Object Recognition using Boosted Discriminants Shyjan Mahamud, Martial Hebert, and Jianbo Shi

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Object Recognition using Boosted Discriminants
Shyjan Mahamud, Martial Hebert, and Jianbo Shi

• Presented by Chang Jia
• As for Pattern Recognition
• Instructor Prof. George Bebis

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Outline

• Introduction
• Review of basic concepts
• Object discrimination method
• The Loss Function
• Boosting Discriminants
• Learning an Efficient Code
• Experimental results
• Conclusions and future work

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Object Recognition

• Recognize object class/ Identify individual
  object in given images
• Face detection, recognizing animals, cars, etc.

• Possible for both instances or object classes (
  Mona Lisa vs. faces or Beetle vs. cars)

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Object Recognition

• The hard part the same object can look
  incredibly different in different images due to
  differences in view points
• A robust recognizer must be tolerant to changes
  in pose, expression, illumination, and occlusion
  etc.

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COIL Object Database
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Code Space for Objects
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Boosting Algorithm

• Boosting - is an algorithm for constructing a
  strong classifier out of a linear combination
• of simple weak classifiers It
  provides a method of choosing the weak
  classifiers and setting the weights

• Terminology

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Example combination of linear classifiers
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Correlation Function

• Distance Measure in code space
• Related to the Hamming distance when the weight
  all set to 1
• Given an input image the class label
  corresponding to the training image that has the
  highest correlation with the input image is
  reported.

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Proposed Method

• Idea
• Various candidate discriminants are constructed
  by optimizing a pair-wise formulation of a
  generalization of the Fisher criteria.
• The candidate discriminant that reduces the total
  loss the most is chosen.
• The discriminants chosen so far are weighted and
  combined to give the final correlation function
  to be used at run-time.

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The Loss Function

• The exponential loss function
• The logistic cost function
• To simplify the presentation, use the first one

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Boosting Discriminants

• Goal Learning a good code. It requires finding
  good discriminants hk and the associated weights
• Assume that we are given a continuous feature
  space.
• For example, the pixel intensities in a localized
  m x m window around a given location in an input
  image lies in the continuous feature space R.
• We would like to find a discriminant in the
  feature space that satisfies some specific
  criteria.

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Finding Good Discriminants

• Criteria for good discriminants

• focus on pairs of training images that have been
  difficult to classify so far (high )

• pairs of training images from the same object
  class (i.e., yij 1) should be put in the same
  partition induced by the discriminant, while
  pairs of training images from different object
  classes (i.e., yij -1) should be put in
  different partitions

• the training images are partitioned into two
  well- separate groups, each of which is tightly
  clustered

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Discriminant Function
Between-classes scatter
Fisher Linear Discriminant
Within-classes scatter
Distance Function (a Kernel)
Indicator variables
Final Fisher Discriminant Function
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Iterative Optimization

• Maximizing J keeping l fixed solve for s in
  continuous interval -1, 1 instead of binary
  values -1, 1
• Maximizing J keeping s fixed return a value in
  -1, 1

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Pseudo-code for finding optimal discriminants

• Alternate between maximizing J w.r.t. s and l by
  solving for the corresponding eigenvector
  problems, until convergence.

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Illustration on a synthetic example in a
continuous 2D feature space
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Choosing Threshold

• Finding the optimal threshold ? is a one
  dimensional problem along the discriminant
  hyperplane l
• Use a simple brute-force search
• The optimal value for ? is that which minimizes
  the total loss
• Determine ? as follows sort the projections onto
  the optimal l of all the vis, find the total
  loss for each value of that are mid-points (for
  robustness at run-time) between successive sorted
  projections, and choose the that gives the
  minimum.

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Learning an Efficient Code

• Composing Discriminants
• Compose discriminants in a tree Tk to be more
  powerful in practice
• Partition function
• Corresponding loss function

if Tk maps both images xi and xj to the same
partition (i.e. same leaf node of Tk)
if Tk maps both images xi and xj to the same
partition (i.e. same leaf node of Tk)
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Composing Discriminants

• Composing simple discriminants into a tree of
  discriminants.

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Optimizing Parameter

• Optimizing
• Smoothing in practice
• due to limited training data the optimal estimate
  can be large in value
• Introduce

W is the total loss of all pairs of training
examples that were correctly classified, while W-
is the total loss of all incorrectly classified
pairs by the kth discriminant.
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Overall Scheme
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Experimental Data

• FERET database
• Training Data
• Pairs of frontal images of 41 individuals
• Test Data
• Also pairs of frontal images of the same
  individuals but taken around a month apart from
  the training images with differences in hair,
  lighting and expressions.
• Faces are rigidly aligned

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Results
Used the prominent regions around the eyes, nose
and mouth as features
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Results

• Use eigenspace based method
• Both training and testing data were projected
  onto the first 50 PCA components
• a search for the nearest training image for each
  testing image was performed
• The resulting recognition rate was 92.6.
• Use presented method
• After training, we classified a test image by
  finding the training image that was most
  correlated with the test image using the
  correlation function output. In other words, we
  found the nearest neighbor in code-space.
• The resulting recognition rate was 95.2.

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Results

• Parameters to be set
• total number of discriminants ( set as twice the
  number of discriminants that gives a training
  error of 0)
• a regularization constant of ? 1 was used to
  smooth the weights
• Time
• The training time for our approach was around 6
  hours, while the run-time was around 2 seconds.

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Conclusions and Future Work

• Presented an approach to learning good
  discriminators that can be thought of as that of
  learning good codes.
• Good discriminators are determined sequentially
  that focus on the currently hard to classify
  training images.
• Such discriminators are weighted and combined in
  an energy minimization scheme
• Can explore feature spaces in which distance
  measures can be non-linear by using more powerful
  non-linear kernels

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Thank you!