A Novel Fisher Discriminant for Biometrics Recognition: 2DPCA plus 2DFLD

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A Novel Fisher Discriminant for Biometrics
Recognition 2DPCA plus 2DFLD

• R.M. Mutelo, L.C. Khor, W.L. Woo, and S.S. Dlay
• Signals Systems and Communications (SSC) Group
• School of Electrical, Electronic and Computer
  Engineering - University of Newcastle upon Tyne

risco.mutelo_at_ncl.ac.uk
l.c.khor_at_ncl.ac.uk
w.l.woo_at_ncl.ac.uk
s.s.dlay_at_ncl.ac.uk
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Introduction

• Growing interest in biometric authentication
• National ID cards, Airport security,
  Surveillance, Human search engine.
• Fingerprint, iris, hand geometry, gait, voice,
  vein and face.
• Several advantages of face recognition over other
  biometrics
• Covert operation.
• Human readable media.
• Public acceptance.
• Data required is easily obtained and readily
  available.
• Approach used
• Appearance-Based.

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Two Dimensional PCA 2DPCA
Review

• 2DPCA is applied to a training set of facial
  images of size m by n and the top d eigenvectors
  with the highest eigenvalues taken to represent
  face space.
• Any face image can then be projected into face
  space as a matrix of m by d coefficients,
  indicating the contribution of each
  corresponding eigenimage.

Two dimensional FLD 2DFLD

• Similar to the 2DPCA approach, yet able to
  account for variations between multiple images of
  the same person.
• Utilises a larger training set containing
  multiple images of each person.
• The low dimensional sub-space created maximises
  between-class scatter, while minimising
  within-class scatter.

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Limitations
Problems
System effectiveness is highly dependant on image
scatter matrices.

• Scatter matrices dimensions.
• Same dimensions as the number of image columns,
  which can be very large.
• Not very easy to evaluate the scatter matrices
  accurately when the number of columns is large.
• Time to determine the corresponding eigenvectors
  is large
• Variation in Image projection.
• Templates are not accurately obtained, projection
  by inaccurately computed eigenvectors.

Meaning face recognition systems are usually not
as accurate as other biometrics, producing error
rates that are too high for many applications.
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Possible Solution
Objective

• The goal is to reduce the dimensionality of the
  data while retaining as much as possible of the
  variation present in the dataset. There are many
  benefits on operating on low dimensionality data
• Better generalization to unseen images
• Accurate faster evaluation of scatter matrices.
• Better projection, small variation.
• Noise reduction.
• Such methods are known to improve face
  recognition systems.
• However, it is not known how these improvements
  vary between different approaches.

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Two dimensional PCA
Methodology

• Motivation - 2DPCA on dimensionality optimal
  signal reconstruction in the sense of minimum
  mean square error (MSE) when only a subset of
  principal components is used to represent the
  original signal.

Input Image
Transformed Image
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Apply Two dimensional FLD
Methodology

• Motivation - 2DFLD on discrimination seeking a
  high discrimination index, characteristic of
  separable low-dimensional patterns.

Variables

• N sample Images.

• C classes.

• Average of each class Total average.

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Scatter Matrices
Mathematical Formulation

• Scatter of class i.

• Within class scatter.

• Between class scatter.

• 2DPCA 2DFLD projection.

• Desired projection.

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Results
Comparison of the top recognition accuracy
Comparison of CPU times (seconds) using 15
eigenvectors, 200 images for training
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Conclusion

• 2DPCA 2DFLD is based on the image matrix, thus
  simpler and more straightforward to use for image
  feature extraction.
• Outperforms both fisherface and 2DFLD in terms of
  recognition accuracy, achieving a 95.50
  accuracy.
• No significant difference in terms of speed
  compared to 2DFLD but it is 84.4 times faster
  than Fisherface.
• Evaluates the between and with scatter matrices
  more accurate than 2DFLD.