PCA Channel

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PCA Channel

• Student Fangming JI u4082259
• Supervisor Professor Tom Geoden

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Organization of the Presentation

• PCA and problems
• PCA channel idea
• Use the channel for automatic classification
• Channel
• Corrected Channel
• Conclusion
• Future work

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Principle Component Analysis

• A statistic tool
• Maximizes the scatter of all projected samples in
  the image space.
• Tries to capture the most important features and
  reduce the dimensions at the same time
• Each eigenvector is a principle component

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Algorithm of PCA

• Given a training set of M images with the same
  size, convert each of them into a single
  dimension vector (I1, I2, Im) Then, find the
  average image by calculating the mean of the
  training set ? (?In) / M, n 1, m. Each
  training image differs from the average by Fn
  In - ?. Then, the covariance matrix C is found by
• where A F1, F2, Fm and C is a
  matrix. It is too big to be used in practice. But
  fortunately, there are only M-1 non-zero
  eigenvalues and they can be found more
  efficiently with an M x M computation. This means
  that we can compute the eigenvector vi of
  instead of computing the eigenvector ui of .
  Also we can notice that the M best eigenvalues of
  are equal to the M best eigenvalues of .
  Then we can get M best eigenvalues of ui by Avi.
  At the end we will select a value K, to keep only
  K largest eigenvalues.

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Eigenfaces
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Problems of PCA based methods

• Avalanche disaster
• Up to a certain limit, these methods are robust
  over a wide range of parameter.
• Algorithm breaks down dramatically beyond that
  point

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Constant Features and Inconstant Features

• Holistic features
• Local features inconstant features
• Local Features (constant features)
• Inconstant features (such as view, illumination
  and expressions)
• Little change from inconstant gt Little change
  for holistic one
• Great change of inconstant gt maybe great change
  for the holistic one

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Distribution in the Image Space

• Images from the same personality may sit in
  totally different regions of the images space.
• Distance between the images beyond the range of
  being correctly recognized

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The PCA Channel

• Holistic features Local features inconstant
  features
• Positions decided by both local features and
  inconstant features
• Incremental changes in the inconstant features,
  should produce incremental changed holistic
  features or positions
• This incremental changed position looks like a
  channel so we call it PCA Channel

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Experiment Preparation And Tools

• Collecting images with incremental changes in the
  orientations -- Mingtaos software
• 45 images from three identities (15 images for
  each identity which are changed incrementally in
  orientation)
• Dozens of images from another three identities,
  randomly oriented with some expression images
• Face Recognition Practitioner Software
  developed by me

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Existence of The Channel

• Take view for example

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Automatic Image Classification

• Original PCA method
• The PCA channel method

• 1)Given an input image
• 2)Recognize it
• 3) Compute the PCA again with the new recognized
  image
• 4) Go to step 1)

• 1) Give an input image
• 2) Recognize it
• 3) Put it into the training set
• 4) Go to step 1)

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Performance Comparison

• If the training set is carefully selected the
  performance of PCA channel is better than the
  original one
• Problems
• Sensitive to the selection of the training set
• Contagious problem

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Contagious Problem
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The Corrected PCA Channel

• Cut off the root of the mismatching
• Improve the robustness

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Implementation

• Set up two threshold Low(L) and High(H)
• If the distance between the input image and the
  its nearest image in the training set lt L,
  recognize it. If the distance gt H, put it for
  future recognition if L lt distance lt H, make it
  a new group.
• Calculate the PCA again and cut off the
  mismatching at here
• Match again

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Results

• The success rate Match to Original Training Set
  Match to New Group
• The success rate 44.1550.65 94.80
• The success rate 44.1551.94 96.09
• 59.74

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New Groups
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Conclusion

• Properly build up image database and the PCA
  channel with cautious implementation, we can get
  very good performance for face recognition.
• But from the above experiment we can see that,
  the strength but also the weakness of the PCA
  channel is the images database.
• 3D face reconstruction system.
• Large computational load. But it can also be
  appropriate in some situations where the focus is
  more on accuracy than response time.

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Future Works

• Verify Our Research On Larger Data Set
• Preprocess the images before recognition
• Build Up a 3D-Face Morphable Model System
• Research in Hybrid Methods