A paper review

1. Spatially coherent latent topic model for concurrent object segmentation and classification Authors: Liangliang Cao, Li Fei-Fei Presenter: Shao-Chuan Wang

2. Outline Motivation A Review on Graphical Models Today’s topic: the paper Their Results

3. Motivation: Real world problem often full of “noises” Bags of words (local features) Spatial relationships of objects are ignored (has its limit) When classify a test image, what is its “subject” ? Flag? Banner? People? Sports field? From Prof. Fei-Fei’s ICCV09 tutorial slide

4. Outline Motivation A Review on Graphical Models Today’s topic: the paper Their Results

5. Generative vs Discriminative Generative model: model p(x, y) or p(x|y)p(y) Discriminative model: model p(y|x) 0.1 0.05 0 0 10 20 30 40 50 60 70 1 0.5 0 0 10 20 30 40 50 60 70 x = data From Prof. Antonio Torralba course slide

6. Naïve Bayesian model (c: class, w: visual words) Once we have learnt the distribution, for a query image Generative model: An example Bayesian Networks c w1 wn …

7. Generative model: Another example Mixture Gaussian Model How to infer from unlabeled data even if we know the underlining probability distribution structure? ?

11. Use Gibbs sampling from the Posterior

12. Slow to converge

13. Variational method/Variational Message Passing (VMP)

14. Algorithms that convert inference problems into optimization problems (Opper and Saad 2001; Wainwright and Jordan 2003)Image from Wikipedia

15. Outline Motivation A Review on Graphical Models Today’s topic: the paper Their Results

17. Homogeneous Appearance ar: average of color or texture features

18. SIFT-based visual words: wr

20. Spatial Latent Topic Model (Unsupervised) Multinomial Dirichlet prior Maximize Log-likelihood an optimization problem: close-formed solution is intractable

21. Variaitional Message Passing (Winn 2005) Coupling hidden variables θ, α, β makes the maximization intractable Instead, maximize the lower bound of L Goal: Find a tractable Q(H) that closely approximates the true posterior distribution P(H|V) (equality holds for any distribution Q) ←Or equivalently, minimize KL(Q||P)

22. Variaitional Message Passing (Winn 2005) Further factorization assumptions (Jordan et al., 1999; Jaakkola, 2001; Parisi, 1988) (restrict the family of distributions Q) Entropy term = Where,

23. Variaitional Message Passing (Winn 2005) Eqn. (6) in the paper Bayesian networks representation Markov blanket:

24. Spatial Latent Topic Model (Supervised) Now it becomes C x K matrix, i.e. θ depends on observed c For a query image,Id , find its most probable category c:

25. Process Training step maximize total likelihood of training images, subject λ, α, θ and zr The learned λ, α are fixed Testing phase, for a query Image Id Estimate its θd and zr For classification task, find its most probable latent topics as its category For segmentation task, for the same zr, merge it. (3)

26. Outline Motivation A Review on Graphical Models Today’s topic: the paper Their Results

27. Experimental Results Unsupervised segmentation Occlusion case:

28. Experimental Results Supervised segmentation Dataset 13 classes of nature scenes # of training images: 100 # of topics: 60 # of categories: 13

29. Experimental Results Supervised classification Dataset 28 classes from Caltech 101 # of training images: 30 # of test images: 30 # of topics in category: 28 # of topics in clutter: 34 6 background classes are left unlabeled

30. ~ Thank you ~

31. Variaitional Message Passing Following this framework, and use the graphical model provided by this paper: