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A Probabilistic Model for Component-Based Shape Synthesis

This paper presents a generative model that synthesizes plausible 3D shapes automatically by understanding and representing shape variability across structural, geometric, and stylistic dimensions. The model is learned without supervision from a set of segmented shapes and captures the latent causes of the observed variability in shape. We demonstrate its ability to combine components from various categories to create new shapes, thereby advancing the state of shape synthesis in computer graphics.

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A Probabilistic Model for Component-Based Shape Synthesis

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  1. A Probabilistic Model for Component-Based Shape Synthesis EvangelosKalogerakis, Siddhartha Chaudhuri, Daphne Koller, VladlenKoltun Stanford University

  2. Goal: generative model of shape

  3. Goal: generative model of shape

  4. Challenge: understand shape variability • Structural variability • Geometric variability • Stylistic variability Our chair dataset

  5. 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] [Allen et al. 03] Scanned bodies

  6. Related work: probabilistic reasoning for assembly-based modeling [Chaudhuri et al. 2011] Inference Modeling interface Probabilistic model

  7. Related work: probabilistic reasoning for assembly-based modeling

  8. Randomly shuffling components of the same category

  9. Our probabilistic model • Synthesizes plausibleand complete shapesautomatically

  10. Our probabilistic model • Synthesizes plausibleand complete shapesautomatically • Represents shape variability at hierarchical levels of abstraction

  11. Our probabilistic model • Synthesizes plausibleand complete shapesautomatically • Represents shape variability at hierarchical levels of abstraction • Understands latent causes of structural and geometric variability

  12. Our probabilistic model • Synthesizes plausibleand complete shapesautomatically • 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

  13. Learning stage

  14. Synthesis stage

  15. Learning shape variability We model attributes related to shape structure: Shape type Component types Number of components Component geometry P( R, S, N, G)

  16. R P(R)

  17. R P(R)

  18. R Nl L Π P(R)[P(Nl|R)] l ∈L

  19. R Nl Sl L Π P(R)[P(Nl|R) P (Sl|R )] l ∈L

  20. R Nl Sl L Π P(R)[P(Nl|R) P (Sl|R )] l ∈L

  21. R Nl Sl Dl Cl L Π P(R)[P(Nl|R) P (Sl|R ) P(Dl|Sl ) P(Cl| Sl )] l ∈L

  22. R Nl Sl Width Dl Cl L Height Π P(R)[P(Nl|R) P (Sl|R ) P(Dl|Sl ) P(Cl| Sl)] l ∈L

  23. R Latent object style Nl Sl Latent component style Dl Cl L Π P(R)[P(Nl|R) P (Sl|R ) P(Dl|Sl ) P(Cl| Sl )] l ∈L

  24. R Nl Sl Learn from training data: latent styles lateral edges parameters of CPDs Dl Cl L

  25. Learning Given observed data O, find structure G that maximizes:

  26. Learning Given observed data O, find structure G that maximizes:

  27. Learning Given observed data O, find structure G that maximizes:

  28. Learning Given observed data O, find structure G that maximizes:

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

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

  31. Learning Given observed data O, find structure G that maximizes: Assuming uniform prior over structures, maximize marginal likelihood: Parameter priors

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

  33. Learning Given observed data O, find structure G that maximizes: Assuming uniform prior over structures, maximize marginal likelihood: Cheeseman-Stutz approximation

  34. Our probabilistic model: synthesis stage

  35. Shape Synthesis Enumerate high-probability instantiations of the model {} {R=1} {R=2} {R=1,S1=1} {R=1,S1=2} {R=2,S1=2} {R=2,S1=2} …

  36. Component placement Unoptimizednew shape Optimizednew shape Sourceshapes

  37. Database Amplification - Airplanes

  38. Database Amplification - Airplanes

  39. Database Amplification - Chairs

  40. Database Amplification - Chairs

  41. Database Amplification - Ships

  42. Database Amplification - Ships

  43. Database Amplification - Animals

  44. Database Amplification - Animals

  45. Database Amplification – Construction vehicles

  46. Database Amplification – Construction vehicles

  47. Interactive Shape Synthesis

  48. User Survey Synthesized shapes Training shapes

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

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

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