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

1

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

7

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

36

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

49

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

50

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/

55