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2004/03/03 Sheun-Huei Guan, CML, NTU 1
3D Model Retrieval
After Shape Distributions
2004/03/03 Sheun-Huei Guan, CML, NTU 2
Agenda
• Shape Distributions and selected descendants.– Shape Distributions– S.D. on Solid Models– AD & AAD
• Princeton Shape Benchmark– Statistics– Benchmark
• Statistical tools to our system
2004/03/03 Sheun-Huei Guan, CML, NTU 3
Papers
• R. Osada, T. Funkhouser, B. Chazelle, D. Dobkin, Shape Distributions, ACM ToG 2002.
• C. Ip, D. Lapadat, L. Sieger, W. Regli, Using Shape Distributions to Compare Solid Models, 7th ACM/SIGGRAPH Symp. on Solid Modeling and Applications 2002.
• R. Ohbuchi, T. Minamitani, T. Takei, Shape-Similarity Search of 3D Models by using Enhanced Shape Functions, Theory and Practice of Computer Graphics 2003.
• P. Shilane, P. Min, M. Kazhdan, T. Funkhouser, The Princeton Shape Benchmark, Shape Modeling International 2004.
2004/03/03 Sheun-Huei Guan, CML, NTU 4
Shape Distributions
2004/03/03 Sheun-Huei Guan, CML, NTU 5
Shape Distributions
2004/03/03 Sheun-Huei Guan, CML, NTU 6
Shape Functions
2004/03/03 Sheun-Huei Guan, CML, NTU 7
Shape Function: D2
• Sample points on mesh uniformly
• For each point p, get D2 (histogram)
• Sum all D2 (histogram)
• Transform the histogram to coefficients
2004/03/03 Sheun-Huei Guan, CML, NTU 8
Shape Distributions
2004/03/03 Sheun-Huei Guan, CML, NTU 9
Comparing Shape Distributions
• Bhattacharyya: D(f, g) = 1 –
• PDF LN: Minkowski LN norm
• L1 norm
• L2 norm
• …
fg
2004/03/03 Sheun-Huei Guan, CML, NTU 10
Issues
• Point sampling!
• Gross shape properties!
2004/03/03 Sheun-Huei Guan, CML, NTU 11
Issue: point sampling
• Pseudo Random Number Generator?!
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Issue: gross shape properties
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Solid Model
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Solid Model
• Gross D2 on surface is not enough.
• Accumulate Distribution of Classification
2004/03/03 Sheun-Huei Guan, CML, NTU 15
Histogram (IN, OUT, MIXED)
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Only D2?
2004/03/03 Sheun-Huei Guan, CML, NTU 17
Enhanced Shape Functions
• Angle and Distance (AD) & Absolute Angle and Distance (ADD).
2004/03/03 Sheun-Huei Guan, CML, NTU 18
AD & AAD
• AD/AAD is a 2D histogram
2004/03/03 Sheun-Huei Guan, CML, NTU 19
Results with AD & AAD
2004/03/03 Sheun-Huei Guan, CML, NTU 20
Statistical Analysis Methods
2004/03/03 Sheun-Huei Guan, CML, NTU 21
Statistics
• Given a class with |C| members• The percentage of models in the query’s
class that appear within the top K matches.
• 1-tier: K = |C| - 1• 2-tier: K = 2(|C| - 1)• nearest neighbor: K = 1• Discounted Cumulative Gain (DCG)
2004/03/03 Sheun-Huei Guan, CML, NTU 22
Precision / Recall
• P := γ/ (γ+α)
• R := γ/ (γ+β)
2004/03/03 Sheun-Huei Guan, CML, NTU 23
Diagram
Precision
Recall
1
0
1
1/4
3/4
2/4
4/8
3/4
5/15
4/4
1
1
Recall
0
Precisionideal
2004/03/03 Sheun-Huei Guan, CML, NTU 24
Princeton Shape Benchmark
2004/03/03 Sheun-Huei Guan, CML, NTU 25
What is PSB
• Providing a standard 3D model database.
• Classifying models by semantic, function and shape.
• Doing benchmark.
2004/03/03 Sheun-Huei Guan, CML, NTU 26
Results: Precision-Recall
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Results: Statistics
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Results: Different Classification
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3D Model Retrieval byLight Field
2004/03/03 Sheun-Huei Guan, CML, NTU 30
Matching (I)
1
2
3
4
5
…………
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
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5
1
2
3
4
Matching (II)
……
……
12345
1
2
3
4
5
1
2
3
4
5……
1
2
3
4
5
2004/03/03 Sheun-Huei Guan, CML, NTU 32
Matching (III)
……
……
12345
1
2
3
4
5
1
2
3
4
5
2
1
54
3……
1
2
3
4
5
2004/03/03 Sheun-Huei Guan, CML, NTU 33
Matching (IV)
……5
43
1
2
……
12345
1
2
3
4
5
1
2
3
4
5
Minimum error from all corresponding 2D shapes
……
1
2
3
4
5
2004/03/03 Sheun-Huei Guan, CML, NTU 34
To be more robust in rotation(I)
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To be more robust in rotation(II)
1-160
1-10600
10-105460
Different rotation:(Mx(N-1)+1)x60
2004/03/03 Sheun-Huei Guan, CML, NTU 36
Matching as Histogram
Similarity0 1
1
0
Num
ber
2004/03/03 Sheun-Huei Guan, CML, NTU 37
Matching as Histogram with IQR
Similarity0 1
1
0
Num
ber
Median
Q3
Q1
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Results with IQR
2004/03/03 Sheun-Huei Guan, CML, NTU 39
Thank You
See you in the next retrieval.