Crawl through Neighbors: A Simple Curve Reconstruction Algorithm

Given a planar point set sampled from an object boundary, the process of approximating the original shape is called curve reconstruction. In this paper, a novel non‐parametric curve reconstruction algorithm based on Delaunay triangulation has been proposed and it has been theoretically proved that t...

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Vydané v:	Computer graphics forum Ročník 35; číslo 5; s. 177 - 186
Hlavní autori:	Parakkat, Amal Dev, Muthuganapathy, Ramanathan
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Oxford Blackwell Publishing Ltd 01.08.2016
Predmet:	Algorithms Analysis Approximation Boundaries Categories and Subject Descriptors (according to ACM CCS) Computer graphics Corners Delaunay triangulation I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation Image processing systems Reconstruction Sketches Skips Studies Topological manifolds
ISSN:	0167-7055, 1467-8659
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Abstract	Given a planar point set sampled from an object boundary, the process of approximating the original shape is called curve reconstruction. In this paper, a novel non‐parametric curve reconstruction algorithm based on Delaunay triangulation has been proposed and it has been theoretically proved that the proposed method reconstructs the original curve under ε‐sampling. Starting from an initial Delaunay seed edge, the algorithm proceeds by finding an appropriate neighbouring point and adding an edge between them. Experimental results show that the proposed algorithm is capable of reconstructing curves with different features like sharp corners, outliers, multiple objects, objects with holes, etc. The proposed method also works for open curves. Based on a study by a few users, the paper also discusses an application of the proposed algorithm for reconstructing hand drawn skip stroke sketches, which will be useful in various sketch based interfaces.
AbstractList	Given a planar point set sampled from an object boundary, the process of approximating the original shape is called curve reconstruction. In this paper, a novel non-parametric curve reconstruction algorithm based on Delaunay triangulation has been proposed and it has been theoretically proved that the proposed method reconstructs the original curve under [epsi]-sampling. Starting from an initial Delaunay seed edge, the algorithm proceeds by finding an appropriate neighbouring point and adding an edge between them. Experimental results show that the proposed algorithm is capable of reconstructing curves with different features like sharp corners, outliers, multiple objects, objects with holes, etc. The proposed method also works for open curves. Based on a study by a few users, the paper also discusses an application of the proposed algorithm for reconstructing hand drawn skip stroke sketches, which will be useful in various sketch based interfaces. Given a planar point set sampled from an object boundary, the process of approximating the original shape is called curve reconstruction. In this paper, a novel non‐parametric curve reconstruction algorithm based on Delaunay triangulation has been proposed and it has been theoretically proved that the proposed method reconstructs the original curve under ε‐sampling. Starting from an initial Delaunay seed edge, the algorithm proceeds by finding an appropriate neighbouring point and adding an edge between them. Experimental results show that the proposed algorithm is capable of reconstructing curves with different features like sharp corners, outliers, multiple objects, objects with holes, etc. The proposed method also works for open curves. Based on a study by a few users, the paper also discusses an application of the proposed algorithm for reconstructing hand drawn skip stroke sketches, which will be useful in various sketch based interfaces. Given a planar point set sampled from an object boundary, the process of approximating the original shape is called curve reconstruction. In this paper, a novel non-parametric curve reconstruction algorithm based on Delaunay triangulation has been proposed and it has been theoretically proved that the proposed method reconstructs the original curve under epsilon -sampling. Starting from an initial Delaunay seed edge, the algorithm proceeds by finding an appropriate neighbouring point and adding an edge between them. Experimental results show that the proposed algorithm is capable of reconstructing curves with different features like sharp corners, outliers, multiple objects, objects with holes, etc. The proposed method also works for open curves. Based on a study by a few users, the paper also discusses an application of the proposed algorithm for reconstructing hand drawn skip stroke sketches, which will be useful in various sketch based interfaces.
Author	Muthuganapathy, Ramanathan Parakkat, Amal Dev
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Cites_doi	10.1007/BF01889981 10.1016/S0925-7721(99)00051-6 10.1145/2816795.2818067 10.1006/gmip.1998.0465 10.1145/2487381.2487382 10.1109/TIT.1983.1056714 10.1111/j.1467-8659.2011.02033.x 10.1007/978-3-540-77974-2 10.1145/304893.304973 10.1016/j.cag.2015.05.025 10.1049/iet-cvi.2009.0079 10.1016/j.patcog.2008.03.023 10.1016/S0925-7721(01)00015-3 10.1109/MCG.2011.84 10.1016/j.cad.2014.12.002 10.1007/BFb0054315
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References_xml	– reference: Edelsbrunner H., Kirkpatrick D., Seidel R.: On the shape of a set of points in the plane. IEEE Transactions on Information Theory 29, 4 (Jul 1983), 551-559. 1, 2, 5 – reference: Peethambaran J., Muthuganapathy R.: A non-parametric approach to shape reconstruction from planar point sets through delaunay filtering. Computer-Aided Design 62 (2015), 164-175. 2, 6 – reference: Liu X., Wong T.-T., Heng P.-A.: Closure-aware sketch simplification. ACM Trans. Graph. 34, 6 (Oct. 2015), 168:1-168:10. 3 – reference: Gheibi A., Davoodi M., Javad A., Panahi F., Aghdam M.M., Asgaripour M., Mohades A.: Polygonal shape reconstruction in the plane. IET Computer Vision 5, 2 (March 2011), 97-106. 2, 5 – reference: Duckham M., Kulik L., Worboys M., Galton A.: Efficient generation of simple polygons for characterizing the shape of a set of points in the plane. Pattern Recognition 41, 10 (2008), 3224-3236. 2, 5 – reference: Dey T.K., Mehlhorn K., Ramos E.A.: Curve reconstruction: Connecting dots with good reason. Computational Geometry 15, 4 (2000), 229-244. 2 – reference: Methirumangalath S., Parakkat A.D., Muthuganapathy R.: A unified approach towards reconstruction of a planar point set. Computers & Graphics 51 (2015), 90-97. International Conference Shape Modeling International. 2, 5 – reference: Dey T.K., Wenger R.: Reconstructing curves with sharp corners. Computational Geometry 19, 2-3 (2001), 89-99. Combinatorial Curves and Surfaces. 2 – reference: Berg M. d., Cheong O., Kreveld M. v., Overmars M.: Computational Geometry: Algorithms and Applications, 3rd ed. Springer-Verlag TELOS, Santa Clara, CA, USA, 2008. 3 – reference: de Goes F., Cohen-Steiner D., Alliez P., Desbrun M.: An optimal transport approach to robust reconstruction and simplification of 2d shapes. Computer Graphics Forum 30, 5 (2011), 1593-1602. 2, 5 – reference: Figueiredo L.H., Miranda Gomes J.: Computational morphology of curves. The Visual Computer 11, 2, 105-112. 1, 2 – reference: Amenta N., Bern M., Eppstein D.: The crust and the βskeleton: Combinatorial curve reconstruction. Graphical Models and Image Processing 60, 2 (1998), 125-135. 1, 2, 3, 4, 5, 6 – reference: Olsen L., Samavati F., Jorge J.: Naturasketch: Modeling from images and natural sketches. IEEE Comput. Graph. Appl. 31, 6 (Nov. 2011), 24-34. 3 – volume: 30 start-page: 1593 issue: 5 year: 2011 end-page: 1602 article-title: An optimal transport approach to robust reconstruction and simplification of 2d shapes publication-title: Computer Graphics Forum – volume: 15 start-page: 229 issue: 4 year: 2000 end-page: 244 article-title: Curve reconstruction: Connecting dots with good reason publication-title: Computational Geometry – volume: 51 start-page: 90 year: 2015 end-page: 97 article-title: A unified approach towards reconstruction of a planar point set publication-title: Computers & Graphics – start-page: 121 year: 2012 end-page: 130 – volume: 19 start-page: 89 issue: 2 year: 2001 end-page: 3 99 article-title: Reconstructing curves with sharp corners publication-title: Computational Geometry – volume: 29 start-page: 551 issue: 4 year: 1983 end-page: 559 article-title: On the shape of a set of points in the plane publication-title: IEEE Transactions on Information Theory – start-page: 61 year: 2013 end-page: 68 – start-page: 207 year: 1999 end-page: 216 – volume: 60 start-page: 125 issue: 2 year: 1998 end-page: 135 article-title: The crust and the βskeleton: Combinatorial curve reconstruction publication-title: Graphical Models and Image Processing – volume: 62 start-page: 164 year: 2015 end-page: 175 article-title: A non‐parametric approach to shape reconstruction from planar point sets through delaunay filtering publication-title: Computer‐Aided Design – year: 2008 – volume: 11 start-page: 105 issue: 2 end-page: 112 article-title: Computational morphology of curves publication-title: The Visual Computer – volume: 5 start-page: 97 issue: 2 year: 2011 end-page: 106 article-title: Polygonal shape reconstruction in the plane publication-title: IET Computer Vision – volume: 41 start-page: 3224 issue: 10 year: 2008 end-page: 3236 article-title: Efficient generation of simple polygons for characterizing the shape of a set of points in the plane publication-title: Pattern Recognition – start-page: 893 year: 1999 end-page: 894 – start-page: 119 year: 1998 end-page: 132 – volume: 31 start-page: 24 issue: 6 year: 2011 end-page: 34 article-title: Naturasketch: Modeling from images and natural sketches publication-title: IEEE Comput. Graph. Appl. – year: 2015 – volume: 34 start-page: 168:1 issue: 6 year: 2015 end-page: 168:10 article-title: Closure‐aware sketch simplification publication-title: ACM Trans. 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SubjectTerms	Algorithms Analysis Approximation Boundaries Categories and Subject Descriptors (according to ACM CCS) Computer graphics Corners Delaunay triangulation I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation Image processing systems Reconstruction Sketches Skips Studies Topological manifolds
Title	Crawl through Neighbors: A Simple Curve Reconstruction Algorithm
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