a probabilistic model for component-based shape synthesis
DESCRIPTION
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 variability. - PowerPoint PPT PresentationTRANSCRIPT
A Probabilistic Model for Component-Based Shape Synthesis
A Probabilistic Model for Component-Based Shape SynthesisEvangelos Kalogerakis, Siddhartha Chaudhuri, Daphne Koller, Vladlen Koltun
Stanford University
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Goal: generative model of shape2
Goal: generative model of shape3Challenge: understand shape variability
Structural variability
Geometric variability
Stylistic variabilityOur chair dataset4
Related work: variability in human body and faceA 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] 5Related work: probabilistic reasoning for assembly-based modeling [Chaudhuri et al. 2011]
Probabilistic modelModeling interfaceInference6Related work: probabilistic reasoning for assembly-based modeling
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Randomly shuffling components of the same category
8Our probabilistic modelSynthesizes plausible and complete shapes automatically9Our probabilistic modelSynthesizes plausible and complete shapes automatically
Represents shape variability at hierarchical levels of abstraction
10Our probabilistic modelSynthesizes plausible and complete shapes automatically
Represents shape variability at hierarchical levels of abstraction
Understands latent causes of structural and geometric variability11Our probabilistic modelSynthesizes 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 shapes12
Learning stage13Synthesis stage
14Learning shape variabilityWe model attributes related to shape structure:
Shape typeComponent typesNumber of componentsComponent geometry P( R, S, N, G)15R P(R)16R P(R)
17R P(R) [P( Nl | R)] l LNlL18RSlNlL P(R) [P( Nl | R) P ( Sl | R )] l L19RSlNlL P(R) [P( Nl | R) P ( Sl | R )] l L
20ClRSlL P(R) [P( Nl | R) P ( Sl | R ) P( Dl | Sl ) P( Cl | Sl )] l LDlNl21ClRSlL P(R) [P( Nl | R) P ( Sl | R ) P( Dl | Sl ) P( Cl | Sl )] l LDlNl
HeightWidth22ClRSlL P(R) [P( Nl | R) P ( Sl | R ) P( Dl | Sl ) P( Cl | Sl )] l LDlNlLatent object styleLatent component style23ClRSlLDlNlLearn from training data:
latent styles
lateral edges
parameters of CPDs
24LearningGiven observed data O, find structure G that maximizes:
25LearningGiven observed data O, find structure G that maximizes:
26LearningGiven observed data O, find structure G that maximizes:
27LearningGiven observed data O, find structure G that maximizes:
28LearningGiven observed data O, find structure G that maximizes:
Assuming uniform prior over structures, maximize marginal likelihood:
29LearningGiven observed data O, find structure G that maximizes:
Assuming uniform prior over structures, maximize marginal likelihood:
Complete likelihood30LearningGiven observed data O, find structure G that maximizes:
Assuming uniform prior over structures, maximize marginal likelihood:
Parameter priors31LearningGiven observed data O, find structure G that maximizes:
Assuming uniform prior over structures, maximize marginal likelihood:
32LearningGiven observed data O, find structure G that maximizes:
Assuming uniform prior over structures, maximize marginal likelihood:
Cheeseman-Stutz approximation33Our probabilistic model: synthesis stage
34Shape 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 model35Component placementSourceshapesUnoptimizednew shapeOptimizednew shape
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Database Amplification - Airplanes37
Database Amplification - Airplanes38
Database Amplification - Chairs39
Database Amplification - Chairs40
Database Amplification - Ships41
Database Amplification - Ships42
Database Amplification - Animals43
Database Amplification - Animals44Database Amplification Construction vehicles
45Database Amplification Construction vehicles
46Interactive Shape Synthesis
47User Survey
TrainingshapesSynthesizedshapes
48Results
Source shapes(colored parts are selected for the new shape)New shape
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ResultsSource shapes(colored parts are selected for the new shape)New shape
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RN1N2C1C2S1S2D1D2Results of alternative models: no latent variables
51Results of alternative models: no part correlations
RN1N2C1C2S1S2D1D252SummaryGenerative 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 constraints53Future WorkOur 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
54Thank you!Acknowledgements: Aaron Hertzmann, Sergey Levine, Philipp Krhenbhl, Tom Funkhouser
Our project web page:http://graphics.stanford.edu/~kalo/papers/ShapeSynthesis/
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