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Statistical Modeling and Learning in Vision --- cortex-like generative models Ying Nian Wu

Statistical Modeling and Learning in Vision --- cortex-like generative models Ying Nian Wu UCLA Department of Statistics JSM, August 2010. Outline Primary visual cortex (V1) Modeling and learning in V1 Layered hierarchical models. http://www.stat.ucla.edu/~ywu/ActiveBasis

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Statistical Modeling and Learning in Vision --- cortex-like generative models Ying Nian Wu

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  1. Statistical Modeling and Learning in Vision --- cortex-like generative models Ying Nian Wu UCLA Department of Statistics JSM, August 2010

  2. Outline • Primary visual cortex (V1) • Modeling and learning in V1 • Layered hierarchical models http://www.stat.ucla.edu/~ywu/ActiveBasis Matlab/C code, Data

  3. Visual cortex: layered hierarchical architecture bottom-up/top-down V1: primary visual cortex simple cells complex cells Source: Scientific American, 1999

  4. Simple V1 cellsDaugman, 1985 Gabor wavelets: localized sine and cosine waves Transation, rotation, dilation of the above function

  5. V1 simple cells respond to edges image pixels

  6. Complex V1 cells Riesenhuber and Poggio,1999 • Larger receptive field • Less sensitive to deformation V1 complex cells Local max V1 simple cells Local sum Image pixels

  7. Independent Component AnalysisBell and Sejnowski, 1996 Laplacian/Cauchy

  8. Hyvarinen, 2000

  9. Sparse codingOlshausen and Field, 1996 Laplacian/Cauchy/mixture Gaussians

  10. Sparse coding / variable selection Inference: sparsification, non-linear lasso/basis pursuit/matching pursuit mode and uncertainty of p(C|I) explaining-away, lateral inhibition Learning: A dictionary of representational elements (regressors)

  11. Olshausen and Field, 1996

  12. Restricted Boltzmann Machine Hinton, Osindero and Teh, 2006 hidden, binary visible P(C|I): factorized no-explaining away P(I|C)

  13. Energy-based model Teh, Welling, Osindero and Hinton, 2003 Features, no explaining-away Maximum entropy with marginals Exponential family with sufficient stat Markov random field/Gibbs distribution Zhu, Wu, and Mumford, 1997 Wu, Liu, and Zhu, 2000

  14. Zhu, Wu, and Mumford, 1997 Wu, Liu, and Zhu, 2000

  15. Visual cortex: layered hierarchical architecture bottom-up/top-down What is beyond V1? Hierarchical model? Source: Scientific American, 1999

  16. Hierchical ICA/Energy-based model? Larger features Must introduce nonlinearities Purely bottom-up

  17. Hierarchical RBM Hinton, Osindero and Teh, 2006 J Unfolding, untying, re-learning C I I P(C)  P(J,C) P(I,C) = P(C)P(I|C) Discriminative correction by back-propagation

  18. Hierarchical sparse coding Attributed sparse coding elements transformation group topological neighborhood system Layer above : further coding of the attributes of selected sparse coding elements

  19. Hierarchical sparse coding Wu, Si, Fleming, Zhu, 2007 Residual  generalization Active basis

  20. Shared matching pursuit Wu, Si, Fleming, Zhu, 2007 • Local maximization in step 1: complex cells, Riesenhuber and Poggio,1999 • Arg-max in step 2: inferring hidden variables • Explaining-away in step 3: lateral inhibition

  21. Active basis Two different scales

  22. Putting multiple scales together

  23. More elements added Residual images

  24. Statistical modeling Wu, Si, Gong, Zhu, 2010 orthogonal Strong edges in background Conditional independence of coefficients Exponential family model

  25. ……

  26. ……

  27. Detection by sum-max maps Wu, Si, Gong, Zhu, 2010

  28. Complex V1 cells Riesenhuber and Poggio,1999 • Larger receptive field • Less sensitive to deformation V1 complex cells Local max V1 simple cells Local sum Image pixels

  29. SUM-MAX maps(bottom-up/top-down) SUM2 operator: what “cell”? Local maximization: complex cells Riesenhuber and Poggio,1999 Gabor wavelets: simple cells Olshausen and Field, 1996

  30. Bottom-up scoring and top-down sketching SUM2 MAX1 arg MAX1 SUM1 Bottom-up detection Top-down sketching Sparse selective connection as a result of learning Explaining-away in learning but not in inference

  31. Adjusting Active Basis Model by L2 Regularized Logistic Regression By Ruixun Zhang L2 regularized logistic regression re-estimated lambda’s Conditional on: (1) selected basis elements (2) inferred hidden variables (1) and (2)  generative learning • Exponential family model, q(I) negatives  Logistic regression • Generative learning without negative examples • Discriminative correcting of conditional independence assumption (with hugely reduced dimensionality)

  32. Learning from non-aligned training images

  33. Learning from non-aligned training images

  34. EM mixture

  35. EM mixture MNIST

  36. Active bases as part-templates Split bike template to detect and sketch tandem bike

  37. Is there a tandem bike here? Is there a wheel nearby? Is there a wheel here? Is there an edge nearby? Is there an edge here? Soft scoring instead of hard decision

  38. Learning part templates or visual words

  39. Shape script model Si and Wu, 2010 Shape motifs: elementary geometric shapes

  40. Layers of attributed sparse coding elements

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