Progressive Encoding of Complex Iso-Surfaces

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Progressive Encoding of ComplexIso-Surfaces

• Peter Schröder
• Caltech ASCI Alliance Center for Simulation of
  Dynamic Response of Materials
• Joint work with Haeyoung Lee Mathieu Desbrun
  (USC)
• Review
• October 28, 2003

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Motivation

• Big simulations produce big data
• many times relevant results given as iso-surface
• Many other applications
• MRI, CT, Laser Scan
• science, medicine, industry, art history

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Background on Compression

• Mesh Encoding vs. Geometry Encoding
• Connectivity Geometry, or Geometry only
• Single-rate vs. Progressive Compression
• Progressivity is essential for very large datasets

Progressive
T r a n s m i s s i o n
Single-rate
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Our Context

• High genus and many components
• Remeshing impractical
• best known coders unusable!
• Extracted from volume data
• Very special mesh structure

V 280039CC183Genus 425
Skull, extracted from 257x257x257 MRI volume data
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Previous Work

• 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
• Progressive Isosurface Compression
• Laney et al. 2002
• Distance transformation wavelet decomposition
• Samet and Kochut 2002
• Octree encoding, without explicit geometry
• Far worse rates than general mesh encoders

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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

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Definitions

• Volume data
• Binary Sign
• Isosurface
• Piercing edge
• Homogeneous
• Inhomogeneous

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Our Design Choices

• Adaptive Octree for Connectivity Encoding
• Enable progressive localization
• Provide contexts for entropy coding
• Avoid redundancy
• Dual Contouring Ju et al 02, SW02
• Watertight meshes
• Sharp features for hermite data
• Vertices in cells, not on edges

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Our Encoder at a Glance

• Read in Process volume data
• Build Octree
• Create Isosurface by DC

• Encode Connectivity
• during a breadth-first traversal

• Encode Geometry

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Connectivity Encoding

• Sign bits (Inside/Outside)
• Encode binary signs at grid vertices
• Cells with children encode necessary signs
• Cells without children deduce from parent
• Leaf bits (Leaf/Non-leaf)
• Encode the presence of children
• Identify non-empty cells
• Context modeling in coder
• Sign bitstream
• 15-bit context (best bit rates)
  7 neighbors
  8 of parent
• Leaf bitstream
• 1-bit context previous bit (best bit rates)

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Geometry Encoding?

• Sometimes, octree bits enough!
• Octree provides coarse geometry during decoding
• Barycenters of midpoints of the piercing edges

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Implementation Details

• 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
• Beware of Memory Footprint!
• Octree data structure can be overkill
• 2573 grids use up more than 1Gb
• We use a linearized data structure
• Unfolds the octree in a bitmap
• No pointers, no recursive calls
• Allows 10253 grids (or bigger) on your PC

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Results

• Total 6.10b/v on average out of 10 models
• Connectivity
• 0.65 b/v on average
• 24 better than Taubins single-rate BLIC
• Geometry
• 5.45 b/v on average
• For a distortion similar to 12-bit quantization

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Results
5 622 303.47
8 100 geo. 145,708 0.47
Oct. level Bytes Distort (10-4)
7 8,411 32.72
8 20,324 3.66
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Results
Octree level Bytes passed Distortion(10-4)
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Results

• For High Genus, High Complexity Geometry

30Kb 115Kb 602Kb
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Results

• Encoding a raw mesh often requires gt 15b/v

3.95 b/v (0.58 3.37)
3.21 b/v (0.51 2.70)
3.45 b/v (0.09 3.39)
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Conclusion Future Work

• 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
• Reducing bit rate further
• Sophisticated binary valued wavelet?
• View-dependent compression
• View-dependent encoding
• View-dependent decoding
• Volume compression
• Neighboring isosurfaces