1. Part 2: part-based models by Rob Fergus (MIT)

2. Problem with bag-of-words All have equal probability for bag-of-words methods Location information is important

3. Overview of section Representation –Computational complexity –Design choices Recognition Learning –Automated methods

4. Representation

5. Model: Parts and Structure

6. Representation Object as set of parts –Generative representation Model: –Relative locations between parts –Appearance of part Issues: –How to model location –How to represent appearance –Sparse or dense (pixels or regions) –How to handle occlusion/clutter Figure from [Fischler73]

7. Example scheme Model shape using Gaussian distribution on location between parts Model appearance as pixel templates Represent image as collection of regions –Extracted by template matching: normalized-cross correlation Manually trained model –Click on training images

8. Sparse representation + Computationally tractable (10 5 pixels  10 1 -- 10 2 parts) + Generative representation of class + Avoid modeling global variability + Success in specific object recognition - Throw away most image information - Parts need to be distinctive to separate from other classes

9. History of Idea Fischler & Elschlager 1973 Yuille ‘91 Brunelli & Poggio ‘93 Lades, v.d. Malsburg et al. ‘93 Cootes, Lanitis, Taylor et al. ‘95 Amit & Geman ‘95, ‘99 Perona et al. ‘95, ‘96, ’98, ’00 Felzenszwalb & Huttenlocher ’00 Many papers since 2000

10. The correspondence problem Model with P parts Image with N possible locations for each part N P combinations!!!

11. Connectivity of parts Complexity is given by size of maximal clique in graph Consider a 3 part model –Each part has set of N possible locations in image –Location of parts 2 & 3 is independent, given location of L –Each part has an appearance term, independent between parts. L 32 Shape Model S(L,2)S(L,3)A(L)A(2)A(3) L32 Variables Factors ShapeAppearance Factor graph S(L)

12. Connectivity of parts To find best match in image, we want most probable state of L, Run max-product message passing Take O(N 2 ) to compute: For each of the N values of L, need to find max over N states S(L,2)S(L,3)A(L)A(2)A(3) L32 mbmb mcmc mdmd S(L) mama

13. Different graph structures 1 3 45 6 2 1 3 45 6 2 Fully connected Star structure 1 3 4 5 6 2 Tree structure O(N 6 )O(N 2 ) Sparser graphs cannot capture all interactions between parts

14. from Sparse Flexible Models of Local Features Gustavo Carneiro and David Lowe, ECCV 2006 Different connectivity structures O(N 6 )O(N 2 )O(N 3 ) O(N 2 ) Fergus et al. ’03 Fei-Fei et al. ‘03 Crandall et al. ‘05 Fergus et al. ’05 Crandall et al. ‘05 Felzenszwalb & Huttenlocher ‘00 Bouchard & Triggs ‘05Carneiro & Lowe ‘06 Csurka ’04 Vasconcelos ‘00

15. Some class-specific graphs Articulated motion –People –Animals Special parameterisations –Limb angles Images from [Kumar05, Felzenszwalb05]

16. Regions or pixels # Regions << # Pixels Regions increase tractability but lose information Generally use regions: –Local maxima of interest operators –Can give scale/orientation invariance Figures from [Kadir04]

17. Hierarchical representations Pixels  Pixel groupings  Parts  Object Images from [Amit98,Bouchard05] Multi-scale approach increases number of low-level features Amit and Geman ’98 Ullman et al. Bouchard & Triggs ’05 Zhu and Mumford Jin & Geman ‘06 Zhu & Yuille ’07 Fidler & Leonardis ‘07

18. How to model location? Explicit: Probability density functions Implicit: Voting scheme Invariance –Translation –Scaling –Similarity/affine –Viewpoint Similarity transformation Translation and Scaling Translation Affine transformation

19. Probability densities –Continuous (Gaussians) –Analogy with springs Parameters of model,  and  –Independence corresponds to zeros in  Explicit shape model

20. Shape Shape is “what remains after differences due to translation, rotation, and scale have been factored out”. [Kendall84] Statistical theory of shape [Kendall, Bookstein, Mardia & Dryden] X Y Figure Space U V Shape Space  Figures from [Leung98]

21. Euclidean & Affine Shape Translation, rotation and scaling Euclidean Shape Removal of camera foreshortenings Affine Shape Assume Gaussian density in figure space What is the probability density for the shape variables in each of the different spaces? Feature spaceEuclidean shape Affine shape    Translation Invariant shape  Figures from [Leung98]

22. Translation-invariant shape Figure space density: Translation-invariant form Shape space density is still Gaussian e.g. P=3, move 1 st part to origin

23. Affine Shape Density Affine Shape density (Dryden-Mardia): Euclidean Shape density is of similar form [Leung98],[Welling05] Can learnt parameters of DM density with EM!

24. Other invariance methods Search over transformations –Large space (# pixels x # scales ….) –Closed form solution for translation and scale (Helmer and Lowe ’04) Features give information –Characteristic scale –Characteristic orientation (noisy) invariance of the characteristic scale Figures from Mikolajczyk & Schmid

25. Implicit shape model Spatial occurrence distributions x y s x y s x y s x y s Probabilistic Voting Interest Points Matched Codebook Entries Recognition Learning Learn appearance codebook –Cluster over interest points on training images Learn spatial distributions –Match codebook to training images –Record matching positions on object –Centroid is given Use Hough space voting to find object Leibe and Schiele ’03,’05

26. Deformable Template Matching Query Template Berg et al. CVPR 2005 Formulate problem as Integer Quadratic Programming O(N P ) in general Use approximations that allow P=50 and N=2550 in <2 secs

27. Multiple views Component 1 Component 2 Full 3-D location model Mixture of 2-D models –Weber CVPR ‘00 Frontal Profile 020406080100 50 55 60 65 70 75 80 85 90 95 100 Orientation Tuning angle in degrees % Correct

28. Representation of appearance Dependencies between parts –Common to assume independence –Need not be –Symmetry Needs to handle intra-class variation –Task is no longer matching of descriptors –Implicit variation (VQ appearance) –Explicit probabilistic model of appearance (e.g. Gaussians in SIFT space or PCA space)

29. Representation of appearance Invariance needs to match that of shape model Insensitive to small shifts in translation/scale –Compensate for jitter of features –e.g. SIFT Illumination invariance –Normalize out –Condition on illumination of landmark part

30. Appearance representation Decision trees Figure from Winn & Shotton, CVPR ‘06 SIFT PCA [Lepetit and Fua CVPR 2005]

31. Representation of occlusion Explicit –Additional match of each part to missing state Implicit –Truncated minimum probability of appearance Log probability Appearance space µ part

32. Representation of background clutter Explicit model –Generative model for clutter as well as foreground object Use a sub-window –At correct position, no clutter is present

33. Hierarchical representations Pixels  Pixel groupings  Parts  Object Images from [Amit98,Bouchard05] Multi-scale approach increases number of low-level features Amit and Geman ’98 Ullman et al. Bouchard & Triggs ’05 Zhu and Mumford Jin & Geman ‘06 Zhu & Yuille ’07 Fidler & Leonardis ‘07

34. Felzenszwalb, Mcallester, Ramanan, CVPR 2008 2-scale model –Whole object –Parts HOG representation + SVM training to obtain robust part detectors Distance transforms allow examination of every location in the image

35. Felzenszwalb, Mcallester, Ramanan, CVPR 2008

36. Stochastic Grammar of Images S.C. Zhu and D. Mumford

37. A Stochastic Grammar of Images Grammar –Hierarchical representation –Embodied in a simple And–Or graph representation –A probabilistic model for the natural occurrence frequency of objects and parts as well as their relations –Includes a series of visual dictionaries and organizes them through graph composition

38. animal head instantiated by tiger head animal head instantiated by bear head e.g. discontinuities, gradient e.g. linelets, curvelets, T- junctions e.g. contours, intermediate objects e.g. animals, trees, rocks Context and Hierarchy in a Probabilistic Image Model Jin & Geman (2006) Constructing probabilistic hierarchical image models, Designed to accommodate arbitrary contextual relationships

39. A Hierarchical Compositional System for Rapid Object Detection Long Zhu, Alan L. Yuille, 2007. Able to learn #parts at each level Objects are represented by graphical models Hierarchical tree –Root: full object –Lower-level elements: simpler features Passing simple messages up and down the tree

40. A Hierarchical Compositional System for Rapid Object Detection Long Zhu, Alan L. Yuille, 2007. Able to learn #parts at each level

41. A Hierarchical Compositional System for Rapid Object Detection Long Zhu, Alan L. Yuille, 2007.

42. Learning a Compositional Hierarchy of Object Structure Fidler & Leonardis, CVPR’07; Fidler, Boben & Leonardis, CVPR 2008 The architecture Parts model Learned parts

43. Learning Hierarchical Compositional Representations of Object Structure Hierarchical compositionality, statistical, bottom-up learning. The nodes are formed as compositions that, recursively, model loose spatial relationships between their constituent components. Oriented Edge Contour compositions Fidler & Leonardis, CVPR’07; Fidler, Boben & Leonardis, CVPR 2008

44. Learning Hierarchical Compositional Representations of Object Structure Fidler & Leonardis, CVPR’07; Fidler, Boben & Leonardis, CVPR 2008

45. Learning Hierarchical Compositional Representations of Object Structure Cross-layered compositional representation learned from the visual data. The category-specific layers can make use of all the necessary features stemming from all hierarchical layers Fidler & Leonardis, CVPR’07; Fidler, Boben & Leonardis, CVPR 2008

46. Repeatability of parts by using calculated similarity ’Circle’ part detections across different layers Fidler & Leonardis, CVPR’07; Fidler, Boben & Leonardis, CVPR 2008

47. Recognition

48. What task? Classification –Object present/absent –Sum over all matches (Bayesian) –Take best Detection –Localize object within the frame –Slide sub-window across image –Use features to define a basis

49. Efficient search methods Interpretation tree (Grimson ’87) –Condition on assigned parts to give search regions for remaining ones –Branch & bound, A*

50. Parts and Structure demo Gaussian location model – star configuration Translation invariant only –Use 1 st part as landmark Appearance model is template matching Manual training –User identifies correspondence on training images Recognition –Run template for each part over image –Get local maxima  set of possible locations for each part –Impose shape model - O(N 2 P) cost –Score of each match is combination of shape model and template responses.

51. Demo images Sub-set of Caltech face dataset Caltech background images

52. Demo Web Page

53. Demo (2)

54. Demo (3)

55. Demo (4)

56. Distance transforms –O(N 2 P)  O(NP) for tree structured models How it works –Assume location model is Gaussian (i.e. e -d 2 ) –Consider a two part model with µ =0, σ=1 on a 1-D image f(d) = -d 2 Appearance log probability at x i for part 2 = A 2 (x i ) xixi Image pixel Log probability L 2 Model Felzenszwalb and Huttenlocher ’00 & ’05

57. Distance transforms 2 For each position of landmark part, find best position for part 2 –Finding most probable x i is equivalent finding maximum over set of offset parabolas –Upper envelope computed in O(N) rather than obvious O(N 2 ) via distance transform (see Felzenszwalb and Huttenlocher ’05). Add A L (x) to upper envelope (offset by µ) to get overall probability map xixi xgxg xjxj xlxl xhxh A 2 (x i ) A 2 (x l ) A 2 (x j ) A 2 (x g ) A 2 (x h ) A 2 (x k ) xkxk Log probability Image pixel

58. Demo: efficient methods

59. How much does shape help? Crandall, Felzenszwalb, Huttenlocher CVPR’05 (CODE)(CODE) Shape variance increases with increasing model complexity Do get some benefit from shape http://www.cs.cornell.edu/~dph/papers/kfans.p df

60. Learning

61. Learning situations Varying levels of supervision –Unsupervised –Image labels –Object centroid/bounding box –Segmented object –Manual correspondence (typically sub-optimal) Generative models naturally incorporate labelling information (or lack of it) Discriminative schemes require labels for all data points Contains a motorbike

63. Task:Estimation of model parameters Learning using EM Let the assignments be a hidden variable and use EM algorithm to learn them and the model parameters Chicken and Egg type problem, since we initially know neither: - Model parameters - Assignment of regions to parts

64. Learning procedure E-step:Compute assignments for which regions belong to which part M-step:Update model parameters Find regions & their location & appearance Initialize model parameters Use EM and iterate to convergence: Trying to maximize likelihood – consistency in shape & appearance

65. Example scheme, using EM for maximum likelihood learning... Image 1 Image 2 Image i 2. Assign probabilities to constellations Large P Small P 1. Current estimate of  pdf 3. Use probabilities as weights to re-estimate parameters. Example:  Large Px+Small Px new estimate of  + … =

66. Priors Implicit –Structure of dependencies in model –Parameterisation of model –Feature detectors Explicit –p(  ) –MAP / Bayesian learning –Fei-Fei ‘03 model (  ) space 11 22 nn p(  n ) p(  2 ) p(  1 )

67. Learning Shape & Appearance simultaneously Fergus et al. ‘03

68. Learn appearance then shape Parameter Estimation Choice 1 Model 1 Choice 2 Parameter Estimation Model 2 Predict / measure model performance (validation set or directly from model) Preselected Parts (  100) Weber et al. ‘00

69. Discriminative training Sparse so parts need to be distinctive of class Boosted parts and structure models –Amores et al. CVPR 2005 –Bar Hillel et al. CVPR 2005 Discriminative features –Weber et al. 2000 –Ullman et al. Train discriminatively on parameters of generative model –Holub, Welling, Perona ICCV 2005

70. Number of training images More supervision, fewer images needed –Few unknown parameters Less supervision, more images. –Lots of unknown parameters Over-fitting problems

71. Number of training examples Priors 6 part Motorbike model

72. Parts and Structure models Summary Hierarchical models allow for more parts Correspondence problem between image and model Efficient methods for large # parts and # positions in image Challenge to get representation with desired invariance Minimal supervision Future directions: Multiple views Approaches to learning Multiple category training

73. References 2. Parts and Structure

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