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

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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.

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Shape Distributions

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Shape Distributions

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Shape Functions

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Shape Function: D2

• Sample points on mesh uniformly

• For each point p, get D2 (histogram)

• Sum all D2 (histogram)

• Transform the histogram to coefficients

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Shape Distributions

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Comparing Shape Distributions

• Bhattacharyya: D(f, g) = 1 –

• PDF LN: Minkowski LN norm

• L1 norm

• L2 norm

• …

fg

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Issues

• Point sampling!

• Gross shape properties!

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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

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Histogram (IN, OUT, MIXED)

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Only D2?

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Enhanced Shape Functions

• Angle and Distance (AD) & Absolute Angle and Distance (ADD).

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AD & AAD

• AD/AAD is a 2D histogram

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Results with AD & AAD

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Statistical Analysis Methods

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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)

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Precision / Recall

• P := γ/ (γ+α)

• R := γ/ (γ+β)

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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

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Princeton Shape Benchmark

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What is PSB

• Providing a standard 3D model database.

• Classifying models by semantic, function and shape.

• Doing benchmark.

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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

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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

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Matching (III)

……

……

12345

1

2

3

4

5

1

2

3

4

5

2

1

54

3……

1

2

3

4

5

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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

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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

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Matching as Histogram

Similarity0 1

1

0

Num

ber

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Matching as Histogram with IQR

Similarity0 1

1

0

Num

ber

Median

Q3

Q1

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Results with IQR

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Thank You

See you in the next retrieval.