Kumar, Roger

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Progressive 3D Mesh Coding
Kumar, Roger Sepiashvili, David Xie, Dan
18-796 Professor Chen April 19, 1999
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3D Models - MPEG-4 Overview

• Synthetic/Natural Hybrid Coding (SNHC) in MPEG-4
• A/V plane with 2D overlays, text, 3D objects,
  faces, etc.
• MPEG-4 System and Description Languages (MSDL)
• MSDL will provide flexible run-time environment
  for invoking decompression tools, algorithms,
  etc.
• MSDL will include class libraries for A/V object
  types along with their bitstream syntax.
• Client will download A/V object types for a
  specific session from the server at start up.
• MSDL A/V Objects
• VRML
• ActiveX Animation
• Java Media 3D
• etc.

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3D Models - MPEG-4 Overview

• MPEG-4 V2 will provide tools for coding 3-D
  Objects
• Coding of generic 3-D Meshes
• Level of Detail (LOD) Scalability
• Decoder can render simplified version of the mesh
• Useful for viewing distant objects for
  less-powerful rendering engines.
• Spatial Scalability
• Decoder can render the mesh at reduced spatial
  resolution
• Used in combination with LOD Scalability
• Progressive Transmission
• to receive progressively better approximations to
  the model
• possible approaches are
• transmission of successive LOD approximations
• progressive mesh coding (discussed later)

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Compression of 3D Models

• Texture Coding and Compression
• Static textures can be compressed by JPEG
• Moving textures can be compressed by MPEG-1 or
  H.263
• Geometry Coding and Compression
• There is no standard for geometry coding and
  compression.
• Most often geometry is represented by a
  triangular 3D mesh.
• Algorithms that quantize vertex positions and
  normals, and then apply Huffman or entropy
  encoding can achieve compression in the range of
  151 to 651, depending on the nature of the
  model.
• Mechanical models are easier to compress than
  anatomical.
• Need for Geometry Compression
• Each vertex represented by three floating pt.
  numbers.
• If each vertex shared by six polygons, and max
  number
• of vertices per model is 220, then 76
  bits/triangle needed.
• Several hundred Kilobytes for
• average model (just geometry)

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Why Progressive Mesh Coding ?

• Progressive Mesh (PM) addresses these issues
• Progressive Transmission
• show progressively better approximations to the
  model
• Smooth Visual Transition (geomorphs)
• transit smoothly between different levels of
  approximation
• Selective Refinement
• spatial refinement
• level of detail refinement
• Mesh Optimization
• constructing approximation
• meshes from non-optimal scanned
• meshes with smaller number of vertices
• Mesh Compression
• mesh simplification algorithm allows very
  efficient coding
• Can Be Lossless (if no optimization was done)

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Progressive Mesh (PM)

• Original mesh M is stored as a coarse mesh M0
  and n detail records that indicate how to refine
  M0 into the original mesh M.
• Mesh Optimization
• reduction of number of faces
• Mesh Simplification
• construction of a coarse mesh M0
• Mesh Compression
• storage space reduction

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PM - Mesh Optimization

• Find mesh M that accurately fits the model and
  has a small number of vertices.
• Goal is to optimize for rendering efficiency
• Often requires significant user intervention
• Done by minimizing the energy function
• Edist(M) total squared distance of points of
  original model from the mesh
• measures accuracy
• Erep(M) is proportional to the number of vertices
  in the mesh
• measures conciseness
• Espring(M) is energy of a spring placed on each
  edge of a mesh
• penalizes vertices that are too far away from
  adjacent vertices

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PM - Mesh Simplification

• Original mesh M is stored as a coarse mesh M0
  and n detail records that indicate how to refine
  M0 into the original mesh M.
• Can simplify mesh using edge collapse, edge
  split, edge swap. Only edge collapse is needed.
• Edge collapse is fully invertible, so inverse
  transformation reconstructs the original mesh.

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PM - Mesh Simplification

• Done by minimizing the energy function
• Edist(M), Espring(M) are same as before
• Escalar(M) measures accuracy of scalar attributes
• are properties of corners (i.e. vertex,face
  tuples)
• examples are diffuse color, texture, etc.
• Edisc(M) measures geometric accuracy of
  discontinuity curves
• preserving sharp edges is important
• Edisc(M) is equal to the total squared distance
  of a set of points sampled from sharp edges
  (discontinuity curves) of M to the discontinuity
  curve they belong.
• Algorithm
• mark all candidates for edge collapse in terms of
  priority, where priority of each transformation
  is estimated by energy cost ?E.
• starting with top at priority queue, perform edge
  collapse and recompute priorities of edges in
  neighborhood of this edge collapse.
• Keep doing until desired number of faces is met.

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References

• Progressive Meshes (Microsoft Research)
• http//www.research.microsoft.com/hoppe
• Java 3D API - 3D Geometry Compression
• http//www.javasoft.com/products/java-media/3D
• /forDevelopers/j3dguide/AppendixCompress.doc.html

All movies are made by Hugues Hoppe http//www.res
earch.microsoft.com/hoppe
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Question 1

• Did you mention that "Java3D also does
  compression"? How?
• Our first slide stated that the MPEG-4 System and
  Description Languages (MSDL) will allow 3D
  geometry to be compressed with different
  algorithms, one of which could be Java Media 3D
  (Java3D). MPEG-4 will also specify an built-in
  algorithm for geometry compression (most likely
  Progressive Mesh). If a better compression scheme
  is developed a few years later, MSDL would allow
  MPEG-4 to use this algorithm.
• Java3D specifies an algorithm for geometry
  compression. This algorithm does not allow for
  progressive transmission of meshes, as the
  Progressive Mesh (PM) algorithm does.
• In the Java3D algorithm, a 3D geometry is
  converted into a generalized triangular mesh. In
  Java3D, the vertex points are quantized, and then
  difference between two quantized vertex points is
  Huffman encoded. The vertex information is stored
  along with values for diffuse color and a normal
  vector.
• Color information is also quantized and Huffman
  encoded, whereas Normal information is encoded
  using a more complicated scheme (mapping normals
  to points on the unit sphere, please see
  http//www.javasoft.com/products/java-media/3D/for
  Developers/j3dguide/AppendixCompress.doc.html
  section B.8).
• If no color or normal information is sent for a
  vertex, the color or normal information for the
  previously-sent vertex is used.

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Question 2

• What is the speed for Mesh Optimization?
• In our presentation, we stated that Mesh
  Optimization is quite slow. Below are exact
  numbers and examples.

Mesh Optimization 3152 faces to 334
faces 17.0 minutes
Mesh Optimization 18,274 faces to 1348
faces 47.0 minutes
Mesh Optimization 8073 faces to 515
faces 44.5 minutes
Mesh Optimization 3832 faces to 432
faces 10.2 minutes
Timings preformed by Hugues Hoppe on a DEC
Workstation in 1993. http//research.microsoft.com
/hoppe