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A Face Fairness Framework for 3D Meshes

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Abstract

In this paper, we present a face fairness framework for 3D meshes that preserves the regular shape of faces and is applicable to a variety of 3D mesh restoration tasks. Specifically, we present a number of desirable properties for any mesh restoration method and show that our framework satisfies them. We then apply our framework to two different tasks—mesh-denoising and mesh-refinement, and present comparative results for these two tasks showing improvement over other relevant methods in the literature.

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References

  • Babuška, I., & Aziz, A. K. (1976). On the angle condition in the finite element method. SIAM Journal on Numerical Analysis, 13(2), 214–226.

    Article  MathSciNet  Google Scholar 

  • Chatterjee, A., & Govindu, V. M. (2015). Photometric refinement of depth maps for multi-albedo objects. In IEEE conference on computer vision and pattern recognition, IEEE (pp. 933–941).

  • Cheng, X., Zeng, M., & Liu, X. (2014). Feature-preserving filtering with \(\ell _0\)-gradient minimization. Computers & Graphics, 38, 150–157.

    Article  Google Scholar 

  • Curless, B., & Levoy, M. (1996). A volumetric method for building complex models from range images. In 23rd Annual conference on computer graphics and interactive techniques, ACM (pp. 303–312).

  • Desbrun, M., Meyer, M., Schröder, P., & Barr, A. H. (1999). Implicit fairing of irregular meshes using diffusion and curvature flow. In 26th Annual conference on computer graphics and interactive techniques (pp. 317–324). ACM Press/Addison-Wesley Publishing Co.

  • Du, D. Z., & Hwang, F. (1995). Computing in Euclidean geometry (Vol. 4). Singapore: World Scientific.

    Book  Google Scholar 

  • El Ouafdi, A., & Ziou, D. (2008). A global physical method for manifold smoothing. In IEEE international conference on shape modeling and applications, 2008. SMI 2008 (pp. 11–17).

  • Fan, H., Yu, Y., & Peng, Q. (2010). Robust feature-preserving mesh denoising based on consistent subneighborhoods. IEEE Transactions on Visualization and Computer Graphics, 16(2), 312–324.

    Article  Google Scholar 

  • Field, D. A. (1988). Laplacian smoothing and delaunay triangulations. Communications in Applied Numerical Methods, 4(6), 709–712.

    Article  Google Scholar 

  • Fleishman, S., Drori, I., & Cohen-Or, D. (2003). Bilateral mesh denoising. ACM Transactions on Graphics, 22(3), 950–953.

    Article  Google Scholar 

  • Fried, I. (1960). Condition of finite element matrices generated from nonuniform meshes. Communications on Pure and Applied Mathematics, 13, 217–237.

    Article  MathSciNet  Google Scholar 

  • Furukawa, Y., & Ponce, J. (2010). Accurate, dense, and robust multi-view stereopsis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(8), 1362–1376.

    Article  Google Scholar 

  • Haque, S. M., & Govindu, V. M. (2015). Global mesh denoising with fairness. In 3rd international conference on 3D vision.

  • Haque, S. M., & Govindu, V. M. (2017). Multi-view non-rigid refinement and normal selection for high quality 3D reconstruction. In IEEE international conference on computer vision.

  • Haque, S. M., Chatterjee, A., & Govindu, V. M. (2014). High quality photometric reconstruction using a depth camera. In IEEE conference on computer vision and pattern recognition (pp. 2275–2282).

  • He, L., & Schaefer, S. (2013). Mesh denoising via \(\ell _0\)-minimization. ACM Transactions on Graphics, 32(4), 64.

    Google Scholar 

  • Hoppe, H., DeRose, T., Duchamp, T., & McDonald, J., & Stuetzle, W. (1993). Mesh optimization. In: 20th Annual conference on Computer graphics and interactive techniques (pp. 19–26), ACM.

  • Innmann, M., Zollhöfer, M., Nießner, M., Theobalt, C., & Stamminger, M. (2016) Volumedeform: Real-time volumetric non-rigid reconstruction. In European conference on computer vision (pp. 362–379), Springer.

  • Ji, Z., Liu, L., & Wang, G. (2005). A global Laplacian smoothing approach with feature preservation. In Ninth International Conference on Computer Aided Design and Computer Graphics (pp. 269–274). IEEE Computer Society.

  • Jones, T. R., Durand, F., & Desbrun, M. (2003). Non-iterative, feature-preserving mesh smoothing. ACM Transactions on Graphics, 22(3), 943–949.

    Article  Google Scholar 

  • Kim, K., Torii, A., & Okutomi, M. (2016) Multi-view inverse rendering under arbitrary illumination and albedo. In European conference on computer vision (pp. 750–767). Springer International Publishing

  • Liu, L., Tai, C. L., Ji, Z., & Wang, G. (2007). Non-iterative approach for global mesh optimization. Computer Aided Design, 39(9), 772–782.

    Article  Google Scholar 

  • Lu, X., Chen, W., & Schaefer, S. (2017a). Robust mesh denoising via vertex pre-filtering and l1-median normal filtering. Computer Aided Geometric Design.

  • Lu, X., Deng, Z., & Chen, W. (2016). A robust scheme for feature-preserving mesh denoising. IEEE Transactions on Visualization and Computer Graphics, 22(3), 1181–1194.

    Article  Google Scholar 

  • Lu, X., Liu, X., Deng, Z., & Chen, W. (2017b). An efficient approach for feature-preserving mesh denoising. Optics and Lasers in Engineering, 90, 186–195.

    Article  Google Scholar 

  • Max, N. (1999). Weights for computing vertex normals from facet normals. Journal of Graphics Tools, 4(2), 1–6.

    Article  Google Scholar 

  • Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003). Discrete differential-geometry operators for triangulated 2-manifolds. In Visualization and mathematics III (pp. 35–57). Springer

  • Nealen, A., Igarashi, T., Sorkine, O., & Alexa, M. (2006) Laplacian mesh optimization. In: 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia, ACM (pp. 381–389).

  • Nehab, D., Rusinkiewicz, S., Davis, J. E., & Ramamoorthi, R. (2005). Efficiently combining positions and normals for precise 3D geometry. ACM Transactions on Graphics, 24(3), 536–543.

    Article  Google Scholar 

  • Ohtake, Y., Belyaev, A., & Seidel, H. (2002) Mesh smoothing by adaptive and anisotropic Gaussian filter applied to mesh normals. In Vision modeling and visualization.

  • Or El, R., Rosman, G., Wetzler, A., Kimmel, R., & Bruckstein, A. M. (2015) Rgbd-fusion: Real-time high precision depth recovery. In IEEE conference on computer vision and pattern recognition.

  • Sun, X., Rosin, P. L., Martin, R. R., & Langbein, F. C. (2008). Random walks for feature-preserving mesh denoising. Computer Aided Geometric Design, 25(7), 437–456.

    Article  MathSciNet  Google Scholar 

  • Sun, X., Rosin, P., Martin, R., & Langbein, F. (2007). Fast and effective feature-preserving mesh denoising. IEEE Transactions on Visualization and Computer Graphics, 13(5), 925–938.

    Article  Google Scholar 

  • Taubin, G. (1995). A signal processing approach to fair surface design. In 22nd annual conference on computer graphics and interactive techniques, ACM, New York, NY, USA, SIGGRAPH ’95 (pp. 351–358).

  • Taubin, G. (2001). Linear anisotropic mesh filtering. Res Rep RC2213 IBM.

  • Thürrner, G., & Wüthrich, C. A. (1998). Computing vertex normals from polygonal facets. Journal of Graphics Tools, 3(1), 43–46.

    Article  Google Scholar 

  • Wang, P. S., Liu, Y., & Tong, X. (2016). Mesh denoising via cascaded normal regression. ACM Transactions on Graphics (SIGGRAPH Asia), 35(6), 232.

    Google Scholar 

  • Wang, R., Yang, Z., Liu, L., Deng, J., & Chen, F. (2014). Decoupling noise and features via weighted \(\ell _1\)-analysis compressed sensing. ACM Transactions on Graphics, 33(2), 18:1–18:12.

    Article  Google Scholar 

  • Wei, M., Yu, J., Pang, W. M., Wang, J., Qin, J., Liu, L., et al. (2015). Bi-normal filtering for mesh denoising. IEEE Transactions on Visualization and Computer Graphics, 21(1), 43–55.

    Article  Google Scholar 

  • Wu, C., Liu, Y., Dai, Q., & Wilburn, B. (2011a). Fusing multiview and photometric stereo for 3d reconstruction under uncalibrated illumination. IEEE Transactions on Visualization and Computer Graphics, 17(8), 1082–1095.

    Article  Google Scholar 

  • Wu, C., Wilburn, B., Matsushita, Y., & Theobalt, C. (2011b) High-quality shape from multi-view stereo and shading under general illumination. In IEEE conference on computer vision and pattern recognition (pp. 969–976).

  • Zhang, H., Wu, C., Zhang, J., & Deng, J. (2015a). Variational mesh denoising using total variation and piecewise constant function space. IEEE Transactions on Visualization and Computer Graphics, 21(7), 873–886.

    Article  Google Scholar 

  • Zhang, W., Deng, B., Zhang, J., Bouaziz, S., & Liu, L. (2015b). Guided mesh normal filtering. Computer Graphics Forum, 34(7), 23–34.

    Article  Google Scholar 

  • Zheng, Y., Fu, H., Au, O. C., & Tai, C. L. (2011). Bilateral normal filtering for mesh denoising. IEEE Transactions on Visualization and Computer Graphics, 17(10), 1521–1530.

    Article  Google Scholar 

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Correspondence to Sk. Mohammadul Haque.

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Communicated by Michael Bronstein.

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This work was done when Sk. Mohammadul Haque was a PhD student at Indian Institute of Science, Bengaluru, India.

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Haque, S.M., Govindu, V.M. A Face Fairness Framework for 3D Meshes. Int J Comput Vis 128, 1565–1579 (2020). https://doi.org/10.1007/s11263-019-01268-z

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  • DOI: https://doi.org/10.1007/s11263-019-01268-z

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