A Probabilistic Model for Component Based Shape Synthesis Evangelos - - PowerPoint PPT Presentation

a probabilistic model for component based shape synthesis
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A Probabilistic Model for Component Based Shape Synthesis Evangelos - - PowerPoint PPT Presentation

A Probabilistic Model for Component Based Shape Synthesis Evangelos Kalogerakis, Siddhartha Chaudhuri, Daphne Koller, Vladlen Koltun Stanford University Goal: generative model of shape Goal: generative model of shape Challenge: understand shape


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A Probabilistic Model for Component‐Based Shape Synthesis

Evangelos Kalogerakis, Siddhartha Chaudhuri, Daphne Koller, Vladlen Koltun Stanford University

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Goal: generative model of shape

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Goal: generative model of shape

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Challenge: understand shape variability

  • Structural variability
  • Geometric variability
  • Stylistic variability

Our chair dataset

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Related work: variability in human body and face

  • A morphable model for the synthesis of 3D faces [Blanz & Vetter 99]
  • The space of human body shapes [Allen et al. 03]
  • Shape completion and animation of people [Anguelov et al. 05]

Scanned bodies

[Allen et al. 03]

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Related work: probabilistic reasoning for assembly‐based modeling

[Chaudhuri et al. 2011]

Probabilistic model Modeling interface Inference

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Related work: probabilistic reasoning for assembly‐based modeling

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Randomly shuffling components of the same category

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Our probabilistic model

  • Synthesizes plausible and complete shapes automatically
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Our probabilistic model

  • Synthesizes plausible and complete shapes automatically
  • Represents shape variability at hierarchical levels of abstraction
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Our probabilistic model

  • Synthesizes plausible and complete shapes automatically
  • Represents shape variability at hierarchical levels of abstraction
  • Understands latent causes of structural and geometric variability
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Our probabilistic model

  • Synthesizes plausible and complete shapes automatically
  • Represents shape variability at hierarchical levels of abstraction
  • Understands latent causes of structural and geometric variability
  • Learned without supervision from a set of segmented shapes
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Learning stage

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Synthesis stage

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Learning shape variability

We model attributes related to shape structure:

Shape type Component types Number of components Component geometry

P( R, S, N, G)

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R

P(R)

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R

P(R)

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R

P(R)

[P( Nl | R)]

Π

l ∈ L

Nl

L

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R Sl Nl

L

P(R)

[P( Nl | R) P ( Sl | R )]

Π

l ∈ L

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R Sl Nl

L

P(R)

[P( Nl | R) P ( Sl | R )]

Π

l ∈ L

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Cl R Sl

L

P(R)

[P( Nl | R) P ( Sl | R ) P( Dl | Sl ) P( Cl | Sl )]

Π

l ∈ L

Dl Nl

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Cl R Sl

L

P(R)

[P( Nl | R) P ( Sl | R ) P( Dl | Sl ) P( Cl | Sl )]

Π

l ∈ L

Dl Nl

Height Width

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Cl R Sl

L

P(R)

[P( Nl | R) P ( Sl | R ) P( Dl | Sl ) P( Cl | Sl )]

Π

l ∈ L

Dl Nl

Latent object style Latent component style

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Cl R Sl

L

Dl Nl

Learn from training data: latent styles lateral edges parameters of CPDs

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Learning

Given observed data O, find structure G that maximizes:

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Learning

Given observed data O, find structure G that maximizes:

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Learning

Given observed data O, find structure G that maximizes:

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Learning

Given observed data O, find structure G that maximizes:

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Learning

Given observed data O, find structure G that maximizes: Assuming uniform prior over structures, maximize marginal likelihood:

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Learning

Given observed data O, find structure G that maximizes: Assuming uniform prior over structures, maximize marginal likelihood:

Complete likelihood

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Learning

Given observed data O, find structure G that maximizes: Assuming uniform prior over structures, maximize marginal likelihood:

Parameter priors

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Learning

Given observed data O, find structure G that maximizes: Assuming uniform prior over structures, maximize marginal likelihood:

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Learning

Given observed data O, find structure G that maximizes: Assuming uniform prior over structures, maximize marginal likelihood:

Cheeseman‐Stutz approximation

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Our probabilistic model: synthesis stage

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Shape Synthesis

{} {R=1} {R=2} {R=1,S1=1} {R=1,S1=2} {R=2,S1=2} {R=2,S1=2}

Enumerate high‐probability instantiations of the model

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Component placement

Source shapes Unoptimized new shape Optimized new shape

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Database Amplification ‐ Airplanes

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Database Amplification ‐ Airplanes

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Database Amplification ‐ Chairs

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Database Amplification ‐ Chairs

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Database Amplification ‐ Ships

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Database Amplification ‐ Ships

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Database Amplification ‐ Animals

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Database Amplification ‐ Animals

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Database Amplification – Construction vehicles

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Database Amplification – Construction vehicles

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Interactive Shape Synthesis

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User Survey

Training shapes Synthesized shapes

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Results

Source shapes (colored parts are selected for the new shape) New shape

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Results

Source shapes (colored parts are selected for the new shape) New shape

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R N1 N2 C1 C2 S1 S2 D1 D2

Results of alternative models: no latent variables

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Results of alternative models: no part correlations

R N1 N2 C1 C2 S1 S2 D1 D2

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Summary

  • Generative model of component‐based shape synthesis
  • Automatically synthesizes new shapes from a domain

demonstrated by a set of example shapes

  • Enables shape database amplification or

interactive synthesis with high‐level user constraints

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Future Work

  • Our model can be used as a shape prior ‐ applications to

reconstruction and interactive modeling

  • Synthesis of shapes with new geometry for parts
  • Model locations and spatial relationships of parts
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Thank you!

Acknowledgements: Aaron Hertzmann, Sergey Levine, Philipp Krähenbühl, Tom Funkhouser Our project web page:

http://graphics.stanford.edu/~kalo/papers/ShapeSynthesis/