×

3D intelligent scissors for dental mesh segmentation. (English) Zbl 1431.92072

Summary: Teeth segmentation is a crucial technologic component of the digital dentistry system. The limitations of the live-wire segmentation include two aspects: (1) computing the wire as the segmentation boundary is time-consuming and (2) a great deal of interactions for dental mesh is inevitable. For overcoming these disadvantages, 3D intelligent scissors for dental mesh segmentation based on live-wire is presented. Two tensor-based anisotropic metrics for making wire lie at valleys and ridges are defined, and a timesaving anisotropic Dijkstra is adopted. Besides, to improve with the smoothness of the path tracking back by the traditional Dijkstra, a 3D midpoint smoothing algorithm is proposed. Experiments show that the method is effective for dental mesh segmentation and the proposed tool outperforms in time complexity and interactivity.

MSC:

92C50 Medical applications (general)

Software:

libigl; OpenMesh
Full Text: DOI

References:

[1] Zhuang, Y.; Zou, M.; Carr, N.; Ju, T., Anisotropic geodesics for live-wire mesh segmentation, Computer Graphics Forum, 33, 7, 111-120 (2014) · doi:10.1111/cgf.12479
[2] Mortensen, E. N.; Barrett, W. A., Intelligent scissors for image composition, Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, ACM · doi:10.1145/218380.218442
[3] Yuan, T.; Liao, W.; Dai, N.; Cheng, X.; Yu, Q., Single-tooth modeling for 3D dental model, International Journal of Biomedical Imaging, 2010, 1-14 (2010) · doi:10.1155/2010/535329
[4] Kronfeld, T.; Brunner, D.; Brunnett, G., Snake-based segmentation of teeth from virtual dental casts, Computer-Aided Design and Applications, 7, 2, 221-233 (2010) · doi:10.3722/cadaps.2010.221-233
[5] Wu, K.; Chen, L.; Li, J.; Zhou, Y., Tooth segmentation on dental meshes using morphologic skeleton, Computers & Graphics, 38, 199-211 (2014) · doi:10.1016/j.cag.2013.10.028
[6] Liao, S.-h.; Liu, S.-j.; Zou, B.-j.; Ding, X.; Liang, Y.; Huang, J.-h., Automatic tooth segmentation of dental mesh based on harmonic fields, BioMed Research International, 2015 (2015) · doi:10.1155/2015/187173
[7] Li, Z.; Wang, H., Interactive tooth separation from dental model using segmentation field, PLoS One, 11, 8 (2016) · doi:10.1371/journal.pone.0161159
[8] Chen, X.; Golovinskiy, A.; Funkhouser, T., A benchmark for 3D mesh segmentation, ACM Transactions on Graphics, 28, 3, 1 (2009) · doi:10.1145/1531326.1531379
[9] Rodrigues, R. S. V.; Morgado, J. F. M.; Gomes, A. J. P., Part-based mesh segmentation: a survey, Computer Graphics Forum, 37, 6, 235-274 (2018) · doi:10.1111/cgf.13323
[10] Chazelle, B., Strategies for polyhedral surface decomposition: an experimental study, Computational Geometry, 7, 5-6, 297-305 (1997) · Zbl 1133.52305 · doi:10.1016/s0925-7721(96)00024-7
[11] Bergamasco, F.; Albarelli, A.; Torsello, A., Semi-supervised segmentation of 3D surfaces using a weighted graph representation, Proceedings of the International Conference on Graph-Based Representations in Pattern Recognition
[12] Bergamasco, F.; Albarelli, A.; Torsello, A., A graph-based technique for semi-supervised segmentation of 3D surfaces, Pattern Recognition Letters, 33, 15, 2057-2064 (2012) · doi:10.1016/j.patrec.2012.03.015
[13] Benjamin, W.; Polk, A. W.; Vishwanathan, S. V. N.; Ramani, K., Heat walk: robust salient segmentation of non-rigid shapes, Computer Graphics Forum, 30, 7, 2097-2106 (2011) · doi:10.1111/j.1467-8659.2011.02060.x
[14] Shlafman, S.; Tal, A.; Katz, S., Metamorphosis of polyhedral surfaces using decomposition, Computer Graphics Forum, 21, 3, 219-228 (2010) · doi:10.1111/1467-8659.00581
[15] Saha, R.; Donofrio, R. S.; Goeres, D. M.; Bagley, S. T., Variational mesh decomposition, ACM Transactions on Graphics, 31, 3, 1-14 (2012) · doi:10.1145/2167076.2167079
[16] Katz, S.; Tal, A., Hierarchical mesh decomposition using fuzzy clustering and cuts, ACM Transactions on Graphics, 22, 3, 954-961 (2003) · doi:10.1145/882262.882369
[17] Zhang, H.; Li, C.; Gao, L.; Li, S.; Wang, G., Shape segmentation by hierarchical splat clustering, Computers & Graphics, 51, 136-145 (2015) · doi:10.1016/j.cag.2015.05.012
[18] Golovinskiy, A.; Funkhouser, T., Randomized cuts for 3D mesh analysis, ACM Transactions on Graphics, 27, 5, 1-12 (2008) · doi:10.1145/1409060.1409098
[19] Zheng, Y.; Tai, C.-L., Mesh decomposition with cross-boundary brushes, Computer Graphics Forum, 29, 2, 527-535 (2010) · doi:10.1111/j.1467-8659.2009.01622.x
[20] Zheng, Y.; Tai, C.-L.; Au, O. K.-C., Dot scissor: a single-click interface for mesh segmentation, IEEE Transactions on Visualization and Computer Graphics, 18, 8, 1304-1312 (2012) · doi:10.1109/TVCG.2011.140
[21] Zhao, J.; Xin, S.; Liu, Y., A survey on the computing of geodesic distances on meshes, Scientia Sinica Informationis, 45, 3, 313-335 (2015)
[22] Chen, J.; Han, Y., Shortest paths on a polyhedron, Proceedings of the Sixth Annual Symposium on Computational Geometry · doi:10.1145/98524.98601
[23] Surazhsky, V.; Surazhsky, T.; Kirsanov, D.; Gortler, S. J.; Hoppe, H., Fast exact and approximate geodesics on meshes, ACM Transactions on Graphics, 24, 3, 553 (2005) · doi:10.1145/1073204.1073228
[24] Ying, X.; Wang, X.; He, Y., Saddle vertex graph (SVG), ACM Transactions on Graphics, 32, 6, 1-12 (2013) · doi:10.1145/2508363.2508379
[25] Campen, M.; Heistermann, M.; Kobbelt, L., Practical anisotropic geodesy, Computer Graphics Forum, 32, 5, 63-71 (2013) · doi:10.1111/cgf.12173
[26] Crane, K.; Weischedel, C.; Wardetzky, M., Geodesics in heat, ACM Transactions on Graphics, 32, 5, 1-11 (2013) · doi:10.1145/2516971.2516977
[27] Crane, K.; Weischedel, C.; Wardetzky, M., The heat method for distance computation, Communications of the ACM, 60, 11, 90-99 (2017) · doi:10.1145/3131280
[28] Yang, F.; Cohen, L. D., Geodesic distance and curves through isotropic and anisotropic heat equations on images and surfaces, Journal of Mathematical Imaging and Vision, 55, 2, 210-228 (2016) · Zbl 1338.65216 · doi:10.1007/s10851-015-0621-9
[29] Andreux, M.; Rodolà, E.; Aubry, M.; Cremers, D., Anisotropic Laplace-Beltrami operators for shape analysis, Proceedings of the Workshop on Non-rigid Shape Analysis & Deformable Image Alignment
[30] Dijkstra, E. W., A note on two problems in connexion with graphs, Numerische Mathematik, 1, 1, 269-271 (1959) · Zbl 0092.16002 · doi:10.1007/bf01386390
[31] Vaxman, A.; Campen, M.; Diamanti, O., Directional field synthesis, design, and processing, Computer Graphics Forum, 35, 2, 545-572 (2016) · doi:10.1111/cgf.12864
[32] Botsch, M.; Steinberg, S.; Bischoff, S.; Kobbelt, L.; Aachen, R., OpenMesh: a generic and efficient polygon mesh data structure, Proceedings of the Opensg Symposium
[33] Polthier, K.; Schmies, M., Straightest geodesics on polyhedral surfaces, Proceedings of the ACM SIGGRAPH 2006 · doi:10.1145/1185657.1185664
[34] Lévy, B.; Petitjean, S.; Ray, N.; Maillot, J., Least squares conformal maps for automatic texture atlas generation, ACM Transactions on Graphics, 21, 3, 362-371 (2002) · doi:10.1145/566654.566590
[35] Jacobson, A.; Panozzo, D.; Schüller, C., {libigl}: A Simple {C++} Geometry Processing Library, 2018, https://libigl.github.io/
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.