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A unified method for appearance and geometry completion of point set surfaces

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Abstract

This paper presents a novel approach for appearance and geometry completion over point-sampled geometry. Based on the result of surface clustering and a given texture sample, we define a global texture energy function on the point set surface for direct texture synthesis. The color texture completion is performed by minimizing a constrained global energy using the existing surface texture on the surface as the input texture sample. We convert the problem of context-based geometry completion into a task of texture completion on the surface. The geometric detail is then peeled and converted into a piece of signed gray-scale texture on the base surface of the point set surface. We fill the holes on the base surface by smoothed extrapolation and the geometric details over these patches are reconstructed by a process of gray-scale texture completion. Experiments show that our method is flexible, efficient and easy to implement. It provides a practical texture synthesis and geometry completion tool for 3D point set surfaces.

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References

  1. Alexa, M., Klug, T., Stoll, C.: Direction fields over point-sampled geometry. J. WSCG 11(1), 27–32 (2003)

    Google Scholar 

  2. Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R.: Reconstruction and representation of 3D objects with radial basis functions. In: Proceedings of SIGGRAPH, pp. 67–76 (2001)

  3. Clarenz, U., Diewald, U., Dziuk, G., Rumpf, M., Rusu, R.: A finite element method for surface restoration with smooth boundary conditions. Comput. Aided Geom. Des. 21(5), 427–445 (2004)

    MATH  MathSciNet  Google Scholar 

  4. Clarenz, U., Rumpf, M., Telea, A.: Finite elements on point based surfaces. In: Proceedings of the EG Symposium of Point Based Graphics, pp. 201–211 (2004)

  5. Criminisi, A., Perez, P., Toyama, K.: Object removal by exemplar-based inpainting. In: IEEE Proceedings of Conference on Computer Vision and Pattern Recognition, pp. 417–424 (2003)

  6. Davis, J., Davis, S., Marschner, R., Garr, M., Levoy, M.: Filling holes in complex surfaces using volumetric diffusion. In: 1st International Symposium on 3D Data Processing, Visualization, Transmission, pp. 428–438 (2002)

  7. Dellaert, F., Kwatra, V., Oh, S.M.: Mixture trees for modeling and fast conditional sampling with applications in vision and graphics. In: IEEE Proceedings of Conference on Computer Vision and Pattern Recognition Recognition, pp. 619–624 (2005)

  8. Desbrun, M., Meyer, M., Schroer, P., Barr, A.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of SIGGRAPH, pp. 317–324 (1999)

  9. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proceedings of SIGGRAPH, pp. 71–78 (1992)

  10. Ju, T.: Robust repair of polygonal models. ACM Trans. Graph. 23(3), 888–895 (2004)

    Article  Google Scholar 

  11. Kwatra, V., Essa, I.A., Bobick, A.F., Kwatra, N.: Texture optimization for example-based synthesis. ACM Trans. Graph. 24(3), 795–802 (2005)

    Article  Google Scholar 

  12. Lai, Y.-K., Hu, S.-M., Gu, D.X., Martin, R.: Geometric texture synthesis and transfer via geometry images. In: Proceedings of the ACM Symposium on Solid and Physical Modeling, pp. 15–26 (2005)

  13. Levy, B.: Dual domain extrapolation. ACM Trans. Graph. 22(3), 364–369 (2003)

    Article  Google Scholar 

  14. Liepa, P.: Filling holes in meshes. In: Proceedings of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 200–205 (2003)

  15. Magda, S., Kriegman, D.: Fast texture synthesis on arbitrary meshes. In: Proceedings of the 14th Eurographics Workshop on Rendering, pp. 82–89 (2003)

  16. Nguyen, M.X., Yuan, X., Chen, B.: Geometry completion and detail generation by texture synthesis. In: Proceeding of Pacific Graphics, pp. 23–32 (2005)

  17. Ohtake, Y., Belyaev, A., Seidel, H.-P.: A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions. In: Proceedings of the Shape Modeling International, pp. 153–161 (2003)

  18. Park, S., Guo, X., Shin, H., Qin, H.: Shape and appearance repair for incomplete point surfaces. In: Proceedings of the International Conference on Computer Vision, pp. 1260–1267 (2005)

  19. Pauly, M., Gross, M., Kobbelt, L.: Efficient simplification of point-sampled surfaces. In: Proceedings of IEEE Visualization, pp. 163–170 (2002)

  20. Pauly, M., Mitra, N., Giesen, J., Gross, M., Guibas, L.J.: Example-based 3D scan completion. In: Symposium on Geometry Processing, pp. 23–32 (2005)

  21. Savchenko, V., Kojekine, N.: An approach to blend surfaces. In: Proceedings of Computer Graphics International, pp. 139–150 (2002)

  22. Sharf, A., Alexa, M., Cohen-Or, D.: Context-based surface completion. ACM Trans. Graph. 23(3), 878–887 (2004)

    Article  Google Scholar 

  23. Soler, C., Cani, M., Angelidis, A.: Hierarchical pattern mapping. In: Proceedings of SIGGRAPH, pp. 673–680 (2002)

  24. Sun, J., Yuan, L., Jia, J., Shum, H.Y.: Image completion with structure propagation. In: Proceedings of SIGGRAPH 24(3), 861–868 (2005)

    Google Scholar 

  25. Turk, G.: Texture synthesis on surfaces. In: Proceedings of SIGGRAPH, pp. 347–354 (2001)

  26. Verdera, J., Caselles, V., Bertalmio, M., Sapiro, G.: Inpainting surface holes. In: Proceedings of International Conference on Image Processing, pp. 903–906 (2003)

  27. Wei, L.-Y., Levoy, M.: Texture synthesis over arbitrary manifold surfaces. In: Proceedings of SIGGRAPH, pp. 355–360 (2001)

  28. Xiao, C., Miao, Y., Liu, S., Peng, Q.: A dynamic balanced flow for filtering point-sampled geometry. Vis. Comput. 22(3), 210–219 (2006)

    Article  Google Scholar 

  29. Ying, L., Hertzmann, A., Biermann, H., Zorin, D.: Texture and shape synthesis on surfaces. In: Proceedings of the Eurographics Symposium on Rendering, pp. 301–312 (2001)

  30. Zhou, K., Wang, X., Tong, Y., Desbrun, M., Guo, B., Shum, H.Y.: Texture montage: seamless texturing of arbitrary surfaces from multiple images. In: Proceedings of SIGGRAPH, pp. 1148–1155 (2005)

  31. Zigelman, G., Kimmel, R., Kiryati, N.: Texture mapping using surface flattening via multidimensional scaling. IEEE Trans. Visual. Comput. Graph. 8(2), 198–207 (2002)

    Article  Google Scholar 

  32. Zhang, J., Zhou, K., Velho, L., Guo, B., Shum, H.: Synthesis of progressively-variant textures on arbitrary surfaces. In: Proceedings of SIGGRAPH, pp. 295–302 (2003)

  33. Zelinka, S., Garland, M.: Interactive texture synthesis on surfaces using jump maps. In: Proceedings of 14th Eurographics Symposium on Rendering, pp. 673–680 (2003)

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Authors and Affiliations

  1. State Key Lab of CAD&CG, Zhejiang University, 38 Zheda Road, Hangzhou, P.R. China

    Chunxia Xiao, Wenting Zheng, Yongwei Miao, Yong Zhao & Qunsheng Peng

  2. Computer School, Wuhan University, Wuhan, P.R. China

    Chunxia Xiao

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  1. Chunxia Xiao
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  2. Wenting Zheng
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  3. Yongwei Miao
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  4. Yong Zhao
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  5. Qunsheng Peng
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Correspondence to Chunxia Xiao.

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Xiao, C., Zheng, W., Miao, Y. et al. A unified method for appearance and geometry completion of point set surfaces. Visual Comput 23, 433–443 (2007). https://doi.org/10.1007/s00371-007-0115-x

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