Object Recognition using
Boosted Discriminants
Shyjan Mahamud, Martial Hebert, and Jianbo Shi
Presented by: Chang Jia
As for: Pattern Recognition
Instructor: Prof. George Bebis
04-28-2006
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Outline
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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
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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
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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
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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
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Terminology
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Example: combination of linear
classifiers
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Correlation Function
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Distance Measure in code space
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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
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Idea:
• Various candidate discriminants are constructed
•
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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
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The exponential loss function
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The logistic cost function
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To simplify the presentation, use the first one
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Boosting Discriminants
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Goal: Learning a good code. It requires finding
good discriminants hk and the associated weights
k
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Assume that we are given a continuous feature
space.
•
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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
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Criteria for good discriminants:
I.
II.
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
III. the training images are partitioned into two wellseparate 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
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Maximizing J keeping l fixed – solve for s in
continuous interval [-1, +1] instead of binary values {1, +1}
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Maximizing J keeping s fixed – return a value in [-1,
+1]
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Pseudo-code for finding optimal
discriminants
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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
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Finding the optimal threshold ө is a one dimensional
problem along the discriminant hyperplane l
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Use a simple brute-force search
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The optimal value for ө is that which minimizes the total
loss
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Determine ө as follows: sort the projections onto the
optimal l of all the vi’s, 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
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Composing Discriminants
•
•
Compose discriminants in a “tree” Tk to be more
powerful in practice
Partition function:
if Tk maps both
images xi and xj to
the same partition
(i.e. same leaf
node of Tk)
•
Corresponding loss function:
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Composing Discriminants
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Composing simple discriminants into a tree of
discriminants.
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Optimizing Parameter
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Optimizing  k
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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Smoothing  k in practice
•
•
due to limited training data the optimal estimate can be
large in value
Introduce
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Overall Scheme
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Experimental Data
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FERET database
Training Data
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Test Data
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• Pairs of frontal images of 41 individuals
• 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.
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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
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Use eigenspace based method:
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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:
•
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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
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Parameters to be set:
• total number of discriminants ( set as twice the
•
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number of discriminants that gives a training error
of 0)
a regularization constant of γ= 1 was used to
smooth the weights  k
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
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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!
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