Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric...

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

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

Dinesh Shikhare

National Centre for Software Technology (NCST)

Mumbai, India.


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


Large polygon mesh models


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/GigaWalk/)

Double Eagle Tanker(82 million triangles)


Large polygon mesh models…

Digital Michelangelo Project (Statue of David)4,128,614 vertices8,254,150 triangles

Digital Michelangelo Project (St. Matthew)186,810,938 vertices372,422,615 triangles

http://graphics.stanford.edu/projects/mich/


3D Data on the Web…

Collaborative CADhttp://www.cocreate.com

Notre Dame Cathedral Walk-throughhttp://www.vrndproject.com


3D Data on the Web…

Fatehpur Sikri Walkthroughhttp://rohini.ncst.ernet.in/fatehpur

Virtual Trade Fairhttp://www.cvtf.org.in


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


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


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


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!


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


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


Triangle strips and fans… (OpenGL)

0 1 20 2 30 3 40 4 5...

0

1

2

3

4

5

0 1 2 3 4 5 ...

0 1 22 1 32 3 44 3 5...

0

14

5

2 3


Generalized triangle strips…(Deering95)

Triangle Strip

1

3

5

4

62

Triangle Star

78

9 10

11

1213

14

R1 O2 O3 O4 O5 O6R7 O8 O9 M10 M11 M12 M13 M14

Independent Triangle

15

16

17

R15 O16 O17

Independent Quad

18

19

20

21

R18 O19 O20 O21


Edge-based traversal…


Traversal is not always smooth…


Dual graph traversal + encoding


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


Geometry compression…

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


Recent years of intense research…• Began with Deering ’95 (first geometry compression paper),

and to some degree with Turk ‘92, Rossignac&Borrel, ‘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: Wrap&Zip: Linear decompression of triangle meshes, CGTA, 99– King&Rossignac: 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– Isenburg&Snoeyink, Mesh Collapse Compression, SIBGRAPI 99– Snoeyink, VanKreveld: Linear-time reconstruction of Delauney triangulations, ESA 99– Denny,Sohler: Encoding a triangulation as a permutation of its point set, CCCG, 97– King, Symczak, &Rossignac: Connectivity Compression for Irregular Quadrilateral Meshes, submitted– Isenburg&Snoeyink: Face-Fixer, Siggraph 2000

• Above list does not include the progressive methods, the ones that focus on geometry, ones that change the connectivity


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 -- Touma&Gotsman'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 -- Rossignac&Taubin's Topological Surgery– 5,736,987 -- Drucker&Mitchell's compression method for normals– 5,818,463 -- Tao et al. -- a method for animated 3D model compression using quads,

1998– 5,905,507 -- Rossignac&Taubin'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 -- Gueziec&Taubin -- Cutting&Stitching– 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– 5,870,094 -- Deering's Java3D -- system for transferring compressed 3D– 5,867,167 -- Deering's Java3D compression– 5,842,004 -- Deering's Java3D decompression– 6,028,610 -- Deering's Java3D -- geometry instructions for decompression– 5,933,153 -- Deering's Java3D -- mesh buffer for decompression– 5,905,502 -- Deering's Generalized Triangle Mesh compression

http://164.195.100.11/netacgi/nph-Parser?TERM1=6%2C167%2C159&Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2Fsrchnum.htm&r=0&f=S&l=50

http://164.195.100.11/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2F60467

http://www.3dcompression.com/5,793,371

http://www.3dcompression.com/5,825,369


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.


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 can’t 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.


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


Our ApproachSoup of

Polygons

Connected Components

Component level Instance Detection

Aggregate-level Instance Detection

Unstructured or arbitrarily groupedcollection of polygons along with attributes.

Regrouping of polygons to obtainedge-connected components --“component shapes”.

Detection of repeating componentshapes using 3D registration techniques.

Detection of repeating groups ofcomponent shapes (“aggregates”)by looking for iso-transformationinstances of component shapes.

Sub-component level Instance Detection

Detection of repeating featuresWithin and across components using “feature growth” technique.

Compact encoding


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 modelsplit into 36 components to make shape

matching and instancing possible.


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.


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”.


Matching at Component Level• Hotelling Transform

• Determine the centroid:

n

iip

nm

1

1

TTi

n

ii mmpp

nC

1

1• 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.


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.


Matching at Component Level

Feature i DEFGeom+Conn+Attrib

Feature j DEFGeom+Conn+Attrib

Feature k DEFGeom+Conn+Attrib

FirstInstanceComponentShapes

Instance USE T1

Instance USE T2

Instance USE Tm

Instance USE T3

Instance USE T1

Instance USE Tn

Instance USE T2

Instance USE T1

Instance USE T1

Instance USE T4

Instance USE T2


Sample Models


Results: Repeating Components# Mesh # DEF # USE

Capitol 2662 93 2569Colosseum 1129 20 1109Diwan-i-Khaas 3726 848 2878Helicopter 976 480 496Piping 1051 122 929Taj Mahal 375 45 330

0

500

1000

1500

2000

2500

3000

3500

4000

Capitol Colosseum Diwan-i-Khaas

Helicopter Piping Taj Mahal

# USE

# DEF


Results...# vertices (ORIG) # triangles (ORIG) # vertices (DEF) # triangles (DEF)

Capitol 52606 87258 10347 19944Colosseum 69868 135159 18912 38103Diwan-i-Khaas 295695 162590 44363 46165Helicopter 105079 187929 76231 136372Piping 13103 20794 3753 6366Taj Mahal 65323 126453 28427 55238

0

50000

100000

150000

200000

250000

300000

350000

Capitol Colosseum Diw an-i-Khaas Helicopter Piping Taj Mahal

# vertices (ORIG)

# triangles (ORIG)

# vertices (DEF)

# triangles (DEF)


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


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



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.



Antenna Steering Spring

Rotor Wheel



Object # vertices # features found # vertices classified Largest feature Smallest feature TimeSteering 878 42 554 61 6 0.08Sphere 812 32 296 10 8 0.03Spring 909 18 382 55 9 0.02Antenna 499 10 230 44 10 0.01Rotor 1560 25 334 25 5 0.16Wheel 1282 54 449 10 7 0.13

Large number of vertices belonging to repeating features can be compressed effectively using instancing of vertices and triangles connecting them.


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.


Aggregate features…




FirstInstanceFeatures /Shapes

Instance USE T1

Instance USE T2

Instance USE Tm

Instance USE T3

Instance USE T1

Instance USE Tn

Instance USE T2

Instance USE T1

Instance USE T1

Instance USE T4

Instance USE T2

Structure 1

Structure 2


Aggregate features…


Identification of Erroneous Duplicates




FirstInstanceFeatures /Shapes

Instance USE T1

Instance USE T2

Instance USE Tm

Instance USE T3

Instance USE T1

Instance USE Tn

Instance USE T2

Instance USE T1

Instance USE T1

Instance USE I

Instance USE T2

Structure 1

Structure 2IdenticalTransformations

IdentityTransformation


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


Compressed Storage Scheme


Result of compression…

Model Original size Edgebreaker alone Component-level Aggregate-level Aggr+EB Aggr+[EB]+gzip CRBoeing747 3,499,008 N.A 961,105 956,557 N.A 497,531 0.857808Capitol Bldg 1,790,767 1,094,833 403,887 395,131 349,124 134,377 0.924961Colosseum 2,503,030 1,251,559 516,397 497,689 407,315 217,284 0.913192Diwan-I-Khs 10,072,648 N.A 1,884,970 1,825,001 N.A 603,309 0.940104Helicopter 4,891,936 N.A 1,604,058 1,599,942 N.A 879,214 0.820273Lathe 339,629 N.A 118,829 118,192 N.A 52,800 0.844536Piping 417,545 398,138 150,111 133,781 121,938 34,846 0.916546Taj Mahal 764,702 1,118,178 630,326 629,020 505,325 196,590 0.742919Heritage 3,948,982 2,155,976 506,940 501,224 409,172 246,159 0.937665

(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)


Heritage

Lathe

Boeing 747


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


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?


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?


Outline of the Thesis…

1. Introduction2. 3D Polygon Mesh

Models3. Compression of 3D

Models4. Automatic Discovery

of Repeating Geometric Features

5. A New Compression Scheme for Large 3D Models of Engineering Class

6. Conclusions and Future Directions

AppendicesA. Some claims and

proofsB. Implementation NotesC. Sources of data and

software tools


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


Thank You.


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


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.


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


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.


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.

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