Abstract
This paper proposes an improved decimation of triangle meshes based on curvature. Mesh simplification based on vertex decimation is simple and easy for implementation. But in previous mesh simplification researches based on vertex decimation, algorithms generally focused on the distance error between the simplified mesh and the original mesh. However, a high quality simplified mesh must have low approximation error and preserve geometric features of the original model. According to this consideration, the proposed algorithm improves classical vertex decimation by calculating the mean curvature of each vertex and considering the change of curvature in local ring. Meanwhile, this algorithm wraps the local triangulation by a global triangulation. Experimental results demonstrate that our approach can preserve the major topology characteristics and geometric features of the initial models after simplifying most vertices, without complicated calculation. It also can reduce the influence from noises and staircase effects in the process of reconstruction, and result in a smooth surface.
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Ovreiu, E., Riveros, J.G., Valette, S., Prost, R.: Mesh Simplification Using a Two-Sided Error Minimization. International Proceedings of Computer Science & Information Technology 50 (2012)
He, H., Tian, J., Zhang, X.: Review of mesh simplification. Journal of Software 12 (2002)
Fu, X.: Algorithm research of 3D mesh simplification. Southwest University, Chongqing (2008)
Campomanes-Alvarez, B.R., Damas, S., Cordón, O.: Mesh simplification for 3D modeling using evolutionary multi-objective optimization. In: 2012 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2012)
Schroeder, W.J., Zarge, J.A., Lorensen, W.E.: Decimation of triangle meshes. ACM Siggraph Computer Graphics 26(2), 65–70 (1992)
Hoppe, H.: Progressive meshes. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp. 99–108. ACM (1996)
Hamann, B.: A data reduction scheme for triangulated surfaces. Computer Aided Geometric Design 11(2), 197–214 (1994)
Jun, L., Shi, J.: A Mesh Simplification Method Based on Shape Feature. In: 2006 8th International Conference on Signal Processing, vol. 2 (2006)
Zhao, Y., Liu, Y., Song, R., Zhang, M.: A Retinex theory based points sampling method for mesh simplification. In: 2011 7th International Symposium on Image and Signal Processing and Analysis (ISPA), pp. 230–235. IEEE (2011)
Rossignac, J., Borrel, P.: Multi-resolution 3D approximations for rendering complex scenes. Springer, Heidelberg (1993)
**n, S.Q., Chen, S.M., He, Y., et al.: Isotropic Mesh Simplification by Evolving the Geodesic Delaunay Triangulation. In: 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD), pp. 39–47. IEEE (2011)
Wang, J., Wang, L.R., Li, J.Z., Hagiwara, I.: A feature preserved mesh simplification algorithm. Journal of Engineering and Computer Innovations 6, 98–105 (2011)
Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, pp. 209–216. ACM Press/Addison-Wesley Publishing Co. (1997)
Wei, J., Lou, Y.: Feature preserving mesh simplification using feature sensitive metric. Journal of Computer Science and Technology 25(3), 595–605 (2010)
Gieng, T.S., Hamann, B., Joy, K.I., Schussman, G.L., Trotts, I.J.: Smooth hierarchical surface triangulations. In: Proceedings of the 8th Conference on Visualization 1997, pp. 379–386. IEEE Computer Society Press (1997)
Wang, Y., Zheng, J.: Curvature-guided adaptive T-spline surface fitting. Computer-Aided Design 45(8), 1095–1107 (2013)
Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3D surface construction algorithm. ACM Siggraph Computer Graphics 21(4), 163–169 (1987)
Chen, Y., Wang, Z., Hu, J., Zhao, W., Wu, Q.: The domain knowledge based graph-cut model for liver ct segmentation. Biomedical Signal Processing and Control 7(6), 591–598 (2012)
Chen, Y., Zhao, W., Wu, Q., Wang, Z., Hu, J.: Liver segmentation in CT images for intervention using a graph-cut based model. In: Yoshida, H., Sakas, G., Linguraru, M.G. (eds.) Abdominal Imaging 2011. LNCS, vol. 7029, pp. 157–164. Springer, Heidelberg (2012)
Qing, D., Chen, J., Yu, H., Wang, Z.: Mesh simplification method based on vision feature. In: IET International Communication Conference on Wireless Mobile and Computing (CCWMC 2011), pp. 398–402. IET (2011)
Jian, W., Hai-Ling, W., Bo, Z., Ni, J.: An Efficient Mesh Simplification Method in 3D Graphic Model Rendering. In: 2013 Seventh International Conference on Internet Computing for Engineering and Science (ICICSE), pp. 55–59. IEEE (2013)
Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, pp. 317–324. ACM Press/Addison-Wesley Publishing Co. (1999)
Sullivan, J.M., Schröder, P.: Discrete differential geometry. Birkhäuser, Basel (2008)
Pan, Z., Zhou, K., Shi, J.: A new mesh simplification algorithm based on triangle collapses. Journal of Computer Science and Technology 16(1), 57–63 (2001)
Thomas, D.M., Yalavarthy, P.K., Karkala, D., Natarajan, V.: Mesh simplification based on edge collapsing could improve computational efficiency in near infrared optical tomographic imaging. IEEE Journal of Selected Topics in Quantum Electronics 18(4), 1493–1501 (2012)
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Li, W., Chen, Y., Wang, Z., Zhao, W., Chen, L. (2014). An Improved Decimation of Triangle Meshes Based on Curvature. In: Miao, D., Pedrycz, W., Ślȩzak, D., Peters, G., Hu, Q., Wang, R. (eds) Rough Sets and Knowledge Technology. RSKT 2014. Lecture Notes in Computer Science(), vol 8818. Springer, Cham. https://doi.org/10.1007/978-3-319-11740-9_25
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DOI: https://doi.org/10.1007/978-3-319-11740-9_25
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11739-3
Online ISBN: 978-3-319-11740-9
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