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Sampling-sensitive multiresolution hierarchy for irregular meshes

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Abstract

Previous approaches of constructing multiresolution hierarchy for irregular meshes investigated how to overcome the connectivity and topology constraints during the decomposition, but did not consider the effects of sampling information on editing and signal processing operations. We propose a sampling-sensitive downsampling strategy and design a decomposition framework that produces a hierarchy of meshes with decreasing maximum sampling rates and increasingly regular vertex support sizes. The resulting mesh hierarchy has good quality triangles and enables more stable editing. The detail vectors better approximate the frequency spectrum of the mesh, thus making signal filtering more accurate.

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References

  1. Alliez P, Meyer M, Desbrun M (2002) Interactive geometry remeshing. In: Proceedings SIGGRAPH ’02. Comput Graph 21(3):347–354

    Article  Google Scholar 

  2. Desbrun M, Meyer M, Schröder P, Barr AH (1999) Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings SIGGRAPH ‘99. Comput Graph Proc, Annual Conference Series, pp 317–324

  3. Eck M, DeRose T, Duchamp T, Hoppe H, Lounsbery M, Stuetzle W (1995) Multiresolution analysis of arbitrary meshes. In: Proceedings SIGGRAPH ’95. Comput Graph Proc, Annual Conference Series, pp 173–182

  4. Finkelstein A, Salesin D (1994) Multiresolution curves. In: Proceedings SIGGRAPH ’94. Comput Graph Proc, Annual Conference Series, pp 261–268

  5. Forsey DR, Bartels RH (1988) Hierarchical B-spline refinement. In: Proceedings SIGGRAPH ’88. Comput Graph 22:205–212

    Google Scholar 

  6. Garland M, Heckbert PS (1997) Surface simplification using quadric error metrics. In: Proceedings SIGGRAPH ’97. Comput Graph Proc, Annual Conference Series, pp 209–216

  7. Gu X, Gortler SJ, Hoppe H (2002) Geometry images. In: Proceedings SIGGRAPH ’02. ACM Trans Graph 21(3):355–361

    Article  Google Scholar 

  8. Guskov I, Sweldens W, Schröder P (1999) Multiresolution signal processing for meshes. In: Proceedings SIGGRAPH ’99. Comput Graph Proc, Annual Conference Series, pp 325–334

  9. Guskov I, Vidimce K, Sweldens W, Schröder P (2000) Normal meshes. In: Proceedings SIGGRAPH ’00. Comput Graph Proc, Annual Conference Series, pp 95–102

  10. Hoppe H (1996) Progressive meshes. In: Proceedings SIGGRAPH ’96. Comput Graph Proc, Annual Conference Series, pp 99–108

  11. Igarashi T, Matsuoka S, Tanaka H (1999) Teddy: a sketching interface for 3D freeform design. In: Proceedings SIGGRAPH ’99, Comput Graph Proc, Annual Conference Series, pp 409–416

  12. Khodakovsky A, Schröder P, Sweldens W (2000) Progressive geometry compression. In: Proceedings SIGGRAPH ’00. Comput Graph Proc, Annual Conference Series, pp 271–278

  13. Kim D, Kim J, Ko H-S (1999) Unification of distance and volume optimization in surface simplification. J Graph Models Image Process 61:363–367

    Article  Google Scholar 

  14. Kobbelt L, Bareuther T, Seidel H-P (2000) Multiresolution shape deformations for meshes with dynamic vertex connectivity. Comput Graph Forum 19(3):249–259

    Article  Google Scholar 

  15. Kobbelt L, Campagna S, Seidel H-P (1998) A general framework for mesh decimation. In: Proceedings of Graphics Interface ’98, pp 43–50

  16. Kobbelt L, Campagna S, Vorsatz J, Seidel H-P (1998) Interactive multiresolution modeling on arbitrary meshes. In: Proceedings SIGGRAPH ’98. Comput Graph Proc, Annual Conference Series, pp 105–114

  17. Kobbelt L, Vorsatz J, Seidel H-P (1999) Multiresolution hierarchies on unstructured triangle meshes. Comput Geom 14(1–3):5–24

    Google Scholar 

  18. Lee A, Sweldens W, Schröder P, Cowsar L, Dobkin D (1998) MAPS: Multiresolution adaptive parameterization of surfaces. In: Proceedings SIGGRAPH ’98. Comput Graph Proc, Annual Conference Series, pp 95–104

  19. Lindstrom P, Turk G (1998) Fast and memory efficient polygonal simplification. In: Proceedings IEEE Visualization ’98, pp 279–286

  20. Taubin G (1995) A signal processing approach to fair surface design. In: Proceedings SIGGRAPH ’95. Comput Graph Proc, Annual Conference Series, pp 351–358

  21. Taubin G (2000) Geometric signal processing on polygonal meshes. In: EUROGRAPHICS ’2000

  22. Zorin D, Schröder P (2000) Subdivision for modeling and animation. In: SIGGRAPH 2000 course notes

  23. Zorin D, Schröder P, Sweldens W (1997) Interactive multiresolution mesh editing. In: Proceedings SIGGRAPH ’97. Comput Graph Proc, Annual Conference Series, pp 259–469

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Correspondence to Oscar Kin-Chung Au.

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Au, OC., Tai, CL. Sampling-sensitive multiresolution hierarchy for irregular meshes. Visual Comp 20, 479–493 (2004). https://doi.org/10.1007/s00371-004-0253-3

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