Progressive coding Motivation and goodness measures

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Progressive codingMotivation and goodness
measures

• Jarek Rossignac
• (with Renato Pajarola)
• GVU Center and College of Computing
• Georgia Tech, Atlanta
• http//www.gvu.gatech.edu

2
Progressive refinements

• Previously covered connectivity compression is
  loss-less
• It is complemented by the compression of vertex
  data
• 3D coordinates, normals, colors, texture
  coordinates
• Discussed later in the Geometry section
• Exploiting a lossy quantization
• When these two are insufficient, we can simplify
  the model
• Reduce triangle and vertex count through a
  sequence of edge-collapses
• Select sequence that minimizes the resulting
  (geometric or visual) error
• We can use progressive transmission that
  increases accuracy
• Download compressed crude model first
• When more accuracy is needed, download upgrades
  and refine model
• You may start navigation right away using crude
  model
• Often you may not need to download the complete
  model at all

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Mesh refinement
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Just-in-time upgrades of features

• Download geometry only when images wont do
• Subdivide surface into features (hierarchical)
• Use approximations of feature when acceptable
• Replace by more detailed sub-features as
  necessary
• To upgrade a feature, given its boundary, we must
  construct
• A detailed representation of its (approximate)
  shape
• A partition of the features surface into
  sub-features

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Selective download of feature upgrades
Upgrade Geometry Cost Quality Children 0
g0 a0,r0 p0,e0 1,2,3 1 g1
a1,r1 p1,e1 4,5,6 2 g2 a2,r2 p2,e2 7,8,9
User
Server
viewmodel manipulation
Downloaded upgrades 0,2,3,8,9,10,11,12
Client
crude model (g0)
1
3
2
12
9
10
6
7
4
8
11
5
detailed features
6
Simultaneous access to remote datasets
3D Servers
Client viewers
Compressed crude models and upgrades
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Compressed successive upgrades
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What is a good feature for selective upgrade?

• Connected subset of the boundary
• Surface patch
• Entire surface
• Defined by hierarchical simplification
• Assume its boundary is given
• Outer loops of a connected patch
• One triangle of a solids boundary
• Represent how to stretch the surface between this
  boundary
• Compression bit-efficient model of the internal
  shape

?
?
?
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Simplification process defines features
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Upgrade reverse simplification
compress
Upgrade
decompress
?
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Evaluating progressive transmission
Error for the received model
Bits transmitted (or time)
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Non-progressive transmission
approximation error
bits (time)
nothing
13
Two-step approach Crude-Full
approximation error
bits (time)
nothing
14
Multiple levels of accuracy
approximation error
Longer wait for complete model
bits (time)
nothing
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Optimal, continuous refinement
approximation error
bits (time)
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Simplification, Compression Upgrades

• Simplification
• Reduce the number of triangles that represent a
  3D feature
• Compression
• Reduce the number of bits needed to represent the
  feature
• Upgrade
• Information used to recover an original feature
  from its simplification
• Progressive representation
• Coarse model and a tree of recursive upgrades

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Progressive codingCompressed Progressive Meshes

• Jarek Rossignac
• (with Renato Pajarola)
• GVU Center and College of Computing
• Georgia Tech, Atlanta
• http//www.gvu.gatech.edu

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Problem of compressing updates

• Location
• where does a refinement occur
• Incidence
• how to update the mesh connectivity
• Geometry
• new coordinates

location
incidence
compressed format
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Progressive meshes (Hoppe96)

• Simple simplification and refinement operators
• edge collapse operation (ecol)
• vertex split operation (vsplit)
• defined by split-vertex and cut-edges
• Series of meshes
• defined by crude base mesh M0and sequence of
  vsplits

cut-edges
ecol
vsplit
split-vertex
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Vertex splits (Hoppe)

• The inverse of an edge collapse
• Insert two triangles
• Cut mesh at 2 adjacent edges
• Replicates 2 edges and 1 vertex
• Move new vertex to create gap
• Fill the crack with 2 new triangles
• Specify position of new vertex
• Encode relative displacement (arrow)
• Incidence cost 813 b/T
• Identify a vertex (10ltlogVlt20) bits
• Identify 2 incident edges (6 bits?)

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CPM (PajarolaRossignac 99)

• Sequences of vertex splits (as in Hoppes PM)
• Grouped in batches

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CPM encoding of connectivity

• Avoid log(V) cost by marking all vertices
• 1 bit per vertex in batch
• 30 to 50 vertices are split in each batch
• Better encoding of cut-edges
• log(6)log(2)
• Amortized total connectivity cost 3.6T bits
• 1.5 b/T for marking vertices (amortized)
• 2.1 b/T for identifying cut edges
• PajarolaRossignac, Compressed Progressive
  Meshes, IEEE TVCG99

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CPM butterfly prediction

• Predict geometry based on previous LOD
• approximation using weighted sum of incident
  vertices and subset of topology 2 neighbors

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CPM prediction error encoding

• Estimate edge collapse
• predict original vertices A, B
• predicted edge collapse vector v
• prediction error e v - v
• CPM collapses edge to its mid-point
• Encode prediction error
• Laplace distribution L(x)
• based on prediction error variance of current
  refinement batch
• create corresponding Huffman encoding for e

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Total amortized cost per triangle

• Bunny
• 9666 triangles, 10 LODs, 11.3T bits (3.6
  connectivity 7.7 geometry)
• Horse
• 21622 triangles, 9 LODs, 10.6T bits (3.5 7.1)
• Skull
• 21904 triangles, 7 LODs, 10.9T bits (3.4 7.5)
• Fohe
• 7240 triangles, 7 LODs, 13.7T bits (3.5 10.1)
• Fandisk
• 12950 triangles, 9 LODs, 11.4T bits (3.7 7.7)

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Comparison with TS and PFS
2832 vertices
approximation error
TS Taubin, Rossignac 98 PFS Taubin et al.
98CPM Pajarola, Rossignac 99
bits
crude initial model
TS 100
CPM 125
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Error protection for CPM

• G. Al-Regib, Y. Altunbasak and J. Rossignac. An
  Unequal Error Protection Method for Progressively
  Compressed 3-D Meshes, Int. Conf. on Acoustics,
  Speech and Signal Processing (ICASSP). May 2002.
• Add error correction channel bits to increase the
  chances of recovering from transmission errors
• Adjust level of error protection to the
  importance of the refinement batch (optimization)

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Progressive Transmission of Tetrahedral
MeshesImplant-Spray

• Jarek Rossignac
• (with Renato Pajarola and Andrzej Szymczak)
• GVU Center and College of Computing
• Georgia Tech, Atlanta
• http//www.gvu.gatech.edu

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Progressive Tetrahedral Meshes

• ImplantSpray PajarolaRossignacSzymczak, IEEE
  VIS99
• Vertex split refinement operator
• Extension of vertex split for triangle meshes
  StaadtGross98
• Defined by split-vertex and set of incident
  cut-faces
• Series of tetrahedral meshes defined by sequence
  of vertex-splits
• Send crude model and batches of refinement
  updates
• Mark split-vertices
• Encode cut-faces

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Identifying cut-faces for the split-vertex

• A vertex has roughly
• 12 incident edges
• 30 incident triangular faces
• 20 incident tetrahedra
• A split-vertex has about 6 cut-faces
• We must select about 6 triangular faces out of 30
• Hull The boundary of the star of the
  split-vertex
• A manifold surface
• Skirt Cut-faces
• connected surface around split-vertex
• The skirt boundary
• a cycle of k edges in the hull
• closed path on planar triangle graph

cut-faces
split-vertex
hull
skirt
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Results of Progressive Tetrahedral Meshes

• Turbine blades
• blades and exterior as tetrahedral mesh
• 576576 tetrahedra
• 49 LODs
• 5.02 bits per tetrahedron
• connectivity information
• no geometry data
• Compare to indexed face list
• 4x17 bits per tetrahedron