Southampton, UK.
Title : "Topological Computer Vision" (40min keynote lecture).
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Oral presentations given in 2015
 October 2015,
Computational Geometric and Algebraic Topology, Oberwolfach, Germany.
Title : "HoPeS (cloud segmentations and persistent skeletons)" (15min software demo).  September 2015,
CAT 2015:
Computational Algebraic Topology, Oxford, UK.
Title : "Topological Computer Vision is a new area in Topological Data Analysis" (25min invited talk).  July 2015,
ACA 2015:
Applications of Computer Algebra, Kalamata (Greece).
Title : "Fast and stable topological profiles of noisy 2D images" (30min contributed talk).  July 2015,
ACAT 2015:
Applied and Computational Algebraic Topology, IST Austria.
Title : "A homologically persistent skeleton of an unstructured point cloud" (40min contributed talk).  July 2015,
SGP 2015:
Eurographics Symposium on Geometry Processing, Graz (Austria).
Title : "A homologically persistent skeleton of an unstructured point cloud" (30min talk with the accepted paper).  June 2015,
DyToComp 2015:
Dynamics, Topology and Computation, Bedlewo (Poland).
Title : A Homologically Persistent Skeleton in Computer Vision and beyond (30min contributed talk).  May 2015,
MMMDS:
Mathematical Methods for Massive Data Sets, Edinburgh, UK.
Title : Topological Data Analysis. Applications to Computer Vision (45min invited talk).  May 2015,
TopoInVis 2015:
TopologyBased Methods in Visualization, Annweiler, Germany.
Title : Computing invariants of knotted graphs given by sequences of 3D points (25min talk with the accepted paper).  April 2015,
BAMC:
British Applied Mathematical Colloquium, Cambridge, UK.
Title : Topological Data Analysis. Applications to Computer Vision (20min contributed talk).  March 2015,
IVAPP:
Information Visualization Theory and Applications, Berlin.
Title : A linear time algorithm for visualizing knotted structures in 3 pages (30min talk with the accepted paper).  February 2015,
Algebraic Topology: Computation, Data Analysis, and Applications
workshop at the Oxford Mathematical Institute, United Kingdom.
Title : Homologically persistent skeleton (20min invited talk).  January 2015,
Applied
Algebraic Topology network, Queen Mary University of London, UK.
Title : Topological Data Analysis. Applications to Computer Vision (45min invited talk).  January 2015,
Transpennine
Topology Triangle meeting, University of Sheffield, UK.
Title : Topological Data Analysis. Applications to Computer Vision (1 hour).  January 2015, Winter School on Lowdimensional Topology, La Llagonne, France.
Title : Topological Data Analysis. Applications to Computer Vision (45min invited talk).
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Oral presentations given in 20112014
 September 2014,
CTIC: Computational Topology in Image Context, Romania.
Title : Autocompletion of closed contours based on topological persistence (20 min).
Title : Drawing a graph in 3 pages within its isotopy class in linear time (20 min).  September 2014,
British Topology Meeting,
Southampton, United Kingdom.
Title : Topological Data Analysis. Applications to Computer Vision (30 min).  July 2014,
Applied Algebraic Topology, Castro Urdiales,
CIEM, Spain.
Title : Homologically Persistent Skeleton for visualizing highdimensional data (45 min).  July 2013,
Applied Topology,
Bedlewo Conference Centre, Poland.
Title : Reconstructing persistent structures from noisy images of graphs in a metric space (40 min).  July 2013,
Applied
and Computational Algebraic Topology, Bremen, Germany.
Title : Persistent homotopy types of noisy samples of graphs in the plane (30 min).
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Oral presentations given in 20072010
 June 2010,
Applied Topology:
Methods, Computation, Science, Munster, Germany.
Title : Braid groups of graphs and robot motion planning (30 min).  September 2009,
8th
Mathematics of Networks meeting, Cambridge, UK.
Title : Connectivity of random 1dimensional networks (45 min).  July 2009,
de
Brun Workshop on Computational Algebra, Galway, Ireland.
Title : The metabelian BCH formula and Drinfeld associators (45 min).  June 2008,
Differential Equations and Topology,
Moscow, Russia.
Title : Peripherally specified homomorphs of link groups (20 min).  April 2007,
British
Mathematical Colloquium 2007, Swansea, UK.
Title : Basic embeddings of graphs (20 min).
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Oral presentations given in 20052006
 September 2006,
Lowdimensional Manifolds,
Burgo de Osma, Spain.
Title : Compressed Drinfeld associators (25 min).  August 2006,
International
Congress of Mathematicians 2006,
Madrid, Spain.
Title : Compressed BakerCampbellHausdorff formula (20min oral communication).  May 2006,
Knots,
Groups and 3Manifolds,
Marseille, France.
Title : Peripherally specified homomorphs of link groups (20 min).  April 2006
54th
Transpennine Topology Triangle meeting,
Sheffield, UK.
Title : Compressed BakerCampbellHausdorff formula (1 hour).  April 2006,
Algebraic Geometry,
Singularities, Knots,
Liverpool, UK.
Title : Topological approach to the conjugacy of braids (1 hour).  April 2006,
British Mathematical Colloquium 2006,
Newcastle, UK.
Title : Compressed BakerCampbellHausdorff formula (25 min).  November 2005,
Combinatorial Braid Theory, Brighton, UK.
Title : Oneparameter approach to knot theory (45+45 min).  June 2005, Rencontres du GDR Tresses (braids), Luminy, France.
Title : Fiedler's 1parameter approach to knot theory (30 min).
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Oral presentations given in 19992004
 September 2004,
Rencontres du GDR Tresses (braids), Tatihou, France.
Title : Description of compressed Drinfeld associators (40 min).  July 2004,
Geometry, Topology and Combinatorics (satellite of
ECM 2004), Stockholm, Sweden.
Title : Computing compressed Drinfeld associators (30 min).  June 2004, Rencontres du GDR Tresses (braids), Autrans, France.
Title : A program to compute Drinfeld associators (30 min).  May 2003, Kolmogorov and Contemporary Mathematics, Moscow, Russia.
Title : Basic embeddings of graphs (20 min).  June 2001, Knot Theory and Algebraic Geometry, Liverpool, UK.
Title : Threepage embeddings of spatial 3valent graphs (30 min).  October 2000,
Combinatorcs, Dynamics and Probability, Stockholm, Sweden.
Title : Algebraic classification of spatial 3valent graphs (30 min).  March 2000,
Geometry and Applications,
Novosibirsk, Russia.
Title : Diagrams of spatial 3valent graphs (20 min).  August 1999, Lowdimensional topology and combinatorial group theory,
Chelyabinsk, Russia.
Title : Reduction of framed links to ordinary ones (30 min).
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Coauthors in the alphabetical order
 Alexey Chernov : Senior Lecturer in Statistics at University of Brighton, UK
 Herbert Edelsbrunner : Professor at IST Austria
 Thomas Fiedler : Professor at University of Toulouse III, France
 Andrew Fitzgibbon: Principal Researcher at Microsoft Research Cambridge, UK
 Jeremy Forsythe : former final year project student in the UK
 Mabel IglesiasHam : PhD student at IST Austria
 Cherry Kearton : retired Reader at Durham University, UK
 Daniel Lines : retired Professor at University of Burgundy, Dijon
 Ludmila Mihaylova : Professor at University of Sheffield, UK
 Marjan SafiSamghabadi : Lecturer at Alzahra State University, Iran
 Christopher Smithers : PhD student at Durham University, UK
 Vladimir Vershinin : Professor at University of Montpellier II, France
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