1. Progressive Geometry Compression Zhu Ping 2006.12.06

2. Compression Necessity: 1. Storage; 2. Transmission Base: Information Theory

3. Coding Techniques Huffman coding Arithmetic coding VQ coding LZW coding

4. Geometry Compression Geometry Compression. Siggraph 95 Michael Deering Sun Microsystems an engineer in Java 3D API Interest:virtual reality

6. 1.Vertice buffer 2.Old vertice 3.New vertice

9. Cost: 1. Mesh Buffer 2. Push Selected(one more bit) 3. Reuse Vertice from Buffer

10. Progressive Mesh Progressive Mesh. Siggraph 96 Huges Hoppe. Progressive Procession: M n M n-1 +W n M n-1 predition P W n M n= M n-1 +(P(M n-1 )+ w n )) {M 0,w n, … w 1 }

11. Progressive Compression of Arbitary Trianglar Meshes IEEE Visualization 99. Daniel Cohen-Or David Levin Offir Remez Levin:a professor inSchool of Mathematical Sciences Tel Aviv University,Israel Interest:Subdivision,Image Processing,CAGD, Computer Graphics

12. The 4-color encoding scheme

13. The 2-color encoding scheme

15. Codec Design Input S N eNeN 量化器编码器 eN’eN’ 预测器 解码器 预测器 发送端 输出 ＋－ ＋ ＋ eN’eN’ SN‘SN‘ SN‘SN‘ 接收端 S ’‘ N

16. Mesh Optimization Mesh Optimization. Siggraph 93 Hugues Hoppe Tony DeRose Tom Duchamp Hoppe:a professor in University of Washington,now in Graphics Group of Microsoft. 2 ACM TOGs in 06y 2 ACM TOGs in 05y 4 ACM TOGs in 04y Graphics Award in Siggrpah

17. Interest:Mesh Simplicial,Compression, Texture synthesis Question: 网格优化：指作表面网格的优化，通过删除 和插入一些点，使得表面网格在曲率较大的 地方网格较密，光滑平坦处网格单元较大。 目的是合理布置网格的密度，提高单元格的质量。

18. Mesh Representation

19. Mesh Simplicial

20. Mesh Energy Function

22. Application ： Surface Reconstruction ； Mesh Simplification

23. Geometric Compression For Interactive Transmission Geometric Compression For Interactive Transmission. IEEE Visualization 2000 Olivier Devillers Pierre-Marie Gandoin INRIA Sophia Antipolis,France Overview: the topology of mesh can often be reconstructed from its vertices geometry-centric

24. Analysis

26. The cost of bits

27. Coding and Prediction 1. Arithmetric Coding 2. Prediction

28. Topology Coding

30. Experimental Results

31. Progressive Lossless Compression of Arbitrary Simplical Complexes Progressive Lossless Compression of Arbitrary Simplical Complexes. ACM TOG 2002 Pierre-Marie Gondoin Olivier Devillers Related: [Devillers and Gandoin 2000] [Popovic and Hoppe 1997]

32. Geometry Driven Approach:kd-tree

33. Progressive Simplicial Complexes Jovan Popovic Hugues Hoppe Siggraph 97

35. Analysis:

37. Prediction

38. Results:

39. Future Work: Polygonal Meshes

40. Future Work: Polygonal Meshes

41. Thank You !!