OutofCore Remeshing of Large Polygonal Meshes

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Out-of-Core Remeshing of Large Polygonal Meshes
POSTECH Univ. of Michigan POSTECH

• Minsu Ahn,
• Igor Guskov,
• Seungyong Lee,

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Out-of-Core Meshes

• Meshes with large of vertices and faces
• size of a mesh gtgt main memory

of f 28,055,742 of v 14,027,872
of f 372,422,615 of v 186,810,938
of f 56,230,343 of v 28,184,526
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Out-of-Core Algorithms

• Simplification
• mesh cutting Hoppe 98
• vertex clustering Lindstrom 00, Shaffer 03
• external data structure Cignoni 03
• data streaming Wu 03, Isenburg 03
• Compression
• mesh cutting Ho 01
• external data structure Isenburg 03

? Out-of-core remeshing has not been proposed
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Remeshing

• Create a new mesh to improve
• sampling
• regularity
• shape of elements

Remeshing
Irregular
Regular
Alliez 02
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Remeshing Algorithms

• Simplification subdivision
• Eck 95, Lee 98, Guskov 00, Khodakovsky 03
• Global parameterization
• Gu 00, Alliez 02, Praun 03
• Directly manipulation
• Surazhsky 03 Schreiner 06

? These cannot handle out-of-core meshes
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Out-of-Core Remeshing

• Out-of-core meshes need remeshing
• irregular and densely sampled
• difficult to process
• Improve the structure of out-of-core meshes

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Remeshing
V
F
V
F
Out-of-core mesh
Semi-regular mesh
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Contributions

• Out-of-core remeshing algorithm
• creating semi-regular representations
• Parameterization of out-of-core meshes
• mapping onto a coarse base domain
• Applications for geometry processing
• mesh editing
• map generation
• shape compression

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Basic Approach

• Simplification Refinement
• similar to MAPS algorithm Lee 98
• out-of-core technique

Base mesh
Semi-regular
Input
Mappinginformation
Refinement Resampling
Parameterization
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Why Simplification Approach

• Need only local information at a time
• vs. global parameterization approach
• need the whole mesh at the same time

Simplification
Global parameterization
Alliez 02
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Why Simplification Approach

• Semi-regular meshes
• digital geometry processing
• shape compression
• mesh editing
• Parameterization onto the base domain
• various applications
• editing
• map generation

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Problem

• An out-of-core mesh cannot fit into main memory
  for processing steps of MAPS

Base mesh
Semi-regular
Input
Mappinginformation
Refinement Resampling
Parameterization
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Our Solution

• Streaming approach
• limited-size buffer
• keep only a partial mesh
• read, process, and write

Main memory
Input streaming file
Read
Process
Read
Write
Output streaming file
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Overall Process
Streaming approach
Base mesh
Mappinginformation
Large input
Semi-regular
Parameterization
Refinement Resampling
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Parameterization

• MAPS algorithm

Base mesh
Simplification
Original mesh
Mapping Construction
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Parameterization

• Streaming approach
• two fixed-size buffers

Domain Buffer
Simplification
Original mesh
Map buffer
Mapping Construction
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Out-of-Core Parameterization

• Domain buffer
• for simplification
• Map buffer
• for mapping construction

Write
Read
Simplify
Domain Buffer
Write
Read
Update
Map buffer
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Buffer Maintenance

• Avoid buffer overflow
• write and remove the processed part before
  reading the next part

Write
Read
Read
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Buffer Maintenance

• Determine the write order
• consider the dependency between two buffers

writablefaces
Domain Buffer
Simplification of a partial mesh
Read
Write
writablevertices
Map buffer
Mapping information
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Writable Vertex

• A vertex in the map buffer is writable
• if we have updated its mapping information

?
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Writable Face

• A face in the domain buffer is writable
• if we have updated the mapping information for
  the vertices mapped on it

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Deadlock

• No vertices in the map buffer and no faces in the
  domain buffer are writable
• can neither remove any vertices nor faces
• can neither read any vertices nor faces

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Deadlock Avoidance

• Manage the mesh parts in the buffers to overlap
  each other
• Vertices in the map buffer can find the mapping
  faces in the domain buffer

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Parameterization Example

• Now we have
• base mesh
• mapping between the input and its base mesh

Base mesh
Mapping information
Large input
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Refinement Resampling

• Subdivide the base mesh recursively
• Resample the positions of new vertices
• from the very large input mesh

Original input mesh
Base mesh
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Out-of-Core Resampling

• Divide Conquer
• decompose original triangles to separate sets
• each triangle set corresponds to a base mesh face

Decompose
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Out-of-Core Resampling

• Sequential resampling from a triangle set

Read Evaluation
3D
External sort
Embed
2D
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Experimental Results

• Semi-regular meshes

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Experimental Results

• User-defined feature preservation
• feature preservation is important in remeshing
• base mesh ltlt original mesh
• user can select features in one of the simplified
  meshes or its portion

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Experimental Results
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Applications

• Map conversion
• Mesh editing

• Shape compression

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Application I

• Map conversion
• parameterization process can be split into two
  stages

Our out-of-core parameterization
In-core parameterization
Intermediate base mesh
resampling
resampling
Large input
Coarse mesh
Our out-of-core algorithm
In-core remeshing algorithm
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Application I

• Map conversion
• combine with an in-core parameterization
• Spherical parameterization and remeshingPraun
  03

Normal-map Image(512 X 512)
Geometry Image (257 X 257)
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Application II

• User-guided mesh editing
• edit an input mesh by editing its base mesh
• using the mapping between them
• remove the artifacts of the original surface
• removing the corresponding parts in the base mesh

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Application III

• Shape compression
• Progressive geometry compression Khodakovsky 00

PSNR vs. file size
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Discussion

• Memory footprint
• sizes of buffers as parameter

byte
Read
Simplify
Write
Read
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Discussion

• Algorithm robustness
• extreme conditions of small buffer sizes
• with Max f (Bd) 30K and Max f (Bm) 1
• with Max f (Bd) 12K and Max f (Bm) 3K

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Conclusion Future Work

• First out-of-core remeshing method
• streaming approach based on the MAPS algorithm
• create a mapping between the huge input mesh and
  its simplified mesh
• various applications
• Future work
• globally smooth parameterization of out-of-core
  meshes

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http//cg.postech.ac.kr

• Thank You!!!

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Supplementary Slides
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Time Table
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Compression Performance
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(No Transcript)
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Backup Slides
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Input Mesh

• External breath-first vertex sorting
• Streaming meshes Isenberg 05

Initial
After reordering
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Simplification Criteria

• Quadric error metric
• Roundness of triangles
• Normal of vertices

hecol
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Mapping Information

• Similar to MAPS method
• map information (if, ?)
• map face, if
• barycentric coordinate, ?
• conformal map

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Streaming Approach

• Use a limited-size buffer

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Overall Parameterization Process
Simplification
Update mapping information
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Writable Face

• Counts of the face, fd ? Bd
• map count
• of vertices which are mapped onto f
• update Count
• initially 0
• increase when each vertex is updated
• Writable face , fd ? Bd
• map count update count

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Mapping Construction

• Streaming approach
• map buffer

Vertex
Face
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Mapping Construction

• fd ? Bd
• nothing to do
• fd ? Bd
• removed
• not read
• Hash, Hf
• (if, cm)
• remove face index
• map vertex count

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Parameterization Example
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Write Order

• Decides the shape of mesh parts
• shape of partial mesh read order
• read order write order in the prev. level

Input Streaming file
Read
Write
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Write Order

• Write order in Bd depends on that in Bm
• to overlap each other

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Out-of-Core Resampling

• Preprocessing
• sort triangles in terms of the min. v-coord.
  externally
• sort sample points similarly

v
(0, 1, 0)
(0, 1)
(0, 0, 1)
u
(0, 0)
(1, 0)
(1, 0, 0)
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Out-of-Core Resampling

• Process
• read sequentially
• evaluate map information
• remove

v
(0, 1)
u
(0, 0)
(1, 0)