Abstract
In this paper, we propose a new algorithm for fairing discrete surfaces resulting from stereo-based 3D reconstruction task. Such results are typically too dense, uneven and noisy, which is inconvenient for further processing. Our approach jointly optimises mesh smoothness and regularity. The definition is given on a discrete surface and the solution is found by discrete diffusion of a scalar function. Experiments on synthetic and real data demonstrate that the proposed approach is robust, stable, preserves qualitative shape and is applicable to even moderate-size real surfaces with boundary (0.8M vertices and 1.7M triangles).
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References
Nistér, D.: Automatic dense reconstruction from uncalibrated video sequences. PhD thesis, Royal Institute of Technology KTH, Stockholm, Sweden (2001)
Strecha, C., Tuytelaars, T., van Gool, L.: Dense matching of multiple wide-baseline views. In: Proceedings International Conference on Computer Vision, pp. 1194–1201 (2003)
Kamberov, G., et al.: 3D geometry from uncalibrated images. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Remagnino, P., Nefian, A., Meenakshisundaram, G., Pascucci, V., Zara, J., Molineros, J., Theisel, H., Malzbender, T. (eds.) ISVC 2006. LNCS, vol. 4292, pp. 802–813. Springer, Heidelberg (2006)
Duan, Y., Qin, H.: A novel modeling algorithm for shape recovery of unknown topology. In: Proceedings International Conference on Computer Vision (ICCV 2001), pp. 402–411 (2001)
Dyn, N., Hormann, K., Kim, S., Levin, D.: Optimizing 3D triangulations using discrete curvature analysis. In: Mathematical Methods for Curves and Surfaces, pp. 135–146 (2001)
Kobbelt, L.P.: Discrete fairing and variational subdivision for freeform surface design. The Visual Computer 16, 142–158 (2000)
Taubin, G.: A signal processing approach to fair surface design. In: Proceedings of the SIGGRAPH 1995, pp. 351–358 (1995)
Schneider, R., Kobbelt, L.: Geometric fairing of irregular meshes for free-form surface design. Computer Aided Geometric Design 18, 359–379 (2001)
Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of the SIGGRAPH 1999, pp. 317–324 (1999)
Surazhsky, T., Magid, E., Soldea, O., Elber, G., Rivlin, E.: A comparison of gaussian and mean curvatures estimation methods on triangular meshes. In: IEEE International Conference on Robotics and Automation 2003 (ICRA 2003), pp. 1021–1026 (2003)
Delingette, H.: Simplex meshes: a general representation for 3D shape reconstruction. Research Report 2214, INRIA, Sophia Antipolis (1994)
Yagou, H., Ohtake, Y., Belyaev, A.: Mesh smoothing via mean and median filtering applied to face normals. In: Geometric Modeling and Processing, pp. 124–131 (2002)
Mashiko, T., Yagou, H., Wei, D., Ding, Y., Wu, G.: 3D triangle mesh smoothing via adaptive MMSE filtering. In: Int. Conf. on Computer and Information Technology, pp. 734–740 (2004)
Jones, T.R., Durand, F., Desbrun, M.: Non-iterative, feature-preserving mesh smoothing. In: Proceedings of the SIGGRAPH 2003, pp. 943–949 (2003)
Escobar, J.M., Montero, G., Montenegro, R., Rodríguez, E.: An algebraic method for smoothing surface triangulations on a local parametric space. International Journal for Numerical Methods in Engineering 66, 740–760 (2006)
Kostlivá, J., Šára, R., Matýsková, M.: Inflection point preserving fairing of discrete surfaces with boundary. Research Report CTU–CMP–2008–19, Center for Machine Perception, K13133 FEE Czech Technical University, Prague, Czech Republic (2008)
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Kostlivá, J., Šára, R., Matýsková, M. (2008). Fairing of Discrete Surfaces with Boundary That Preserves Size and Qualitative Shape. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2008. Lecture Notes in Computer Science, vol 5358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89639-5_11
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DOI: https://doi.org/10.1007/978-3-540-89639-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89638-8
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