Transcript Face Recognition Using Face Unit Radial Basis Function Networks

Face Recognition Using
Face Unit Radial Basis
Function Networks
Ben S. Feinstein
Harvey Mudd College
December 1999
Original Project Proposal
• Try to reproduce published results for RBF
neural nets performing face-recognition.
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.
Recap of RBF Networks (2)
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.
Face Unit Architecture (2)
• An p+a 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?
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.
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.
Approach to Problem (2)
• Example of images for 1 person...
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|.
Approach to Problem (4)
• Preprocessing
– Sampling windows and orientations...
Approach to Problem (5)
• Network Setup/Training
– All input vectors were unit normalized, and the
unit normalized gaussian function was used.
– For each p+a 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.
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 => w = A-1d
• Used singular value decomposition method to
approximate A-1 since A is singular.
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.
Results
• Currently have tested 3+6 and 6+12
networks.
• Selection of neuron widths remains a
problem, with manual tweaking necessary
for good results.
• 3+6 performs about like a random classifier.
Results (2)
• 6+12 network performed better (see below)
–
–
–
–
–
–
Min correct
37.8%
Max correct
95.1%
Avg correct
72.6%
Min pro
0
Max pro
100%
Avg. pro
55.0%
Min anti
37.2%
Max anti
98.7%
Avg. ant
73.5%
Results (3)
• Compare with Dr. Howell (see below)
– Avg correct
– 89%
–
–
Min pro
50%
Max pro
100%
Min anti
83
Max anti
100%
• Better, however Dr. Howell used a more
complex preprocessing scheme, yielding
input vectors of |510|.
Future Work
• Devise algorithm to choose appropriate
neuron widths for + and - neurons or
experiment with other radial basis functions
that don’t need widths, such as the thin
spline.
• Implement a network of face units, whose
output will indicate a face’s identity instead
of just an affirmative or negative response.
Future Work (2)
• Implement a confidence threshold to
automatically discard low-confidence
results.
• Expand Gabor preprocessing scheme to
yield more coefficients.
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.
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.
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.
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.