Outputs (20)

Computing invariants of knotted graphs given by sequences of points in 3-dimensional space (2017)
Presentation / Conference Contribution
Kurlin, V., Carr, H., Garth, C., & Weinkauf, T. (2015, May). Computing invariants of knotted graphs given by sequences of points in 3-dimensional space. Presented at Topology-Based Methods in Visualization 2015., Annweiler, Germany

We design a fast algorithm for computing the fundamental group of the complement to any knotted polygonal graph in 3-space. A polygonal graph consists of straight segments and is given by sequences of vertices along edge-paths. This polygonal model i... Read More about Computing invariants of knotted graphs given by sequences of points in 3-dimensional space.

A fast persistence-based segmentation of noisy 2D clouds with provable guarantees (2015)
Journal Article
Kurlin, V. (2016). A fast persistence-based segmentation of noisy 2D clouds with provable guarantees. Pattern Recognition Letters, 83(Part 1), 3-12. https://doi.org/10.1016/j.patrec.2015.11.025

We design a new fast algorithm to automatically segment a 2D cloud of points into persistent regions. The only input is a dotted image without any extra parameters, say a scanned black-and-white map with almost closed curves or any image with detecte... Read More about A fast persistence-based segmentation of noisy 2D clouds with provable guarantees.

Relaxed disk packing (2015)
Presentation / Conference Contribution
Edelsbrunner, E., Iglesias-Ham, M., Kurlin, V., Kouhestani, B., & Rappaport, D. (2015, August). Relaxed disk packing. Presented at 27th Canadian Conference on Computational Geometry., Queen's University, Kingston, Ontario, Canada

Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexago... Read More about Relaxed disk packing.

A one-dimensional Homologically Persistent Skeleton of an unstructured point cloud in any metric space (2015)
Journal Article
Kurlin, V. (2015). A one-dimensional Homologically Persistent Skeleton of an unstructured point cloud in any metric space. Computer Graphics Forum, 34(5), 253-262. https://doi.org/10.1111/cgf.12713

Real data are often given as a noisy unstructured point cloud, which is hard to visualize. The important problem is to represent topological structures hidden in a cloud by using skeletons with cycles. All past skeletonization methods require extra p... Read More about A one-dimensional Homologically Persistent Skeleton of an unstructured point cloud in any metric space.

A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages (2015)
Presentation / Conference Contribution
Kurlin, V. (2015, March). A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages. Presented at IVAPP 2015 : 6th International Conference on Information Visualization Theory and Applications., Berlin, Germany

We introduce simple codes and fast visualization tools for knotted structures in molecules and neural networks. Knots, links and more general knotted graphs are studied up to an ambient isotopy in Euclidean 3-space. A knotted graph can be represented... Read More about A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages.

A fast and robust algorithm to count topologically persistent holes in noisy clouds (2014)
Presentation / Conference Contribution
Kurlin, V. (2023, June). A fast and robust algorithm to count topologically persistent holes in noisy clouds. Presented at CVPR : Computer Vision and Pattern Recognition, Columbus, Ohio, USA

Preprocessing a 2D image often produces a noisy cloud of interest points. We study the problem of counting holes in noisy clouds in the plane. The holes in a given cloud are quantified by the topological persistence of their boundary contours when th... Read More about A fast and robust algorithm to count topologically persistent holes in noisy clouds.

Computing a configuration skeleton for motion planning of two round robots on a metric graph (2014)
Presentation / Conference Contribution
Kurlin, V., & Safi-Samghabadi, M. (2014, October). Computing a configuration skeleton for motion planning of two round robots on a metric graph. Presented at 2014 Second RSI/ISM International Conference on Robotics and Mechatronics (ICRoM), Tehran

A connected metric graph G with n vertices and without loops and multiple edges is given as an n × n-matrix whose entry aij is the length of a single edge between vertices i ≠ j. A robot in the metric graph G is the metric ball with a center x ϵ G an... Read More about Computing a configuration skeleton for motion planning of two round robots on a metric graph.

Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence (2014)
Presentation / Conference Contribution
Kurlin, V., Winkler, F., Negru, V., Ida, T., Jebelean, T., Petcu, D., Watt, S., & Zaharie, D. (2014, December). Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence. Presented at Computational Topology in Image Context (workshop of SYNASC 2014: Symbolic and Numeric Algorithms for Scientific Computing, http://synasc.ro/2014), Timisoara, Romania

We design a new fast algorithm to automatically complete closed contours in a finite point cloud on the plane. The only input can be a scanned map with almost closed curves, a hand-drawn artistic sketch or any sparse dotted image in 2D without any ex... Read More about Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence.

How Many Wireless Sensors are Needed to Guarantee Connectivity of a One-Dimensional Network with Random Inter-Node Spacing? (2013)
Journal Article
Kurlin, V., & Mihaylova, L. (2013). How Many Wireless Sensors are Needed to Guarantee Connectivity of a One-Dimensional Network with Random Inter-Node Spacing?. Journal of applied probability and statistics, 8(2), 27-50

An important problem in wireless sensor networks is to nd an optimal number of randomly deployed sensors to guarantee connectivity of the resulting network with a given probability. The authors describe a general method to compute the probabilities o... Read More about How Many Wireless Sensors are Needed to Guarantee Connectivity of a One-Dimensional Network with Random Inter-Node Spacing?.

Reconstructing persistent graph structures from noisy images (2013)
Journal Article
Chernov, A., & Kurlin, V. (2013). Reconstructing persistent graph structures from noisy images. Imagen-a, 3(5), 19-22

Let a point cloud be a noisy dotted image of a graph on the plane. We present a new fast algorithm for reconstructing the original graph from the given point cloud. Degrees of vertices in the graph are found by methods of persistent topology. Necessa... Read More about Reconstructing persistent graph structures from noisy images.