Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence

Kurlin, V.; Winkler , Franz; Negru, Viorel; Ida, Tetsuo; Jebelean , Tudor; Petcu , Dana; Watt , Stephen; Zaharie, Daniela

doi:10.1109/synasc.2014.85

Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence

Kurlin, V.; Winkler , Franz; Negru, Viorel; Ida, Tetsuo; Jebelean , Tudor; Petcu , Dana; Watt , Stephen; Zaharie, Daniela

Authors

V. Kurlin

Franz Winkler

Viorel Negru

Tetsuo Ida

Tudor Jebelean

Dana Petcu

Stephen Watt

Daniela Zaharie

Abstract

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 extra parameters. The output is a hierarchy of closed contours that have a long enough life span (persistence) in a sequence of nested neighborhoods of the input points. We prove theoretical guarantees when, for a given noisy sample of a graph in the plane, the output contours geometrically approximate the original contours in the unknown graph.

Citation

Kurlin, V., Winkler, F., Negru, V., Ida, T., Jebelean, T., Petcu, D., …Zaharie, D. (2014). Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence. In SYNASC 2014 : 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (594-601). https://doi.org/10.1109/synasc.2014.85

Conference Name	Computational Topology in Image Context (workshop of SYNASC 2014: Symbolic and Numeric Algorithms for Scientific Computing, http://synasc.ro/2014)
Conference Location	Timisoara, Romania
Acceptance Date	Nov 30, 2014
Publication Date	Jan 1, 2014
Deposit Date	Oct 27, 2014
Publicly Available Date	May 14, 2015
Publisher	Institute of Electrical and Electronics Engineers
Pages	594-601
Series Title	Proceedings of Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
Book Title	SYNASC 2014 : 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
DOI	https://doi.org/10.1109/synasc.2014.85

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