matching 3d models with shape distributions
DESCRIPTION
Matching 3D Models With Shape Distributions. Robert Osada, Tom Funkhouser Bernard Chazelle, and David Dobkin Princeton University. Shape Similarity. Determine similarity between 3D shapes. Computer Graphics. Computer Vision. Computational Biology. [Insulin, PDB]. [Caltech]. - PowerPoint PPT PresentationTRANSCRIPT
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Robert Osada, Tom FunkhouserBernard Chazelle, and David
DobkinPrinceton University
Matching 3D Models With Shape Distributions
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Shape Similarity Determine similarity between 3D
shapes
ComputerGraphics
ComputerVision
Computational Biology
[Caltech][Insulin, PDB]
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Previous Work in 2D Shape representations
Fourier analysis [Arbter90] Turning function [Arkin91] Size function [Uras95]
Metrics for comparing curves Hausdorff Fréchet Bottleneck etc.
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Previous Work in 3D High-level representations
Generalized cylinders [Binford71] Medial axis [Bardinet00] Skeletons [Bloomenthal99]
Statistical Moments [Reeves45, Prokop92] Crease angle [Besl94] Shells decomposition around centroid
[Ankerst99] Extended Gaussian Images [Horn84] etc.
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Desired Properties Match global properties of shape Invariance
Rotation, translation, scale, mirror Robustness
Noise, cracks, insertions and deletions Practicality
Concise representation Efficient comparison Working with degenerate models
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Our Approach Shape distributions
Concise shape descriptor Common parameterization Function of random points
3D Model ShapeDistribution
Parameterization
Random sampling
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Our Approach
SimilarityMeasure
Parameterization
Parameterization
3DModel
ShapeDistribution
ShapeFunction
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Issues Which shape function? How to compare shape distributions?
Parameterization
Parameterization
SimilarityMeasure
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Issues Which shape function? How to compare shape distributions?
Parameterization
Parameterization
SimilarityMeasure
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Which Shape Function? Computationally simple options (~
1s) Based on random points Angles, distances, areas, volumes
A3 D1
D2 D3
[Ankerst99]
D4
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Shape Function – D2 Distance between
two random points on surface Line Segment Circle
Triangle Cube
Cylinder Sphere
Two adjacent spheres
Two spheres moving apart
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Which Shape Function? Sneak preview
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Shape Function – Key Questions Invariant?
Rotation, translation, mirror (not scale)
Robust? Noise, cracks, insertions and deletions
Descriptive?
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Issues Which shape function? How to compare shape
distributions?
Parameterization
Parameterization
SimilarityMeasure
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Comparison1. Normalize for scale2. Compare shape distributions
Parameterization Parameterization
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Normalization for Scale
max mean search
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Compare shape distributions Computationally simple options
(~ .1ms) Ln norms of densities (PDF) or
cumulative densities (CDF) More complex options
Earth mover’s distance, Bhattacharyaa distance.
PDF CDF
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Experimental Results Goal is to address the following:
Is the method robust? How well does it classify?
Shape Function
Normalization Comparison
• • •A3 D1 D2D3 D4
Max Mean Search
PDF L1 L2 L
CDF L1 L2 L
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Robustness Experiment 10 Models
Car Chair Human Missile Mug
Phone Plane Skateboard Sub Table
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Robustness Experiment 6 Transforms
Rotate, scale, mirror, noise, delete, insert
Total of 70 models
1% Noise 5% Deletion
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Robustness Results Resulting distributions stable
7 Mugs
Distance
Prob
abilit
y
7 Missiles
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Classification Experiment 133 Models
categorized into25 Groups
Large variety within a group among groups
4 Mugs
6 Cars
3 Boats
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Classification Results
4 Balls5 Animals 2 Belts 3 Blimps 3 Boats
6 Cars 8 Chairs 3 Claws 4 Helicopters11
Humans
3 Lamps 3 Lightnings6
Missiles 4 Mugs4
Openbooks
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Classification Results
Distance
Prob
abilit
y
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4 Balls5 Animals 2 Belts 3 Blimps 3 Boats
6 Cars 8 Chairs 3 Claws 4 Helicopters11
Humans
3 Lamps 3 Lightnings6
Missiles 4 Mugs4
Openbooks
Classification Results
Line Segment Circle
Triangle Cube
Cylinder Sphere
Two adjacent spheres
Two spheres moving apart
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NearestNeighbor1st
Tier2nd
Tier
Classification Results Avoid bias due to varying group sizes
Query
…
Resu
lts
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an ba be bl bo car chair cl he human la li mis mug op pen ph plane ri sk so sp sub ta tank
animal
ballbeltblimpboat
car
chair
claw
helicopter
human
lamplightning
missle
mug
openbook
pen
phone
plane
rifle
skateboard
sofa
spaceship
sub
table
tank
an ba be bl bo car chair cl he human la li mis mug op pen ph plane ri sk so sp sub ta tank
animal
ballbeltblimpboat
car
chair
claw
helicopter
human
lamplightning
missle
mug
openbook
pen
phone
plane
rifle
skateboard
sofa
spaceship
sub
table
tank
Similarity matrix Nearest Neighbor 1st Tier 2nd Tier
Blocks Tanks Mugs Humans Airplanes Boats
Classification Results
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Classification ResultsShape
FunctionFirstTier
SecondTier
Nearest Neighbor
A3 38% 54% 55%D1 35% 48% 56%D2 49% 66% 66%D3 42% 58% 58%D4 32% 42% 47%
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Comparison to Moments Method
Align 1st moments (translation) Align 2nd moments (rotation and scale) Compare using remaining moments (L2)
ShapeFunction
FirstTier
SecondTier
NearestNeighbor
D2 49% 66% 66%M3 35% 46% 63%M4 41% 52% 64%M5 28% 38% 55%M6 34% 44% 54%M7 27% 33% 51%
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Conclusion – Properties Match global properties of shape Invariance
Rotation, translation, scale, mirror Robustness
Noise, cracks, insertions and deletions Practicality
Concise representation Efficient comparison Works for degenerate models
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Conclusion – Key Ideas Sampling gives common
parameterization Simplifies comparison
Comparing distributions is fast and easy Avoids registration, correspondence, etc.
Simple shape functions are discriminating Method suitable as preclassifier
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Future Work Use a larger and more controlled
database Combine shape distributions with
other classifiers into a working shape-based retrieval system
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Thank you Sloan
Foundation NSF