Mesh Snapping: Robust Interactive Mesh Cutting Using Fast Geodesic Curvature Flow
This paper considers the problem of interactively finding the cutting contour to extract components from a given mesh. Some existing methods support cuts of arbitrary shape but require careful and tedious input from the user. Others need little user input however they are sensitive to user input and...
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| Vydáno v: | Computer graphics forum Ročník 29; číslo 2; s. 517 - 526 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford, UK
Blackwell Publishing Ltd
01.05.2010
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | This paper considers the problem of interactively finding the cutting contour to extract components from a given mesh. Some existing methods support cuts of arbitrary shape but require careful and tedious input from the user. Others need little user input however they are sensitive to user input and need a postprocessing step to smooth the generated jaggy cutting contours. The popular geometric snake can be used to optimize the cutting contour, but it cannot deal with the topology change. In this paper, we propose a geodesic curvature flow based framework to overcome all these problems. Since in many cases the meaningful cutting contour on a 3D mesh is locally shortest in the sense of some weighted curve length, the geodesic curvature flow is an ideal tool for our problem. It evolves the cutting contour to the nearby local minimum. We should mention that the previous numerical scheme, discretized geodesic curvature flow (dGCF) is too slow and has not been applied to mesh segmentation. With a careful observation to dGCF, we devise here a fast computation scheme called fast geodesic curvature flow (FGCF), which only needs to solve a smaller and easier problem. The initial cutting contour is generated by a variant of random walks algorithm, which is very fast and gives reasonable cutting result with little user input. Experiment results on the benchmark mesh segmentation data set show that our proposed framework is robust to user input and capable of producing good results reflecting geometric features and human shape perception. |
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| AbstractList | This paper considers the problem of interactively finding the cutting contour to extract components from a given mesh. Some existing methods support cuts of arbitrary shape but require careful and tedious input from the user. Others need little user input however they are sensitive to user input and need a postprocessing step to smooth the generated jaggy cutting contours. The popular geometric snake can be used to optimize the cutting contour, but it cannot deal with the topology change. In this paper, we propose a geodesic curvature flow based framework to overcome all these problems. Since in many cases the meaningful cutting contour on a 3D mesh is locally shortest in the sense of some weighted curve length, the geodesic curvature flow is an ideal tool for our problem. It evolves the cutting contour to the nearby local minimum. We should mention that the previous numerical scheme, discretized geodesic curvature flow (dGCF) is too slow and has not been applied to mesh segmentation. With a careful observation to dGCF, we devise here a fast computation scheme called fast geodesic curvature flow (FGCF), which only needs to solve a smaller and easier problem. The initial cutting contour is generated by a variant of random walks algorithm, which is very fast and gives reasonable cutting result with little user input. Experiment results on the benchmark mesh segmentation data set show that our proposed framework is robust to user input and capable of producing good results reflecting geometric features and human shape perception. [PUBLICATION ABSTRACT] This paper considers the problem of interactively finding the cutting contour to extract components from a given mesh. Some existing methods support cuts of arbitrary shape but require careful and tedious input from the user. Others need little user input however they are sensitive to user input and need a postprocessing step to smooth the generated jaggy cutting contours. The popular geometric snake can be used to optimize the cutting contour, but it cannot deal with the topology change. In this paper, we propose a geodesic curvature flow based framework to overcome all these problems. Since in many cases the meaningful cutting contour on a 3D mesh is locally shortest in the sense of some weighted curve length, the geodesic curvature flow is an ideal tool for our problem. It evolves the cutting contour to the nearby local minimum. We should mention that the previous numerical scheme, discretized geodesic curvature flow (dGCF) is too slow and has not been applied to mesh segmentation. With a careful observation to dGCF, we devise here a fast computation scheme called fast geodesic curvature flow (FGCF), which only needs to solve a smaller and easier problem. The initial cutting contour is generated by a variant of random walks algorithm, which is very fast and gives reasonable cutting result with little user input. Experiment results on the benchmark mesh segmentation data set show that our proposed framework is robust to user input and capable of producing good results reflecting geometric features and human shape perception. |
| Author | Wu, Chunlin Zheng, Jianmin Tai, Xue-cheng Cai, Jianfei Zhang, Juyong |
| Author_xml | – sequence: 1 givenname: Juyong surname: Zhang fullname: Zhang, Juyong organization: Nanyang Technological University, Singapore – sequence: 2 givenname: Chunlin surname: Wu fullname: Wu, Chunlin organization: Nanyang Technological University, Singapore – sequence: 3 givenname: Jianfei surname: Cai fullname: Cai, Jianfei organization: Nanyang Technological University, Singapore – sequence: 4 givenname: Jianmin surname: Zheng fullname: Zheng, Jianmin organization: Nanyang Technological University, Singapore – sequence: 5 givenname: Xue-cheng surname: Tai fullname: Tai, Xue-cheng organization: Nanyang Technological University, Singapore |
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| Cites_doi | 10.1007/BF00133570 10.1016/j.jcp.2006.09.008 10.1145/1015706.1015775 10.1016/0010-0277(84)90022-2 10.1007/PL00013396 10.1145/1531326.1531379 10.1090/S0002-9947-1959-0110078-1 10.1109/34.368173 10.1137/080722758 10.1111/1467-8659.t01-1-00582 10.1111/j.1467-8659.2007.01103.x 10.1007/s003710050192 10.1109/TPAMI.2006.233 10.1080/17445760802337010 10.1016/j.cagd.2005.04.002 10.1006/jcph.2001.6960 10.1145/1364901.1364927 10.1016/0021-9991(88)90002-2 10.1145/1276377.1276459 10.1007/s00371-006-0068-5 |
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| References_xml | – reference: Osher S., Sethian J. A.: Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. Comput. Phys 79, 1 (1988), 12-49. – reference: Federer H.: Curvature Measures. Transactions of the American Mathematical Society 93, 3 (1959), 418-491. – reference: Shamir A.: A survey on Mesh Segmentation Techniques. Computer Graphics Forum 27, 6 (2008), 1539-1556. – reference: Sharf A., Blumenkrants M., Shamir A., Cohen-Or D.: SnapPaste: An Interactive Technique for Easy Mesh Composition. The Visual Computer, 9-11 (2006), 835-844. – reference: Gregory A., State A., Lin M. C., Manocha D., Livingston M. A.: Interactive surface decomposition for polyhedral morphing. The Visual Computer, 9 (1999), 453-470. – reference: Mullen P., McKenzie A., Tong Y., Desbrun M.: A Variational Approach to Eulerian Geometry Processing. ACM Transactions on Graphics (SIGGRAPH) 26, 3 (2007). – reference: Chen X., Golovinskiy A., Funkhouser T.: A Benchmark for 3D Mesh Segmentation. ACM Transactions on Graphics (SIGGRAPH) 28, 3 (2009). – reference: Malladi R., Sethian J. A., Vemuri B. C.: Shape Modeling with Front Propagation: A Level Set Approach. IEEE Trans. Pattern Anal. Mach. Intell. 17, 2 (1995), 158-175. – reference: Lee Y., Leea S., Shamirb A., Cohen-Orc D., Seideld H.-P.: Mesh Scissoring with Minima Rule and Part Salience. Computer Aided Geometric Design, 11 (July 2005), 444-465. – reference: Press W., Teukolsky S., Vetterling W., Flannery B.: Numerical Recipes in C, second ed. Cambrige University Press, 1992. – reference: Kass M., Witkin A. P., Terzopoulos D.: Snakes: Active Contour Models. International Journal of Computer Vision 1, 4 (1988), 321-331. – reference: Grady L.: Random Walks for Image Segmentation. IEEE Trans. Pattern Anal. Mach. 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Phys doi: 10.1016/0021-9991(88)90002-2 – ident: e_1_2_9_17_2 doi: 10.1145/1276377.1276459 – ident: e_1_2_9_21_2 doi: 10.1007/s00371-006-0068-5 |
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| SubjectTerms | Algorithms and systems Computer graphics Curvature Customization Cutting Cutting speed Cutting tools I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems Image processing systems languages Mathematical analysis Segmentation Shape Three dimensional |
| Title | Mesh Snapping: Robust Interactive Mesh Cutting Using Fast Geodesic Curvature Flow |
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