Motivation

1. Object Recognition by Discriminative MethodsSinisa Todorovic1st Sino-USA Summer School in VLPRJuly, 2009

2. Motivation Discriminate yes, but what? Problem 1: What are good features from Kristen Grauman, B. Leibe

3. Motivation Discriminate yes, but against what? Problem 2: What are good training examples from Kristen Grauman, B. Leibe

4. Motivation Discriminate yes, but how? Problem 3: What is a good classifier from Kristen Grauman, B. Leibe

5. Motivation Sliding windows???? What is a non-car? Is Bayes decision optimal? from Kristen Grauman, B. Leibe

6. How to Classify? observable feature class discriminant function Discriminant function may have a probabilistic interpretation

7. image feature How to Classify? Generative From Antonio Torralba 2007

8. image feature How to Classify? Discriminative From Antonio Torralba 2007

9. How to Classify? observable feature class discriminant function Linear discriminant function

10. How to Classify? Var 2 margin = width that the boundary can be increased before hitting a datapoint margin 1 margin 2 Var 1 Large margin classifiers

11. Distance Based Classifiers Given: query:

12. Support Vector Machines Breiman, Fua, Criminisi, Cipolla, Shotton, Lempitsky, Zisserman, Bosch, ... Random Forests Guyon, Vapnik, Heisele, Serre, Poggio, Berg... Outline Nearest Neighbor Shakhnarovich, Viola, Darrell, Torralba, Efros, Berg, Frome, Malik, Todorovic...

13. margin width Maxim-Margin Linear Classifier support vectors

14. Maxim-Margin Linear Classifier Problem: subject to:

15. Maxim-Margin Linear Classifier After rescaling data Problem: subject to:

16. LSVM Derivation

17. s.t. LSVM Derivation Problem: s.t.

18. At solution Dual Problem Solve using Lagrangian

19. Then compute: Only for support vectors for support vectors Dual Problem s.t.

20. Linearly Non-Separable Case trade-off between maximum separation and misclassification s.t.

21. Non-Linear SVMs • Non-linear separation by mapping data to another space • In SVM formulation, data appear only in the vector product • No need to compute the vector product in the new space • Mercer kernels

22. Vision Applications • Pedestrian detection • multiscale scanning windows • for each window compute the wavelet transform • classify the window using SVM “A general framework for object detection,” C. Papageorgiou, M. Oren and T. Poggio -- CVPR 98

23. Vision Applications “A general framework for object detection,” C. Papageorgiou, M. Oren and T. Poggio -- CVPR 98

24. Shortcomings of SVMs • Kernelized SVM requires evaluating the kernel for a test vector and each of the support vectors • Complexity = Kernel complexity × number of support vectors • For a class of kernels this can be done more efficiently [Maji,Berg, Malik CVPR 08] intersection kernel

25. Nearest Neighbor Breiman, Fua, Criminisi, Cipolla, Shotton, Lempitsky, Zisserman, Bosch, ... Random Forests Shakhnarovich, Viola, Darrell, Berg, Frome, Malik, Todorovic... Outline

26. Distance Based Classifiers Given: query:

27. Learning Global Distance Metric • Given query and datapoint-class pairs • Learn a Mahalanobis distance metric that • brings points from the same class closer, and • makes points from different classes be far away “Distance metric learning with application to clustering with side information” E. Xing, A. Ng, and M. Jordan, NIPS, 2003.

28. Learning Global Distance Metric s.t. PROBLEM!

29. Learning Global Distance Metric Problem with multimodal classes before learning after learning

30. Per-Exemplar Distance Learning Frome & Malik ICCV07, Todorovic & Ahuja CVPR08

31. Distance Between Two Images distance between j-th patch in image F and image I

32. Learning from Triplets For each image I in the set we have:

33. PROBLEM! They heuristically select 15 closest images Max-Margin Formulation • Learn for each focal image F independently s.t.

34. Problem: After computing in-class and out-of-class datapoints that have initially been closest may not be closest after learning Max-Margin Formulation distance between j-th patch in image F and image I

35. EM-based Max-Margin Formulation of Local Distance Learning Todorovic&Ahuja CVPR08

36. Learning from Triplets For each image I in the set: Frome, Malik ICCV07: Todorovic et al. CVPR08:

37. CVPR 2008: Results on Caltech-256

38. Breiman, Fua, Criminisi, Cipolla, Shotton, Lempitsky, Zisserman, Bosch, ... Random Forests Outline

39. Decision Trees -- Not Stable • Partitions of data via recursive splitting on a single feature • Result: Histograms based on data-dependent partitioning • Majority voting • Quinlan C4.5; Breiman, Freedman, Olshen, Stone (1984); Devroye, Gyorfi, Lugosi (1996)

40. Random Forests (RF) RF = Set of decision trees such that each tree depends on a random vector sampled independently and with the same distribution for all trees in RF

41. Hough Forests Combine: spatial info + class info “Class-Specific Hough Forests for Object Detection” Juergen Gall and Victor Lempitsky CVPR 2009

42. Hough Forests

43. Hough Forests In the test image all features cast votes about the location of the bounding box “Class-Specific Hough Forests for Object Detection” Juergen Gall and Victor Lempitsky CVPR 2009

44. Hough Forests “Class-Specific Hough Forests for Object Detection” Juergen Gall and Victor Lempitsky CVPR 2009

45. Thank you!