Compressing Texture Coordinates

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CompressingTexture Coordinates
with hSelective
LinearPredictions
Martin Isenburg
Jack Snoeyink
University of North Carolina at Chapel Hill
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Take this home

• We predict texture coordinateswith four
  different rules taking into account the
  presence of mapping discontinuities.
• We compress the corresponding corrective vectors
  with different arithmetic contexts.

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Overview

• Background
• Compressing Vertex Positions
• Linear Prediction Schemes
• Texture Coordinate Mappings
• Compressing Texture Coordinates
• Alternative Approaches
• Summary

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Background
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Meshes - Basic Ingredients

• connectivity
• geometry

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Meshes - Optional Properties

• mapping
• values

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Mesh Compression

• Fast Rendering
• Progressive Transmission
• Maximum Compression

Geometry Compression Deering, 95
Maximum Compression
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Mesh Compression

• Geometry Compression Deering, 95
• Fast Rendering
• Progressive Transmission
• Maximum Compression
• Connectivity
• Geometry
• Properties

Geometry Compression Deering, 95
Maximum Compression
Properties
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Mesh Compression

• Geometry Compression Deering, 95
• Fast Rendering
• Progressive Transmission
• Maximum Compression
• Connectivity
• Geometry
• Properties
• Mapping
• Values

Geometry Compression Deering, 95
Maximum Compression
Properties
Texture Coordinates
Values
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Triangle Mesh Compression
Triangle Mesh Compression Touma Gotsman,
Graphics Interface 98

• Texture Coordinates ???

Yes! But
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Generalization of TG coder
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CompressingVertex Positions
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Compressing Vertex Positions

• Classic approaches 95 98
• linear prediction

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Compressing Vertex Positions

• Classic approaches 95 98
• linear prediction
• Recent approaches 00 02
• spectral
• re-meshing
• space-dividing
• vector-quantization
• feature discovery
• angle-based

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Compressing Vertex Positions

• Classic approaches 95 98
• linear prediction
• Recent approaches 00 02
• spectral
• re-meshing
• space-dividing
• vector-quantization
• feature discovery
• angle-based

Spectral Compressionof Mesh Geometry Karni
Gotsman, 00
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Compressing Vertex Positions

• Classic approaches 95 98
• linear prediction
• Recent approaches 00 02
• spectral
• re-meshing
• space-dividing
• vector-quantization
• feature discovery
• angle-based

Progressive GeometryCompression Khodakovsky et
al., 00
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Compressing Vertex Positions

• Classic approaches 95 98
• linear prediction
• Recent approaches 00 02
• spectral
• re-meshing
• space-dividing
• vector-quantization
• feature discovery
• angle-based

Geometric Compressionfor interactive
transmission Devillers Gandoin, 00
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Compressing Vertex Positions

• Classic approaches 95 98
• linear prediction
• Recent approaches 00 02
• spectral
• re-meshing
• space-dividing
• vector-quantization
• feature discovery
• angle-based

Vertex data compressionfor triangle meshes Lee
Ko, 00
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Compressing Vertex Positions

• Classic approaches 95 98
• linear prediction
• Recent approaches 00 02
• spectral
• re-meshing
• space-dividing
• vector-quantization
• feature discovery
• angle-based

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Compressing Vertex Positions

• Classic approaches 95 98
• linear prediction
• Recent approaches 00 02
• spectral
• re-meshing
• space-dividing
• vector-quantization
• feature discovery
• angle-based

Angle-Analyzer A triangle-quad mesh
codec Lee, Alliez Desbrun, 02
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Linear Prediction Schemes
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Linear Prediction Schemes

1. quantize positions with b bits
2. traverse positions
3. linear prediction from neighbors
4. store corrective vector

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Linear Prediction Schemes

1. quantize positions with b bits
2. traverse positions
3. linear prediction from neighbors
4. store corrective vector

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Linear Prediction Schemes

1. quantize positions with b bits
2. traverse positions
3. linear prediction from neighbors
4. store corrective vector

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Linear Prediction Schemes

1. quantize positions with b bits
2. traverse positions
3. linear prediction from neighbors
4. store corrective vector

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Deering, 95

• Prediction Delta-Coding

processed region

unprocessed region





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Taubin Rossignac, 98

• Prediction Spanning Tree

processed region
unprocessed region
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Touma Gotsman, 98

• Prediction Parallelogram Rule

processed region
unprocessed region
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Parallelogram Rule




good prediction
badprediction
badprediction
non-convex
non-planar
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Not Triangles Polygons!
Face Fixer Isenburg Snoeyink, 00
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Non-triangular Faces

• Question Why would a mesh have a
  non-triangular face?

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Non-triangular Faces

• Question Why would a mesh have a
  non-triangular face?

Answer Because there was no reason to
triangulate it! This face was
convex and planar.
? use this info for better predictions
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within versus across
across-prediction
within-prediction

• ? within-predictions avoid creases

? within-predictions often find existing
parallelograms (? quadrilaterals)
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Texture Coordinate Mappings
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Texture Mapping (1)

• the process of applying a texture image to a
  mesh

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Texture Mapping (2)

• putting every 3D polygon of the mesh in
  correspondence with a2D polygon in the image

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Discontinuities in Mapping (1)

• some vertices of the mesh havemultiple
  corresponding locations in texture
  space

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Discontinuities in Mapping (2)

• vertices may have multiple associated texture
  coordinates

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Encoding the Mapping (1)

• 1. distinguish vertices

1
2. distinguish corners
0
1
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Encoding the Mapping (2)




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24


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25

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Encoding the Mapping (3)






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Why Discontinuities ?

• cuts required to flatten mesh
• no boundary
• non-zero genus
• piece-wise texture mapping
• author / artist decision
• easier for automated techniques
• additional cuts to meet objectives
• angle/area preserving parameterization
• minimizing texture stretch

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Piece-wise Mappings (1)
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Piece-wise Mappings (2)
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CompressingTexture Coordinates
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Selective Linear Prediction

• analyze neighborhood
• use most promising predictor
• ? within (for polygon meshes only)
• ? across
• ? nearby
• ? center
• avoid unreasonable predictions
• compress with different contexts

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Unreasonable Predictions
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Example Scenarios (1)








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11


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Example Scenarios (2)





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Example Scenarios (3)



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Example Scenarios (4)








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80



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Example Bit-Rates (10 bit)
by prediction type
model
within
across
nearby
center
lion wolf raptor
5.6 8.5 9.7 20.2 5.9 9.1 11.1 20.2 5.5 8.4 8.9
19.5
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Selection Histogram
frequency of prediction type
model
within
across
nearby
center
lion wolf raptor
82 14 3 1 84 13 2 1 78 18
5 1
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Alternative Approaches
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Alternative Approaches

• make texture coordinates implicit
• change the mesh (re-meshing)

Geometry Images Gu et al, 02

• change the image (re-texturing)

Bounded Distortion piece-wise Mesh
Parameterization Sorkine et al, 02
Space-Optimized Texture Maps Balmelli et al,
02
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Summary Acknowledgments
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Summary (1)

• use the parallelogram predictor for texture
  coordinates
• avoid unreasonable predictions across
  discontinuities (seams)
• switch to less-promising predictor
• compress resulting corrective vectors with
  separate arithmetic contexts

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Summary (2)

• compressionsoftware asbenchmarkfor
  futureresearch isavailable onthe Web

local link
http//www.cs.unc.edu/isenburg/pmc/
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Acknowledgments
CuriousLabs,California

• ArchaeologyTechnologyLabs,North DakotaState
  University

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• Thank You!

http//www.cs.unc.edu/isenburg/pmc/