2. Point-based techniques Mei ’ e Fang Wednesday, November 1, 2006

3. contents relative c onceptions of point-based surfaces point-based representations point-based geometry processing point-based rendering a paper on computing areas of point-based surfaces

4. main references Leif Kobbelt, Mario Botsch. A survey of point-based techniques in computer graphics. Computers & Graphics, 2004 28: 801-814. Yu-Shen Liu, Jun-Hai Yong, Hui Zhang, Dong-Ming Yan, Jia-Guang Sun. A quasi-Monte Carlo method for computing areas of point-sampled surfaces. CAD, 2006 38: 55-68.

5. Relative c onceptions

6. NURBS → Meshes → Point-clouds The topological consistency becomes more and more simply.

7. neighborhoods and normals two kinds of neighborhoods Euclidean neighborhoods not suited for irregularly sampled surfaces and unreliable in some cases k-nearest neighborhoods a naturally adaptive neighborhood relation

8. Amenta, N., Bern, M., Kamvysselis, M., 1998. A new Voronoi-based surface reconstruction algorithm. In: Proc. of ACM SIGGRAPH 98. Andersson, M., Giesen, J., Pauly, M., Speckmann, B., 2004. Bounds on the k-neighborhood for locally uniformly sampled surfaces. In: Proc. of Symp. on Point-Based Graphics 04. pp. 167–171. J. Sankaranarayanan, H. Samet, and A. Varshney, A Fast k-Neighborhood Algorithm for Large Point Clouds. Proceedings of the Symposium on Point- Based Graphics July 29 - 30, 2006, Boston, MA

9. the estimation of normals the covariance matrix: The eigenvector corresponding to the smallest eigenvalue gives an estimate for the normal direction. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W., 1992. Surface reconstruction from unorganized points. In: Proc. of ACM SIGGRAPH92. pp. 71–78.

10. Point-based representations purely point-based representations surface splats moving least-squares surfaces

11. point clouds purely point-based representations

12. Grossman, J. P., Dally, W. J., 1998. Point sample rendering. In: Proc. Of Eurographics Workshop on Rendering 98. pp. 181–192. Similar to image-based approaches, this representation is also constructed from several views of an input object, but it differs in that each pixel is a surface sample containing geometric position and (view-independent) surface color.

14. Kalaiah, A., Varshney, A., 2003. Statistical point geometry. In: Proc. of Eurographics Symposium on Geometry Processing 03. pp. 107–115. using a hierarchical PCA analysis to partition the geometry and its attributes (normals and colors) into a set of local Gaussian probability distributions

16. Botsch, M., Wiratanaya, A., Kobbelt, L., 2002. Efficient high quality rendering of point sampled geometry. In: Proc. of Eurographics Workshop on Rendering 02. considering the quantization precision to minimize redundancy and using a hierarchical PBR to reduce the memory cost

17. PBR of a circle with different quantization levels (left: 5 bit, right 10 bit) and different sampling densities (top:2  / 32, bottom: 2  / 1024).

18. Zwicker, M., Pfister, H., van Baar, J., Gross, M., 2001. Surface splatting. In:Proc. of ACM SIGGRAPH 01. pp. 371–378. circular disks → elliptical splats surface splats

19. two tangential axes: the principal curvature directions of the underlying surface two respective radii: inversely proportional to the corresponding minimum and maximum curvatures superiorities: the same topological flexibility as pure point clouds; the same approximation order as triangle meshes; locally the best linear approximant to a smooth surface; elliptical splats

20. Pauly, M., Keiser, R., Kobbelt, L., Gross, M., 2003. Shape modeling with point-sampled geometry. In: Proc. of ACG SIGGRAPH 03. representing sharp features

22. moving least-squares surfaces g is found by minimizing H is found by minimizing The weight function

23. Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C. T., 2003. Computing and rendering point set surfaces. IEEE Transactions on Visualization and Computer Graphics 9 (1), 3–15. Alexa, M., Adamson, A., 2004. On normals and projection operators for surfaces defined by point sets.In: Proc. of Symp. on Point- Graphics 04.pp. 149–155.

24. Amenta, N., Kil, Y., 2004. Defining point-set surfaces. In: Proc. of ACM SIGGRAPH 04.

25. Point-based geometry processing

26. noise removal Pauly, M., Gross, M., 2001. Spectral processing of point-sampled geometry. In: Proc. of ACM SIGGRAPH 01.

27. Original Patch Gaussian Wiener noise+blur Layout Filter Filter

29. summary versatile spectral decomposition of point- based models effective filtering adaptive resampling efficient processing of large point- sampled models

30. Pauly, M., Keiser, R., Gross, M., 2003. Multi-scale feature extraction on point-sampled surfaces. In: Proc. of Eurographics 03.

31. Weyrich, T., Pauly, M., Heinzle, S., Keiser, R., Scandella, S., Gross, M., 2004.Post-processing of scanned 3D surface data. In: Proc. of Symp. on Point-Based Graphics 04. pp. 85–94.

32. decimation three kinds of decimation methods Pauly, M., Gross, M., Kobbelt, L., 2002. Efficient simplification of point- sampled surfaces. In: Proc. of IEEE Visualization 02. hierarchical clustering method iterative simplification particle simulation

33. clustering method

34. iterative simplification

35. particle simulation

36. comparison

38. Wu, J., Kobbelt, L., 2004. Optimized subsampling of point sets for surface splatting. In: Proc. of Eurographics 04. a simplification method especially designed for splat-based surface

40. editing Zwicker, M., Pauly, M., Knoll, O., Gross, M., 2002. PointShop 3D: An interactive system for point-based surface editing. In: Proc. of ACM SIGGRAPH02.

41. Adams, B., Wicke, M., Dutr´e, P., Gross, M., Pauly, M., Teschner, M., 2004. Interactive 3D painting on point-sampled objects. In: Proc. of Symp. on Point-Based Graphics 04. pp. 57–66.

43. deformation Pauly, M., Keiser, R., Kobbelt, L., Gross, M., 2003. Shape modeling with point-sampled geometry. In: Proc. of ACG SIGGRAPH 03.

48. PDE-based segmentation, texture synthesis, texture inpainting and geometry smoothing

49. Constructive Solid Geometry technique references Clarenz, U., Rumpf, M., Telea, A., 2004. Finite elements on point based surfaces.In: Proc. of Symp. on Point-Based Graphics 04. pp. 201–211. Adams, B., Dutre, P., 2003. Interactive boolean operations on surfel- bounded solids. In: Proc. of ACM SIGGRAPH 03. pp. 651–656. Adams, B., Dutre, P., 2004. Boolean operations on surfel-bounded solids using programmable graphics hardware. In: Proc. of Symp. on Point- Based Graphics 04. pp. 19–24.

50. Point-based rendering

51. Botsch, M., Spernat, M., Kobbelt, L., 2004.Phong splatting. In: Proc. of Symp. on Point-Based Graphics 04.

53. References Grossman, J. P., Dally, W. J., 1998. Point sample rendering. In: Proc. Of Eurographics Workshop on Rendering 98. pp. 181–192. Dachsbacher, C., Vogelgsang, C., Stamminger, M., 2003. Sequential point trees. In: Proc. of ACM SIGGRAPH 03. Botsch, M., Kobbelt, L., 2003. High-quality point-based rendering on modern GPUs. In: Proc. of Pacific Graphics 03. Guennebaud, G., Paulin, M., 2003. Efficient screen space approach for hardware accelerated surfel rendering. In: Proc. of Vision, Modeling, and Visualization 03. Botsch, M., Spernat, M., Kobbelt, L., 2004. Phong splatting. In: Proc. Of Symp. on Point-Based Graphics 04. Zwicker, M., Räsänen, J., Botsch, M., Dachsbacher, C., Pauly, M., 2004. Perspective accurate splatting. In: Proc. of Graphics Interface 04.

54. Computing the areas of point- based surfaces

55. Quasi-Monte Carlo method Yu-Shen Liu, Jun-Hai Yong, Hui Zhang, Dong-Ming Yan, and Jia-Guang Sun. A quasi-Monte Carlo method for computing areas of point-sampled surfaces. Computer-Aided Design 2006; 38(1): 55-68. Li X, Wang W, Martin RR, Bowyer A. Using low-discrepancy sequences and the Crofton formula to compute surface areas of geometric models. Comput Aided Design 2003;35(9):771–82.

56. the Cauchy–Crofton formula the area formula of B integration approximation

57. steps

58. the smallest enclosing ball of point sets Gärtner B. Fast and robust smallest enclosing balls. In: Proc. 7 th Annual European Symposium on Algorithms (ESA). Volume 1643 of Lecture Notes in Computer Science, Springer-Verlag (1999), p. 325-338, 1999. http://www.inf.ethz.ch/personal/gaertner/miniball.html

59. generating uniformly distributed lines http://mathworld.wolfram.com/SpherePointPicking.html

60. the LPSI algorithm

61. collecting and clustering inclusion points

62. classifying clusters (a) Q contains no intersection point. (b) Q contains only one touching point.

63. (c) Q contains only one intersection point. (d) Q contains two intersection points.

64. approximation errors

66. Ohtake Y., Belyaev A., Alexa M., Turk G., Seidel H.P. Multi-level partition of unity implicits. In: Proceedings of SIGGRAPH’03; 2003. p. 463-470.

68. http://graphics.stanford.edu/data/3Dscanrep/ Desbrun M., Meyer M., Schr Ö der P., Barr A.H. Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of SIGGRAPH’99; 1999. p. 317-324.

69. applications several point-based processing applications such as property computation, area- preserving smoothing, shape recognition, matching …