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18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
18 cv mil_style_and_identity
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18 cv mil_style_and_identity

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  • 1. Computer vision:models, learning and inference Chapter 18 Models for style and identity Please send errata to s.prince@cs.ucl.ac.uk
  • 2. Identity and Style Identity differs, but images similar Identity same, but images quite differentComputer vision: models, learning and inference. ©2011 Simon J.D. Prince 2
  • 3. Structure• Factor analysis review• Subspace identity model• Linear discriminant analysis• Non-linear models• Asymmetric bilinear model• Symmetric bilinear model• Applications Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 3
  • 4. Factor analysis reviewGenerative equation:Probabilistic form: Marginal density: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 4
  • 5. Factor analysisComputer vision: models, learning and inference. ©2011 Simon J.D. Prince 5
  • 6. Factor analysis reviewE-Step:M-Step: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 6
  • 7. Factor analysis vs. Identity model• Each color is a different identity• multiple images lie in similar part of subspace Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 7
  • 8. Subspace identity modelGenerative equation:Probabilistic form: Marginal density: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 8
  • 9. Subspace identity model Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 9
  • 10. Factor analysis vs. subspace identity Factor analysis Subspace identity model Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 10
  • 11. Learning subspace identity modelE-Step:Extract moments: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 11
  • 12. Learning subspace identity modelE-Step:M-Step: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 12
  • 13. Subspace identity model Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 13
  • 14. Subspace identity model Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 14
  • 15. Inference by comparing modelsModel 1 – Faces match (identity shared):Model 2 – Faces dont match (identities differ):Both models have standard form of factor analyzer Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 15
  • 16. Inference by comparing modelsCompute likelihood (e.g. for model zero)whereCompute posterior probability using Bayes rule Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 16
  • 17. Face Recognition Tasks GALLERY PROBE … ? 1. CLOSED SET FACE IDENTIFICATION GALLERY PROBE … NO ? 2. OPEN SET MATCH FACE IDENTIFICATION PROBE NOMATCH ? 3. FACE VERIFICATION ? 4. FACE CLUSTERING Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 17
  • 18. Inference by comparing models Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 18
  • 19. Relation between models Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 19
  • 20. Structure• Factor analysis review• Subspace identity model• Linear discriminant analysis• Non-linear models• Asymmetric bilinear model• Symmetric bilinear model• Applications Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 20
  • 21. Probabilistic linear discriminant analysisGenerative equation:Probabilistic form: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 21
  • 22. Probabilistic linear discriminant analysis Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 22
  • 23. LearningE-Step – write out all images of same person as system of equations – Has standard form of factor analyzer – Use standard EM equationM-Step – write equation for each individual data point – Has standard form of factor analyzer – Use standard EM equation Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 23
  • 24. Probabilistic linear discriminant analyis Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 24
  • 25. InferenceModel 1 – Faces match (identity shared):Model 2 – Faces dont match (identities differ):Both models have standard form of factor analyzerCompute likelihood in standard way Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 25
  • 26. Example results (XM2VTS database) Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 26
  • 27. Structure• Factor analysis review• Subspace identity model• Linear discriminant analysis• Non-linear models• Asymmetric bilinear model• Symmetric bilinear model• Applications Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 27
  • 28. Non-linear models (mixture)Mixture model can describe non-linear manifold.Introduce variable ci whichrepresents which clusterTo be the same identity, must alsobelong to the same cluster Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 28
  • 29. Non-linear models (kernel)• Pass hidden variable through non-linear function f[ ].• Leads to kernelized algorithm• Identity equivalent of GPLVM Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 29
  • 30. Structure• Factor analysis review• Subspace identity model• Linear discriminant analysis• Non-linear models• Asymmetric bilinear model• Symmetric bilinear model• Applications Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 30
  • 31. Asymmetric bilinear model• Introduce style variable sij• indicates conditions in which data was observed• Example: lighting, pose, expression face recognitionAsymmetric bilinear model• Introduce style variable sij• indicates conditions in which data was observed• Example: lighting, pose, expression face recognition Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 31
  • 32. Asymmetric bilinear model Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 32
  • 33. Asymmetric bilinear modelGenerative equation:Probabilistic form:Marginal density: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 33
  • 34. LearningE-Step:M-Step: Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 34
  • 35. Asymmetric bilinear model Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 35
  • 36. Inference – inferring styleLikelihood of stylePrior over styleCompute posterior over style using Bayes’ rule Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 36
  • 37. Inference – inferring identityLikelihood of identityPrior over identityCompute posterior over identity using Bayes’ rule Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 37
  • 38. Inference – comparing identitiesModel 1 – Faces match (identity shared):Model 2 – Faces dont match (identities differ):Both models have standard form of factor analyzerCompute likelihood in standard way, combine with prior in Bayes rule Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 38
  • 39. Inference – Style translation• Compute distribution over identity• Generate in new style Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 39
  • 40. Structure• Factor analysis review• Subspace identity model• Linear discriminant analysis• Non-linear models• Asymmetric bilinear model• Symmetric bilinear model• Applications Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 40
  • 41. Symmetric bilinear modelGenerative equation:Probabilistic form:Mean can also depend on style... Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 41
  • 42. Symmetric bilinear model Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 42
  • 43. Inference – translating style or identity Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 43
  • 44. Multilinear modelsExtension of symmetric bilinear model to more than two factorse.g., Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 44
  • 45. Structure• Factor analysis review• Subspace identity model• Linear discriminant analysis• Non-linear models• Asymmetric bilinear model• Symmetric bilinear model• Applications Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 45
  • 46. Face recognitionComputer vision: models, learning and inference. ©2011 Simon J.D. Prince 46
  • 47. TensortexturesComputer vision: models, learning and inference. ©2011 Simon J.D. Prince 47
  • 48. Synthesizing animationComputer vision: models, learning and inference. ©2011 Simon J.D. Prince 48
  • 49. Discussion• Generative models• Explain data as combination of identity and style factors• In identity recognition, we build models where identity was same or different• Other forms of inference such as style translation also possible Computer vision: models, learning and inference. ©2011 Simon J.D. Prince 49

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