Progressive Encoding of Complex Isosurfaces Haeyoung Lee Mathieu Desbrun Peter Schröder USC USC Caltech

2 MotivationMotivation Largest meshes come from volume data  MRI, CT, Laser Scan  Scientific simulation Challenging to store and/or transmit

3 Background on Compression  Mesh Encoding vs. Geometry Encoding  Connectivity + Geometry, or Geometry only  Single-rate vs. Progressive Compression  Progressivity is preferred for huge meshes T r a n s m i s s i o n Single-rate Progressive

4 Our Context  High genus and many components  Remeshing impractical »best known coders unusable!  Extracted from volume data  Very special mesh structure V: CC:183 Genus: 425 Skull, extracted from 257x257x257 MRI volume data

5 OutlineOutline Definitions Previous Work Our progressive compression  Connectivity  Geometry Our results Conclusion and Future work

6 DefinitionsDefinitions Volume data Binary Sign Isosurface Piercing edge Homogeneous Inhomogeneous

7 Previous Work (1) Single-rate Isosurface Compression  Connectivity: locate piercing edges »Saupe & Kuska ’01,’02: Octree »Zhang et al ’01: Binary sign and cell map »Yang & Wu ’02: 3D chessboard »Taubin ’02 (BLIC): Binary Sign map  Geometry: displacements along piercing edges Much lower rates than general mesh encoders

8 Previous Work (2) Progressive Isosurface Compression  Laney et al »Distance transformation & wavelet decomposition  Samet and Kochut 2002 »Octree encoding, without explicit geometry Problems: »Very limited test sets »Bitrates much worse than single-rate encoders

9 Our Contributions Progressive Isosurface Codec  Connectivity Encoding »Novel octree encoding of binary bitmaps  Geometry Encoding »Dual contouring for crack-free visualization Best bitrates so far  even better than any single-rate isosurface encoders

10 Our Design Choices (1) Adaptive Octree for Connectivity Encoding  Enable progressive localization  Provide contexts for entropy coding  Avoid redundancy Horse: 9*9*9 (level 3) 17*17*17 (level 4) 33*33*33 (level 5)

11 Our Design Choices (2) Dual Contouring [Ju et al 02, SW02]  Watertight meshes  Sharp features for hermite data  Vertices in cells, not on edges

12 Our Encoder At A Glance Read in & Process volume data Build Octree Create Isosurface by DC Encode Geometry Encode Connectivity during a breadth-first traversal

13 Connectivity Encoding  Sign bits (Inside/Outside)  Encode binary signs at grid vertices »Cells with children: encode necessary signs »Cells without children: deduce sign from the parent  Leaf bits (Leaf/Non-leaf)  Encode the presence of children »Identify non-empty cells

14 Context Modeling Compression ratios depend on context choice  Sign bitstream:  15-bit context (best bit rates): 7 neighbors + 8 of parent »Differs from JBIG  Leaf bitstream:  1-bit context: previous bit (best bit rates)

15 Geometry Encoding? Sometimes, octree bits enough!  Octree provides coarse geometry during decoding »Barycenters of midpoints of the piercing edges w/o geo w/ geo w/o geo w/ geo

16 Geometry Encoding Local Coordinate System  Least-square fitted plane »through midpoints of piercing edges  Two passes »normal(z) & tangential(x,y)  Context : 8 signs of the cell Center P P

17 ImplementationImplementation Beware of Memory Footprint!  Octree data structure can be overkill »257 3 grids use up more than 1Gb  We use a “linearized” data structure »Unfolds the octree in a bitmap »No pointers, no recursive calls »Allows grids (or bigger) on your PC

18 Our Results (1) Total: 6.10b/v on average out of 10 models Connectivity:  0.65 b/v on average  24% better than Taubin’s single-rate BLIC Geometry:  5.45 b/v on average  For a distortion similar to 12-bit quantization

19 Our Results (2) Oct. level Bytes Distort (10 -4 ) , , % geo. 145,

20 Our Results (3) Octree level Bytes passed Distortion(10 -4 ) bytes % geo. 92,156 bytes % geo. 226,554 bytes ,605 bytes 22.02

21 Results (4) For High Genus, High Complexity Geometry 30Kb 115Kb 602Kb

22 Results (5) Encoding a raw mesh often requires > 15b/v 3.95 b/v ( ) 3.21 b/v ( ) 3.45 b/v ( )

23 ConclusionConclusion  Progressive isosurface compression  Progressive coding of binary octree  Encoding of dual contouring mesh vertices  Context modeling with arithmetic coding  Competitive compression ratios  24% better than the leading single-rate on connectivity alone

24 Future Work  Reducing bit rate further  Sophisticated binary valued wavelet?  View-dependent compression  View-dependent encoding  View-dependent decoding  Volume compression  Neighboring isosurfaces