Elastic Graph Matching for Face Recognition

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Elastic Graph Matching for Face Recognition

• Group 8 Wang Xiaogang
• Luo Bo
• Li Zhifeng
• Time November 28, 2001

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Abstract

• L. Wiskott proposed a face recognition
  method by elastic bunch graph matching. Face is
  represented by a graph in which nodes are
  fiducial points and labeled by Gabor transform.
  We try to study his method by implementing it on
  the Purdue database. Some experiment results and
  evaluation are given. A demo for face recognition
  will be shown

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Contents

• Recognition Procedure
• Gabor Transformation
• Face Recognition
• Experiment Results
• Elastic Graph Matching

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1 Recognition Procedure

• Face recognition system assists a human expert
  to determine the identity of a test face by
  computing all similarity scored in the system
  database and by ranking them.
• Face authentication system decide itself if a
  test face is assigned to a client (i.e., one who
  claims his/her own identity) or to an impostor
  (i.e., one who pretends to someone else.

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1 Recognition Procedure
Recognition Procedures Feature selection,
extraction, classification Features statistical
or structural local or global information.
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2 Gabor Transformation

• Gabor Function (1-D)
• Gabor Function (2-D)
• Gabor Transform
• Gabor Feature for Face Recognition

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2.1 Gabor Function (1-D)

• Modulated Gaussion function
• Features time limited and frequency limited.
• Advantages characterize signals that only last
  for a short time or whose frequency contents
  change over time.

?(x)
x
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2.2 Gabor Function (2-D)
where
Quantification

• Here is the variable in the space domain,
  determines the frequency, is scale factor and
  is orientation factor. The above parameters
  determine total of Gabor function.

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Gabor Function Examples
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Gabor Function Examples
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Gabor Function Examples
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Gabor Function Examples
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Feature of 2-D Gabor Function

• Characters
• Space localized
• Frequency localized
• Advantage
• Gabor function can detect multi-scale and
  multi-orientation edge strengths at particular
  position.

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2.3 Gabor Transform

• Given an image , its Gabor transformation
  at one particular position is
• Gabor Feature Vector
• Characters Gabor feature extract mutiscale and
  multi-orientation edge strengths at each fiducial
  point.

where
is the Gabor transformation at pi
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2.4 Gabor Feature for Face Recognition

• Similarity measures
• City Block
• Nearest Neighbor Rule for Classification
• Given a testing face and its feature
  vector , the reference feature of a reference
  library are
  the testing face will be recognized as
  the reference face if

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3 Face Recognition

• Face Grid Generating
• Database for Experiment
• Experiment Result

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3.1 Face Grid Generating

• The fiducial points should contain enough local
  information which can distinguish faces. We
  choose the points at eye center, nose tip, head
  boundary, eyebrow end, mouth corner, etc.
• The face grid model

Wiskott97s graph model
Our graph model
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3.1 Face Grid Generating

• Locate the fiducial points automatically by
  elastic matching is time consuming because of the
  large computation, not accurate and stable. I
  takes about an hour to generate a graph ( See
  Section 4 ).
• We locate the fiducial points manually aided by a
  semi-auto system. We use the ideal graph data for
  the experiment of face recognition

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3.2 Database for Experiment

• 780 images of 34 people are selected from the AR
  Face Database (Purdue University) for the
  experiment.
• All these images are of 768 by 576 pixels, 256
  gray, frontal views, and similar face size.
• Each person has 26 pictures, which falls into two
  sessions taken two week apart. Each session
  includes 13 pictures with different expressions,
  lighting conditions or occlusions

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3.2 Database for Experiment
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3.3 Recognition Test
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Experiment Result
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Experiment Result
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Explanation on Experiment

• Global structure is not used
• Robust performance on different test
• Occlusion has greater effect on the performance

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4 Elastic Graph Matching

• We try to use the bunch graph model to locate the
  fiducial points automatically. The algorithm is
  proposed by Wiskott97. But we find that the
  computation is huge using this algorithm, and the
  accuracy is not very high. We apply the algorithm
  to several images, and the matching result we be
  show in this part.

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4.1 Face Bunch Graph

• Given M individual graphs of model faces
• the face bunch graph is
  with
• In practice we use 30 individual graphs which are
  from different people and under different
  conditions

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4.2 Graph Similarity Function

• Define the graph similarity function between a
  bunch graph and an individual face graph
• where is the jet similarity
  function which can use either or
  , is a control parameter

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Jet Similarity Function

• The Jet similarity function can be
  defined in two ways, with or without phase
  information

With phase
Without phase
Where
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4.3 Elastic Matching Step

• Step 1 Sparse scanning / rigid searching

Parameter
scan it over the whole face image (768X576)
with scanning step 20, and calculate the
similarity with face graph generated from the
FBG-corresponding position. The position having
the maximum similarity will be served as the
start point in the next step.
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4.3 Elastic Matching Step

• Step 2 Refine size and aspect ratio

Parameter
we skip the adjustment on aspect ratio
because the face face images have similar
ratio.Starting from the resulting position of
Step1, move the graph within a small window with
fine step. In our experiments, the window for
refine locating is 10 by 10, and searching step
is 1. The similarity measurement here is the
phase sensitive measurement.
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4.3 Elastic Matching Step

• Step 3 Local distortion

Parameter
Move each node of the graph to its neighbor
position, and then compare the jet similarity and
edge similarity regarding current node only, the
best position of each node is the position of the
maximum similarity.
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4.4 Elastic Matching Result
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Summary

• Elastic bunch graph matching shows a
  feasible solution to face recognition problem.
  The Gabor transformation makes the local feature
  robust to lighting variance. But the large
  computation and matching accuracy are the two
  problems encountered in the experiment.