Inference in generative models of images and video

1. Inference in generative models of images and video John Winn MSR Cambridge May 2004

2. Overview • Generative vs. conditional models • Combined approach • Inference in the flexible sprite model • Extending the model

3. Generative vs. conditional models We have an image I and latent variables Hwhich we wish to infer, e.g. object position, orientation, class. There will also be other sources of variability, e.g. illumination, parameterised by θ. Generative model: P(H, θ, I) Conditional model: P(H, θ|I) or P(H|I)

4. Conditional models use features Features are functions of I which aim to be informative about Hbut invariant to θ. Edge features Corner features Blob features

5. Conditional models Using features f(I), train a conditional model e.g. using labelled data Example: Viola & Jones face recognition using rectangle features and AdaBoost

6. Conditional models Advantages • Simple - only model variables of interest • Inference is fast - due to use of features and simple model Disadvantages • Non-robust • Difficult to compare different models • Difficult to combine different models

7. Generative models A generative model defines a process of generating the image pixels Ifrom the latent variables Hand θ, giving a joint distribution over all variables: P(H, θ, I) Learning and inference carried out using standard machine learning techniques e.g. Expectation Maximisation, MCMC, variational methods. No features!

8. Generative models Example: image modeled as layers of ‘flexible’ sprites.

9. Generative models Advantages • Accurate – as the entire image is modeled • Can compare different models • Can combine different models • Can generate new images Disadvantages • Inference is difficult due to local minima • Inference is slower due to complex model • Limitations on model complexity

10. Combined approach Use a generative model, but speed up inference using proposal distributions given by a conditional model. A proposal R(X) suggests a new distribution over some of the latent variables XH, θ. Inference is extended to allow accepting or rejecting the proposal e.g. depending on whether it improves the model evidence.

11. Using proposals in an MCMC framework Generative model: textured regions combined with face and text models Conditional model: face and text detector using AdaBoost (Viola & Jones) Proposals for text and faces Accepted proposals From Tu et al, 2003

12. Using proposals in an MCMC framework Generative model: textured regions combined with face and text models Conditional model: face and text detector using AdaBoost (Viola & Jones) Proposals for text and faces Reconstructed image From Tu et al, 2003

13. Proposals in the flexible sprite model

14. Flexible sprite model Set of images e.g. frames from a video x

15. Flexible sprite model x

16. Flexible sprite model f π Sprite shape and appearance x

17. Flexible sprite model f π Sprite transform for this image (discretised) T m x Transformed mask instance for this image

18. Flexible sprite model b f π Background T m x

19. Inference method & problems • Apply variational inference with factorised Q distribution • Slow – since we have to search entire discrete transform space • Limited size of transform space e.g. translations only (160120). • Many local minima.

20. Proposals in the flexible sprite model • We wish to create a proposalR(T). • Cannot use features of the image directly until object appearance found. • Use features of the inferred mask. π proposal T m

21. Moment-based features Use the first and second moments of the inferred mask as features. Learn a proposal distribution R(T). C-of-G of mask True location Contour of proposal distribution over object location Can also use R to get a probabilistic bound on T.

22. Iteration #1

23. Iteration #2

24. Iteration #3

25. Iteration #4

26. Iteration #5

27. Iteration #6

28. Iteration #7

29. Results on scissors video. Original Reconstruction • On average, ~1% of transform space searched. • Always converges, independent of initialisation. Foreground only

30. Beyond translation

31. Extended transform space Original Reconstruction

32. Extended transform space Original Reconstruction

33. Extended transform space Learned sprite appearance Normalised video

34. Corner features Learned sprite appearance Masked normalised image

35. Corner feature proposals

36. Preliminary results

37. Future directions

38. Extensions to the generative model Very wide range of possible extensions: • Local appearance model e.g. patch-based • Multiple layered objects • Object classes • Illumination modelling • Incorporation of object-specific models e.g. faces • Articulated models

39. Further investigation of using proposals Investigate other bottom-up features, including: • Optical flow • Color/texture • Use of standard invariant features e.g. SIFT • Discriminative models for particular object classes e.g. faces, text

40. b f π T m x N