Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Features

1
Compression of Large Engineering 3D Models using
Automatic Discovery of Repeating Features

• Dinesh Shikhare
• National Centre for Software Technology (NCST)
• Mumbai, India.

2
Overview

• Large 3D polygon mesh models
• Processing tasks for applications
• Storage, transmission, loading, rendering
• Special techniques needed due to the large size
  of models
• Previous work in Geometry Compression
• not best suited for large 3D models of
  engineering class
• Our contributions
• Compression of large engineering models using
  automatic discovery of repeating geometric
  features
• Results

3
Large polygon mesh models
4
Large polygon mesh models
Walk-through of Massive Power Plant Model (13
million triangles) University of North
Carolina, Chapel Hill. (http//gamma.cs.unc.edu/Gi
gaWalk/)
Double Eagle Tanker (82 million triangles)
5
Large polygon mesh models
Digital Michelangelo Project (Statue of
David) 4,128,614 vertices 8,254,150 triangles
Digital Michelangelo Project (St.
Matthew) 186,810,938 vertices 372,422,615
triangles
http//graphics.stanford.edu/projects/mich/
6
3D Data on the Web
Collaborative CAD http//www.cocreate.com
Notre Dame Cathedral Walk-through http//www.vrndp
roject.com
7
3D Data on the Web
Fatehpur Sikri Walkthrough http//rohini.ncst.erne
t.in/fatehpur
Virtual Trade Fair http//www.cvtf.org.in
8
Triangle mesh models

• Common representation
• Shared list of vertices (Geometry)
• each has xyz coordinates
• List of triangles (Connectivity)
• each has 3 indices into the shared vertex list
• Size of storage
• Vertices 3 x V x B bits, (B bits per coordinate
  value)
• Triangles 3 x T x log2V (V no. of vertices)
• Typically, T 2 x V

9
Large file sizes
Model Vertices Triangles File size
Capitol Bld. 52,606 87,258 1,678,368
Colosseum 69,828 135,159 2,459,844
Helicopter 105,079 187,929 3,516,096
Boeing 747 56,364 88,737 1,741,212
Taj Mahal 65,323 126,453 2,301,312

• Even the smallest model will need 204sec to
  transmit at download speeds of 64kbps
• At 500,000 triangles/sec, z-buffer hardware can
  render only 5 frames/sec

10
Large models need special techniques

• Acquisition
• Healing adapting the model for application
• Rendering at interactive speeds
• Fast interactions e.g. collision detection
• Fast transmission
• Progressive disclosure
• Compact storage

11
Compression of Mesh Models

• Compact encoding of information by eliminating
  redundancy in the original data
• Exploit the special knowledge of structure in
  the data to encode the information
• Specialized algorithms perform better than PKZIP,
  gzip, etc.
• e.g. JPEG, MPEG, MP3, etc.
• Polygon meshes have a special structure too!

12
Previous Work

• Connectivity compression
• Compact encoding of meshes based on graph
  traversals
• Geometry compression
• Truncation of precision
• Prediction of vertex positions
• Spectral compression (FT, Wavelets, )
• Compression of attributes
• Separation of Attributes and their mappings
• Quantization of color, normals
• Truncation of precision

13
Connectivity compression

• In a triangle mesh
• triangle count ? 2 (vertex count)
• each vertex gets used in 5 to 7 triangles
• Such large number of repeated references to
  vertices motivates compression of connectivity
  information
• goal minimize repeated references to vertices

14
Triangle strips and fans (OpenGL)
2
3
4
2
1
5
4
0
0
3
1
0 1 2 3 4 5 ...
5
0 1 2 0 2 3 0 3 4 0 4 5 ...
0 1 2 2 1 3 2 3 4 4 3 5 ...
15
Generalized triangle strips(Deering95)
Triangle Strip
Triangle Star
5
9
10
2
6
7
8
11
1
4
14
3
12
13
R1 O2 O3 O4 O5 O6
R7 O8 O9 M10 M11 M12 M13 M14
Independent Triangle
Independent Quad
16
21
19
R15 O16 O17
R18 O19 O20 O21
15
17
18
20
16
Edge-based traversal
17
Traversal is not always smooth
18
Dual graph traversal encoding
19
Geometry Attributes

• Vertex Coordinates
• Truncation of precision
• Prediction schemes
• based on the traversal of connectivity
• parallelogram rule (Touma and Gotsman)
• butterfly scheme (Pajarola and Rossignac)
• Vertex Normals
• global table of quantized normals
• Colour
• Truncation of precision

20
Geometry compression

• Spectral compression of geometry
• Frequency-domain based schemes
• Wavelet based schemes
• Works only on smooth meshes

21
Recent years of intense research

• Began with Deering 95 (first geometry
  compression paper), and to some degree with Turk
  92, RossignacBorrel, 92, Hoppe 93 (the first
  simplification papers)
• Papers on connectivity alone
• Itai,Rodeh Representation of graphs, Acta
  Informatica, 82
• Turan On the succinct representation of graphs,
  Discrete Applied Math, 84
• Naor Succinct representation of general
  unlabeled graphs, Discrete Applied Math, 90
• Keeler,Westbrook Short encoding of planar graphs
  and maps, Discrete Applied Math, 93
• He, Kao,Lu Linear time succinct encodings of
  planar graphs, Siam J. Discrete Math, 99
• Chuang, Garg, He, et al Compact encodings of
  planar graphs, ICALP, 98
• Deering Geometry Compression, Siggraph, 95
• Taubin,Rossignac Geometric compression through
  topological surgery, ACM ToG, 98
• Taubin,Horn,Lazarus,Rossignac Geometry coding
  and VRML, Proc. IEEE, 98
• Touma,Gotsman Triangle Mesh Compression, GI, 98
• Gumbold,Straßer Realtime compression of triangle
  mesh connectivity, Siggraph, 98
• Rossignac Edgebreaker Compressing the incidence
  graph of triangle meshes, TVCG, 99
• Rossignac,Szymczak WrapZip Linear
  decompression of triangle meshes, CGTA, 99
• KingRossignac Guaranteed 3.67V Bit Encoding of
  Planar Triangle Graphs, CCCG, 99
• Bajaj et al. Single resolution compression of
  arbitrary triangle meshes, DCC 99
• Cohen-Or Progressive compression of arbitrary
  triangle meshes, Visualization 99
• IsenburgSnoeyink, Mesh Collapse Compression,
  SIBGRAPI 99

22
Patents

• Companies Intel, Sun, IBM, Microsoft,
  Macromedia, Metacreations
• Startups Virtue3D, Enbaya, WebGlide,
• At least 20 Issued Patents (from
  http//www.3dcompression.com/patents.phtml)
• 6,167,159 -- ToumaGotsman's valence-based mesh
  compression
• 6,046,744 -- Hoppe's Selective Refinement of
  Progressive Meshes
• 5,793,371 -- Deering's Compression used in Java3D
• 5,825,369 -- RossignacTaubin's Topological
  Surgery
• 5,736,987 -- DruckerMitchell's compression
  method for normals
• 5,818,463 -- Tao et al. -- a method for animated
  3D model compression using quads, 1998
• 5,905,507 -- RossignacTaubin's Topological
  Surgery for generalized models
• 5,929,860 -- Hoppe's Progressive Meshes
• 5,963,209 -- Hoppe's Progressive Meshes --
  Encoding and transmission
• 5,966,133 -- Hoppe's Progressive Meshes --
  Geomorphs and variable resolution
• 6,009,435 -- Taubin -- level of detail method
  that sends the highest LOD connectivity
• 6,031,548 -- Gueziec,Lazarus,Taubin --
  Progressive Multi-level transmission
• 6,016,153 -- GueziecTaubin -- CuttingStitching
• 6,169,819 -- Dyer (HP) -- Fast compression of
  surface normals
• 6,169,549 -- Burr, 2001, method for continuous
  LOD control
• 6,088,034 -- Deering's Java3D -- surface normal
  decompression

23
Architectural and Engineering Designs

• Common Characteristics
• Large number of small meshes.
• Many shapes and groups of shapes repeat.
• The model has arbitrary grouping of polygons.
• Instancing information is not captured and
  modeled optimally.

24
Applicability of previous techniques to
Engineering Models?

• Each repeating feature is repeatedly encoded.
• Predictive encoders perform poorly on engineering
  CAD models having sharp edges and corners.
• Spectral methods too cant handle sharp features.
• Vertices are repeated to capture texture
  coordinates, vertex normals.
• Hence graph traversals have many short branches
  in the tree encoding is not very compact.

25
Our Approach

• Attack the redundancy in encoding the shape
  features that repeat within a 3D model
• Automatic discovery of repeating shapes at
  various granularities
• Connected components
• Sub-component features
• Aggregates of above two types
• Compactly encode the repetition of features

26
Our Approach
Unstructured or arbitrarily grouped collection of
polygons along with attributes.
Soup of Polygons
Regrouping of polygons to obtain edge-connected
components -- component shapes.
Connected Components
Detection of repeating component shapes using 3D
registration techniques.
Component level Instance Detection
Detection of repeating features Within and across
components using feature growth technique.
Sub-component level Instance Detection
Detection of repeating groups of component shapes
(aggregates) by looking for iso-transformation i
nstances of component shapes.
Aggregate-level Instance Detection
Compact encoding
27
Preprocessing of Model

• Removal of duplicated geometry
• replicated vertices
• overlapping faces
• Regrouping of the model as a collection of
  connected components
• For the first stage, connected component is the
  unit for matching and instancing.

A single mesh in the original model split into 36
components to make shape matching and instancing
possible.
28
Matching at Component Level

• Problem (Top-Down)
• Determine whether given two component shapes are
  near identical (in the sense of a rigid body
  transformation).
• If they are identical, record the transformation
  (rotation, translation) for instance definition
  and for later reconstruction.
• Various approaches
• graph matching, feature extraction and matching,
  3D registration.

29
Matching at Component Level

• Normalized Orientation
• Obtain an orthonormal basis that describes the
  eccentricities of the component shape.
• Use this basis as a pure rotation matrix to bring
  a shape to its normalized orientation.

30
Matching at Component Level

• Hotelling Transform

• Determine the centroid

• Compute Covariance Matrix

• Determine eigenvectors and eigenvalues of
  matrix C.

• Obtain pure rotation matrix R with normalized
  eigenvectors and translation T-m to get
  rigid body transformation (R, T-m).
• Compute OBB.

31
Matching at Component Level

• Matching two component shapes, M1, M2
• Obtain for both shapes, orthonormal bases and
  centroids (R1, T-m1) and (R2, T-m2). Also
  compute OBBs of the shapes.
• Proceed only if dimensions of OBBs match.
• Proceed if vertex counts and polygon counts
  match.
• Align M2 with M1 using the composite
  transformation T T-m1? R2 ? R1-1 ? Tm2
• Carry out fuzzy comparison of vertices of M1 and
  M2.
• If 99.9 of vertices match, create an instance
  and record T.

32
Matching at Component Level
First Instance Component Shapes
Feature i DEF GeomConnAttrib
Feature j DEF GeomConnAttrib
Feature k DEF GeomConnAttrib
Instance USE T1
Instance USE T3
Instance USE T1
Instance USE T2
Instance USE T1
Instance USE T1
Instance USE T2
Instance USE T2
Instance USE Tm
Instance USE Tn
Instance USE T4
33
Sample Models
34
Results Repeating Components
35
Results...
36
Sub-component features

• Many shape features repeat within and across
  components.
• Examples
• Teeth of a gear geometry and connectivity for
  each tooth is repeatedly described.
• Components of mechanical assemblies are merged to
  obtain a single component, but still has many
  repeating shapes.
• Component level discovery cannot detect
  sub-component level patterns.
• Previous work
• Discovery of repeating motifs in molecular
  structures

37
Sub-component features
38
Sub-component features

• Discovery algorithm (Bottom-up)
• Assign footprints to all vertices in the model
• Create equivalence classes of vertices having
  identical neighborhoods as identified by their
  footprints
• Starting with vertices of each equivalence class
• Carry out identical simultaneous breadth-first
  growth of features
• Verify that the features are indeed geometrically
  identical

39
Sub-component features
Identical simultaneous growth of repeating
features about vertices (seeds) having identical
neighborhoods. Vertex 0 indicates the seeds, and
the numbering indicates the BFS order of
traversal during the growth.
40
Sub-component features
Steering
Spring
Antenna
Rotor
Wheel
41
Sub-component features
Large number of vertices belonging to repeating
features can be compressed effectively using
instancing of vertices and triangles connecting
them.
42
Aggregate features

• Geometry repeats not only at the level of
  connected features, but also as groups of
  features
• e.g. A pillar in an architectural model consists
  of multiple component shapes, and the model can
  have a large number of identical pillars.
• Key Observation
• USE-instances of all meshes of a structure have
  identical transformation associated with them.
• An iso-transformation set gives us structures
  that repeat.

43
Aggregate features
First Instance Features / Shapes
Feature i DEF GeomConnAttrib
Feature j DEF GeomConnAttrib
Feature k DEF GeomConnAttrib
Instance USE T1
Instance USE T3
Instance USE T1
Structure 1
Instance USE T2
Instance USE T1
Instance USE T1
Structure 2
Instance USE T2
Instance USE T2
Instance USE Tm
Instance USE Tn
Instance USE T4
44
Aggregate features
45
Identification of Erroneous Duplicates
First Instance Features / Shapes
Feature i DEF GeomConnAttrib
Feature j DEF GeomConnAttrib
Feature k DEF GeomConnAttrib
Instance USE T1
Instance USE T3
Instance USE T1
Structure 1
Instance USE T2
Instance USE T1
Instance USE T1
Structure 2
Identical Transformations
Instance USE T2
Instance USE T2
Instance USE Tm
Identity Transformation
Instance USE Tn
Instance USE I
46
Compressed Storage

• DEF instances compressed using the best available
  connectivity compression algorithm
• e.g. Edgebreaker (Rossignac 1999)
• USE instances represented as reference to the DEF
  instance and a rigid-body transformation.
• A more general transformation may be used
• similarity transformation
• a sequence of topological operators to take one
  mesh to another

47
Compressed Storage Scheme
48
Result of compression
(1) File sizes in bytes. (2) Note that some
models could not be compressed using Edgebreaker
algorithm because (a) DIK has textures and (b)
others have non-manifold meshes. (3) CR 1
C(M) / O(M)
49
Lathe
Heritage
Boeing 747
50
Summary of contributions

• New algorithms for discovery of repeating
  geometric features at different levels of
  granularity
• A new compression scheme for large 3D models of
  architectural and engineering class
• Extension of compression scheme for incorporation
  of the previously reported compression techniques
• A new technique for automatically eliminating
  erroneously replicated geometry

51
Discussion

• Compression ratio
• Very high CR for architectural / engg. Models
• Speed of compression, decompression
• Slow compression ( large parallelism)
• Fast decompression
• Lossy compression
• Control over lossiness?

52
Future Work

• Matching features that have similar geometry but
  different connectivity
• Use of more general set of transformation for
  shape instance detection and encoding
• More extensive healing techniques
• Extension to simplification and progressive
  disclosure
• Do you have any more ideas?

53
Outline of the Thesis

1. Introduction
2. 3D Polygon Mesh Models
3. Compression of 3D Models
4. Automatic Discovery of Repeating Geometric
   Features

• A New Compression Scheme for Large 3D Models of
  Engineering Class
• Conclusions and Future Directions
• Appendices
• Some claims and proofs
• Implementation Notes
• Sources of data and software tools

54
Acknowledgements...

• Thesis Supervisor Prof. S. P. Mudur
• Funded projects
• Aeronautical Development Agency (ADA)
• Intel Inc.
• Models
• VISIONS, 3dcafe.com, avalon.viewpoint.com
• Expert reviews
• SIGGRAPH01, VMV01, Graphical Models
• Discussions
• colleagues in Graphics CAD division, NCST

55
Thank You.
56
Recent Work

• Improvement of Instance Transforms
• error minimization technique for optimization of
  instance transformation using 3D-3D registration
  technique Haralick, Shapiro
• Connectivity Compression
• Advancing Fan-front algorithm
• Fan-based traversal of triangle mesh for
  compactly encoding
• efficient O(n) algorithm

57
List of Publications

• On Geometric Modeling, Mesh Generation
• A Two-phase Technique for Tessellation of Complex
  Geometric Models
• Tetrahedral Discretization of Complex Volumetric
  Spaces Implementation, Efficiency, Robustness
  and Interactive Control.
• Zeus Surface Modeling, Surface Grid Generation
  and Tetrahedral Volume Discretization.

58
List of Publications...

• On Interactive Visualization
• Graphics Pipeline for Interactive Visualization
  of Very Large 3D Models
• On Geometry Compression
• Discovery of Repeating Feature Patterns in Large
  3D Mesh Models
• Compression of Large 3D Engineering Models using
  Discovery of Repeating Geometric Features

59
List of Publications

• On Geometry Compression
• 3D Compression of Engineering Models for
  Collaborative Computing Applications.
• Compression Techniques for Distributed Use of 3D
  Data -- an Emerging Media-type on the Internet
• Advancing Fan-front An Efficient Connectivity
  Compression Technique for Large 3D Triangle
  Meshes.

60
Other Papers

• Submitted to a journal
• Automatic Discovery of Repeating Geometric
  Features with Application to Compression of Large
  3D Models of Architectural and Engineering Class.
• On the anvil
• Advancing Fan-front an Efficient Connectivity
  Compression Technique.