Abstract
Recent advances in 3D reconstruction allow to quickly acquire highly detailed and complex geometry. However, the outcome of such systems is usually unstructured, noisy and redundant. In order to enable further processing such as CAD modeling, physical measurement or rendering, semantic information about shape and topology needs to be derived from the data. In this paper, a robust approach to the extraction of a feature skeleton is presented. The skeleton reflects the overall structure of an object. It is given by a set of lines that run along ridges or valleys and meet at umbilical points. The computed data is not just useful for building semantic-driven CAD models in reverse engineering disciplines but also to identify geometrical features for tasks like object recognition, registration, rendering or re-meshing. Based on the mean curvature, a Markov random field is used to robustly classify each vertex either belonging to convex, concave or flat regions. The boundaries of the regions are described by a set of points that are robustly estimated using linear interpolation. A novel algorithm is used to extract the feature skeleton based on the Voronoi decomposition of the boundary points. The method has been successfully tested on real world examples and the paper concludes with a detailed evaluation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wekel, T., Hellwich, O.: Selection of an Optimal Polyhedral Surface Model Using the Minimum Description Length Principle. In: Goesele, M., Roth, S., Kuijper, A., Schiele, B., Schindler, K. (eds.) Pattern Recognition. LNCS, vol. 6376, pp. 553–562. Springer, Heidelberg (2010)
Hildebrandt, K., Polthier, K., Wardetzky, M.: Smooth feature lines on surface meshes. In: Proceedings of the third Eurographics Symposium on Geometry Processing, Eurographics Association, Aire-la-Ville (2005)
Cazals, F., Pouget, M.: Estimating differential quantities using polynomial fitting of osculating jets. In: Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP 2003, pp. 177–187. Eurographics Association, Aire-la-Ville (2003)
Chazal, F., Cohen-Steiner, D., Lieutier, A., Thibert, B.: Stability of curvature measures. In: Proceedings of the Symposium on Geometry Processing, SGP 2009, pp. 1485–1496. Eurographics Association, Aire-la-Ville (2009)
Agam, G., Tang, X.: A sampling framework for accurate curvature estimation in discrete surfaces. IEEE Transactions on Visualization and Computer Graphics 11, 573–583 (2005)
Weinkauf, T., Günther, D.: Separatrix persistence: Extraction of salient edges on surfaces using topological methods. CG Forum 28, 1519–1528 (2009)
Ohtake, Y., Belyaev, A., Seidel, H.P.: Ridge-valley lines on meshes via implicit surface fitting. ACM Trans. Graph. 23, 609–612 (2004)
Yoshizawa, S., Belyaev, A., Seidel, H.P.: Fast and robust detection of crest lines on meshes. In: Proceedings of the 2005 ACM Symposium on Solid and Physical Modeling, SPM 2005, pp. 227–232. ACM, New York (2005)
Kim, H.S., Choi, H.K., Lee, K.H.: Feature detection of triangular meshes based on tensor voting theory. Comput. Aided Des. 41, 47–58 (2009)
Cazals, F., Pouget, M.: Topology driven algorithms for ridge extraction on meshes (2005)
Biasotti, S., De Floriani, L., Falcidieno, B., Frosini, P., Giorgi, D., Landi, C., Papaleo, L., Spagnuolo, M.: Describing shapes by geometrical-topological properties of real functions. ACM Comput. Surv. 40, 12:1–12:87 (2008)
Pauly, M., Keiser, R., Gross, M.H.: Multi-scale feature extraction on point-sampled surfaces. Comput. Graph. Forum 22, 281–290 (2003)
Lavoué, G., Wolf, C.: Markov Random Fields for Improving 3D Mesh Analysis and Segmentation. In: Eurographics 2008 Workshop on 3D Object Retrieval (2008)
Benhabiles, H., Lavou, G., Vandeborre, J.P., Daoudi, M.: Learning boundary edges for 3d-mesh segmentation. Computer Graphics Forum 30, 2170–2182 (2011)
Rössl, C., Kobbelt, L., Seidel, H.P.: Extraction of feature lines on triangulated surfaces using morphological operators. In: Proceedings of the AAAI Symposium on Smart Graphics, pp. 71–75 (2000)
Wiegerinck, W., Heskes, T.: Fractional belief propagation. In: NIPS, pp. 438–445. MIT Press (2003)
Mitchell, J.S.B., Mount, D.M., Papadimitriou, C.H.: The discrete geodesic problem. SIAM J. Comput. 16, 647–668 (1987)
Surazhsky, V., Surazhsky, T., Kirsanov, D., Gortler, S.J., Hoppe, H.: Fast exact and approximate geodesics on meshes. ACM Trans. Graph. 24, 553–560 (2005)
Floater, M.S.: Mean value coordinates. Computer Aided Geometric Design 20, 19–27 (2003)
Lévy, B., Petitjean, S., Ray, N., Maillot, J.: Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph. 21, 362–371 (2002)
Saboret, L., Alliez, P., Lvy, B.: Planar parameterization of triangulated surface meshes. In: CGAL User and Reference Manual. 4.0 edn. CGAL Editorial Board (2012), http://www.cgal.org/
Hert, S., Seel, M.: dD convex hulls and Delaunay triangulations. In: CGAL User and Reference Manual, 4th edn. CGAL Editorial Board (2012), http://www.cgal.org/
Computational Geometry Algorithms Library, http://www.cgal.org/
AIM@SHAPE, http://shapes.aim-at-shape.net/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wekel, T., Hellwich, O. (2013). Voronoi-Based Extraction of a Feature Skeleton from Noisy Triangulated Surfaces. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds) Computer Vision – ACCV 2012. ACCV 2012. Lecture Notes in Computer Science, vol 7725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37444-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-37444-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37443-2
Online ISBN: 978-3-642-37444-9
eBook Packages: Computer ScienceComputer Science (R0)