1. Part 1: Bag-of-words models
by Li Fei-Fei (UIUC)

2. Related works Early “bag of words” models: mostly texture recognition
Cula et al. 2001; Leung et al. 2001; Schmid 2001; Varma et al. 2002, 2003; Lazebnik et al. 2003
Hierarchical Bayesian models for documents (pLSA, LDA, etc.)
Hoffman 1999; Blei et al, 2004; Teh et al. 2004
Object categorization
Dorko et al. 2004; Csurka et al. 2003; Sivic et al. 2005; Sudderth et al. 2005;
Natural scene categorization
Fei-Fei et al. 2005

3. Object
Bag of ‘words’

4. retinal, cerebral cortex,
Analogy to documents
Of all the sensory impressions proceeding to the brain, the visual experiences are the dominant ones. Our perception of the world around us is based essentially on the messages that reach the brain from our eyes. For a long time it was thought that the retinal image was transmitted point by point to visual centers in the brain; the cerebral cortex was a movie screen, so to speak, upon which the image in the eye was projected. Through the discoveries of Hubel and Wiesel we now know that behind the origin of the visual perception in the brain there is a considerably more complicated course of events. By following the visual impulses along their path to the various cell layers of the optical cortex, Hubel and Wiesel have been able to demonstrate that the message about the image falling on the retina undergoes a step-wise analysis in a system of nerve cells stored in columns. In this system each cell has its specific function and is responsible for a specific detail in the pattern of the retinal image.
China is forecasting a trade surplus of $90bn (£51bn) to $100bn this year, a threefold increase on 2004's $32bn. The Commerce Ministry said the surplus would be created by a predicted 30% jump in exports to $750bn, compared with a 18% rise in imports to $660bn. The figures are likely to further annoy the US, which has long argued that China's exports are unfairly helped by a deliberately undervalued yuan. Beijing agrees the surplus is too high, but says the yuan is only one factor. Bank of China governor Zhou Xiaochuan said the country also needed to do more to boost domestic demand so more goods stayed within the country. China increased the value of the yuan against the dollar by 2.1% in July and permitted it to trade within a narrow band, but the US wants the yuan to be allowed to trade freely. However, Beijing has made it clear that it will take its time and tread carefully before allowing the yuan to rise further in value.
China, trade,
surplus, commerce,
exports, imports, US,
yuan, bank, domestic,
foreign, increase,
trade, value
sensory, brain,
visual, perception,
retinal, cerebral cortex,
eye, cell, optical
nerve, image
Hubel, Wiesel

6. category models (and/or) classifiers
learning
recognition
feature detection
& representation
codewords dictionary
image representation
category
decision
category models
(and/or) classifiers

7. 2. 1. 3. Representation codewords dictionary feature detection
image representation 3.

8. 1.Feature detection and representation

9. 1.Feature detection and representation
Regular grid
Vogel et al. 2003
Fei-Fei et al. 2005

10. 1.Feature detection and representation
Regular grid
Vogel et al. 2003
Fei-Fei et al. 2005
Interest point detector
Csurka et al. 2004
Sivic et al. 2005

11. 1.Feature detection and representation
Regular grid
Vogel et al. 2003
Fei-Fei et al. 2005
Interest point detector
Csurka et al. 2004
Sivic et al. 2005
Other methods
Random sampling (Ullman et al. 2002)
Segmentation based patches (Barnard et al. 2003)

12. 1.Feature detection and representation
Compute SIFT descriptor
[Lowe’99]
Normalize patch
Detect patches
[Mikojaczyk and Schmid ’02]
[Matas et al. ’02]
[Sivic et al. ’03]
Slide credit: Josef Sivic

13. 1.Feature detection and representation…

14. 2. Codewords dictionary formation…

15. 2. Codewords dictionary formation…
Vector quantization
Slide credit: Josef Sivic

16. 2. Codewords dictionary formation
Fei-Fei et al. 2005

17. Image patch examples of codewords
Sivic et al. 2005

18. 3. Image representation
frequency
…..
codewords

19. 2. 1. 3. Representation codewords dictionary feature detection
image representation 3.

20. category models (and/or) classifiers
Learning and Recognition
codewords dictionary
category
decision
category models
(and/or) classifiers

21. 2 case studies Naïve Bayes classifier
Csurka et al. 2004
Hierarchical Bayesian text models (pLSA and LDA)
Background: Hoffman 2001, Blei et al. 2004
Object categorization: Sivic et al. 2005, Sudderth et al. 2005
Natural scene categorization: Fei-Fei et al. 2005

22. First, some notations wn: each patch in an image
wn = [0,0,…1,…,0,0]T
w: a collection of all N patches in an image
w = [w1,w2,…,wN]
dj: the jth image in an image collection
c: category of the image
z: theme or topic of the patch

23. Case #1: the Naïve Bayes modelw N
Prior prob. of
the object classes
Image likelihood
given the class
Object class
decision
Csurka et al. 2004

24. Csurka et al. 2004

25. Csurka et al. 2004

26. Case #2: Hierarchical Bayesian
text models
Probabilistic Latent Semantic Analysis (pLSA) w N d z D
Hoffman, 2001
Latent Dirichlet Allocation (LDA) w N c z D 
Blei et al., 2001

27. Case #2: Hierarchical Bayesian
text models
Probabilistic Latent Semantic Analysis (pLSA) w N d z D
“face”
Sivic et al. ICCV 2005

28. Case #2: Hierarchical Bayesian
text models
“beach”
Latent Dirichlet Allocation (LDA) w N c z D 
Fei-Fei et al. ICCV 2005

29. w N d z D
Case #2: the pLSA model

30. Codeword distributionsz D
Case #2: the pLSA model
Observed codeword
distributions
Codeword distributions
per theme (topic)
Theme distributions
per image
For that we will use a method called probabilistic latent semantic analysis.
pLSA can be thought of as a matrix decomposition.
Here is our term-document matrix (documents, words) and we want to
find topic vectors common to all documents and mixture coefficients P(z|d) specific to each document.
Note that these are all probabilites which sum to one.
So a column here is here expressed as a convex combination of the topic vectors.
What we would like to see is that the topics correspond to objects.
So an image will be expressed as a mixture of different objects and backgrounds.
Slide credit: Josef Sivic

31. Case #2: Recognition using pLSA
An images is a mixture of learned topic vectors and mixing weights.
Fit the model and use the learned mixing coeficents to classify an image.
In particular assign to the highest P(z|d)
Slide credit: Josef Sivic

32. Case #2: Learning the pLSA parameters
Observed counts of word i in document j
We use maximum likelihood approach to fit parameters of the model.
We write down the likelihood of the whole collection and maximize it using EM.
M,N goes over all visual words and all documents.
P(w|d) factorizes as on previous slide the entries in those matrices are our parameters.
n(w,d) are the observed counts in our data
Maximize likelihood of data using EM
M … number of codewords
N … number of images
Slide credit: Josef Sivic

33. Demo
Course website

34. task: face detection – no labeling

35. Demo: feature detection
Output of crude feature detector
Find edges
Draw points randomly from edge set
Draw from uniform distribution to get scale

36. Demo: learnt parameters
Learning the model: do_plsa(‘config_file_1’)
Evaluate and visualize the model: do_plsa_evaluation(‘config_file_1’)
Codeword distributions
per theme (topic)
Theme distributions
per image

37. Demo: recognition examples

38. Demo: categorization results
Performance of each theme

39. Demo: naïve Bayes Learning the model: do_naive_bayes(‘config_file_2’)
Evaluate and visualize the model: do_naive_bayes_evaluation(‘config_file_2’)

40. category models (and/or) classifiers
Learning and Recognition
codewords dictionary
category
decision
category models
(and/or) classifiers

41. Invariance issues Scale and rotation Implicit
Detectors and descriptors
Kadir and Brady. 2003

42. Invariance issues Scale and rotation Occlusion Implicit in the models
Codeword distribution: small variations
(In theory) Theme (z) distribution: different occlusion patterns

43. Invariance issues Scale and rotation Occlusion Translation
Encode (relative) location information
Sudderth et al. 2005

44. Invariance issues Scale and rotation Occlusion Translation
View point (in theory)
Codewords: detector and descriptor
Theme distributions: different view points
Fergus et al. 2005

45. retinal, cerebral cortex,
Model properties
Of all the sensory impressions proceeding to the brain, the visual experiences are the dominant ones. Our perception of the world around us is based essentially on the messages that reach the brain from our eyes. For a long time it was thought that the retinal image was transmitted point by point to visual centers in the brain; the cerebral cortex was a movie screen, so to speak, upon which the image in the eye was projected. Through the discoveries of Hubel and Wiesel we now know that behind the origin of the visual perception in the brain there is a considerably more complicated course of events. By following the visual impulses along their path to the various cell layers of the optical cortex, Hubel and Wiesel have been able to demonstrate that the message about the image falling on the retina undergoes a step-wise analysis in a system of nerve cells stored in columns. In this system each cell has its specific function and is responsible for a specific detail in the pattern of the retinal image.
sensory, brain,
visual, perception,
retinal, cerebral cortex,
eye, cell, optical
nerve, image
Hubel, Wiesel
Intuitive
Analogy to documents

46. Model properties Intuitive (Could use) generative models
Convenient for weakly- or un-supervised training
Prior information
Hierarchical Bayesian framework
Sivic et al., 2005, Sudderth et al., 2005

47. Model properties Intuitive (Could use) generative models
Learning and recognition relatively fast
Compare to other methods

48. Weakness of the model
No rigorous geometric information of the object components
It’s intuitive to most of us that objects are made of parts – no such information
Not extensively tested yet for
View point invariance
Scale invariance
Segmentation and localization unclear