Face Recognition Using Face Unit Radial Basis Function Networks

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Face Recognition Using Face Unit Radial Basis
Function Networks

• Ben S. Feinstein
• Harvey Mudd College
• December 1999

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Original Project Proposal

• Try to reproduce published results for RBF neural
  nets performing face-recognition.

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Recap of RBF Networks

• Neuron responses are locally-tuned or
  selective for some range of input space.
• Biologically plausible Cochlear stereocilia
  cells in human ear exhibit locally-tuned response
  to frequency.
• Contains 1 hidden layer of radial neurons,
  usually gaussian functions. Hidden layer output
  fed to output layer of linear neurons.

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Recap of RBF Networks (2)
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Face Unit Network Architecture

• First proposed in June 1995 by Dr. A. J. Howell,
  School of Cognitive and Computing Sciences, Univ.
  of Sussex, UK.
• A face unit is structured to recognize only one
  person, using hybrid RBF architecture.
• Network has two linear outputs, one indicating a
  positive ID of the person, the other a negative
  ID.

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Face Unit Architecture (2)

• An pa face unit network has p radial neurons
  linked to the output, and a neurons linked to
  the - output.
• Challenges
• Bitmap faces are big dimensionally
• How to reduce dimensionality of problem,
  extracting only the relevant information?

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Gabor Wavelet Analysis

• Answer Use 2D Gabor wavelets, class of
  orientation and position selective functions.
• In this case, reduces dim from 10,000 (100x100
  pixel sample) to 126.
• Biologically plausible Cells in visual cortex
  respond selectively to stimulation that is both
  local in retinal position and local in angle of
  orientation.

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Approach to Problem

• Sample data
• 10 people x 10 poses of each person ranging from
  0 (head-on) to 90 (side profile) 100 sample
  images
• All images 384x287 pixel grayscale Sun
  rasterfiles, courtesy of Univ. of Sussex face
  database.
• 5 men and 5 women in sample set, mostly Caucasian.

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Approach to Problem (2)

• Example of images for 1 person...

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Approach to Problem (3)

• Preprocessing
• Used a 100x100 pixel window around pixel at tip
  of the nose.
• Wrote NosePicker Java app to display images and
  save manually clicked nose coordinates.
• Used Gabor orientations (0, 60, 120) with sine
  and cosine masks 6 functions.
• Calculated the 6 Gabor masks on 99x99, 4 51x51,
  and 16 25x25 pixel subsamples 126.

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Approach to Problem (4)

• Preprocessing
• Sampling windows and orientations...

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Approach to Problem (5)

• Network Setup/Training
• All input vectors were unit normalized, and the
  unit normalized gaussian function was used.
• For each pa face unit network, fixed set of p
  poses were used to center the neurons.
• For each neuron, the nearest p/a unique
  negative input vectors are used to center p/a -
  neurons.

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Approach to Problem (6)

• Network Setup/Training, Cont.
• Setting appropriate widths for and - neurons
  remains a problem.
• Linear output weights are computed by finding the
  pseudoinverse of the matrix of hidden neuron
  outputs for each input, A.
• Since we want Aw d gt w A-1d
• Used singular value decomposition method to
  approximate A-1 since A is singular.

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Approach to Problem (7)

• Network Setup/Training, Cont.
• Advantages are instantaneous training, since
  training is no longer iterative process, unlike
  gradient descent.
• Only need to find pseudoinverse and perform
  matrix vector multiplication to calculate linear
  output weight vector.

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Results

• Currently have tested 36 and 612 networks.
• Selection of neuron widths remains a problem,
  with manual tweaking necessary for good results.
• 36 performs about like a random classifier.

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Results (2)

• 612 network performed better (see below)
• Min correct Min pro Min anti
• 37.8 0 37.2
• Max correct Max pro Max anti
• 95.1 100 98.7
• Avg correct Avg. pro Avg. ant
• 72.6 55.0 73.5

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Results (3)

• Compare with Dr. Howell (see below)
• Avg correct Min pro Min anti
• 89 50 83
• Max pro Max anti
• 100 100
• Better, however Dr. Howell used a more complex
  preprocessing scheme, yielding input vectors of
  510.

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Future Work

• Devise algorithm to choose appropriate neuron
  widths for and - neurons or experiment with
  other radial basis functions that dont need
  widths, such as the thin spline.
• Implement a network of face units, whose output
  will indicate a faces identity instead of just
  an affirmative or negative response.

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Future Work (2)

• Implement a confidence threshold to automatically
  discard low-confidence results.
• Expand Gabor preprocessing scheme to yield more
  coefficients.

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What Code Was Written?

• Wrote C RBFNet class and rbf app to implement
  RBF net with n dimensional input and 1 linear
  output neuron.
• Uses k-means clustering, global first nearest
  neighbor heuristic, and gradient descent.
• Wrote C FaceUnit class and face_net app to
  implement a scalable face unit network.

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What Code Was Written? (2)

• Wrote Java app to display images and save
  manually clicked nose coordinates.
• Wrote C program to perform image sampling and
  Gabor wavelet preprocessing.
• Wrote perl scripts to generate input files. Hope
  to soon have perl script to automatically run
  input files and compile performance results.

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Acknowledgments

• Dr. A. J. Howell, School of Cognitive and
  Computing Sciences, Univ. of Sussex, UK.
• Provided Gabor data and sample face images.
• Dr. Robert Oostenveld, Dept. of Medical Physics
  and Clinical Neurophysiology, University
  Nijmegen, The Netherlands.
• Provided C routine for SVD pseudoinverse
  calculation.

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Acknowledgments (2)

• Numerical Recipies Software, Numerical Recipies
  in C The Art of Scientific Computing.
• Used their published singular value decomposition
  routine in C.
• And last, but not least Prof. Keller
• Invaluable guidance and advice regarding this
  project.