| [+OVERVIEW+] |
| While it is a relatively
simple matter to either identify a human face or
classify between different ones, it would be very
interesting to see if we could use wavelet transforms
to achieve better and more robust results. One of
most characteristics of wavelet transforms is their
ability to represent a signal into partitions of
time-frequency plane. The popular representation
of wavelet transforms is a multi-resolution wavelet
tree where the each sub space contains information
in a time-frequency domain. Therefore, we want to
design figures of merit to take advantage of those
wavelet spaces to end up with different pruned trees.
The main motivation is to try to design a tree that
is optimal for verification and one which is good
for classification of face images. Their performance
at verification and classification will then be measured
using the figures of merit, and the strategies will
be refined based on the results. In the end, we will
come up with a combined tree that is able to perform
well at both verification and classification.
|
| [+BIOMETRICS+] |
|
| [+WAVELET
TRANSFORMATIONS+] |
Wavelet
transformations are a method of representing signals
across space and frequency. The signal is divided
across several layers of division in space and frequency
and then analyzed. The goal is to determine which
space/frequency bands contain the most information
about an image's unique features, both the parts
that define an image as a particular type (fingerprint,
face, etc.) and those parts which aid in classification
between different images of the same type.
One type of discrete wavelet transform (DWT) is
the orthogonal DWT. The orthogonal DWT projects an
image onto a set of orthogonal column vectors to
break the image down into coarse and fine features. |
 |
 |
| A
typical two-level full wavelet decomposition is shown
above. Each of the subspaces is obtained by taking
the original input and filtering it with a combination
of high-pass and low-pass filters, designed to maximize
the amount of information obtained within each subspace.
This decomposition can be repeated for n-levels. The
image can later be reconstructed from these subspaces.
By removing subspaces that contain comparatively low
amounts of information from a reconstruction, we can
achieve an image that is nearly as good as the original
but takes less space to store. This can be useful if
we are storing a large number of similar images. |
| [+CORRELATION
FILTERS+] |
| There
are many different classifiers out there that have
proved to be very effective in classifying faces.
We will be using advanced correlation filters, specifically
the Minimum Average Correlation Energy filter (MACE).
Correlation filter techniques are attractive candidates
for the matching needed in face verification. Correlation
filters can be used on any biometrics as long as
they are in the form of images. Advanced correlation
filters can offer a very good matching performance
in the presence of variability such as facial expression
and illumination changes. Furthermore, they are of
less complexity and are shift invariant. |
 |
A correlation
filter takes an image and has a very tall and thin
peak at the origin when the image matches. A correlation
filter could also be used on an image subspace and
this is done when using wavelet decompositions. If
the image does not match, the peak is much shorter
and wider.
|
| [+EXPERIMENT+] |
 |
Expression database: Joy
20 classes, 20 faces each
This is an example of the dataset that has been
used for the purpose of this experiment. The
faces available are part of the same class (same
individual) but with facial deformation, from
a neutral position to a peak deformation position. |
|
| The procedure
I'm going to use to test the effectivenes of wavelet
domain correlation filters is described as follows. |
 |
| The
figure of merit is based on the fact that
we are trying to optimize the tree for classification.
Intuitively, by measuring the false positive rate
that a given correlation filter yields, we can
define a measure of performance. A false positive
is recorded whenever, a test image is said to belong
to a class other than its real class. Therefore,
for a given space and its corresponding correlation
filter, the PCE value of all the classes other
than the class it belongs to, are computed and
used as a measuere of effectiveness of that wavelet
correlation filter. |
|
Each correlation filter is tested against trainimages
of
classes other than itself |
|
| [+EXPERIMENTAL
RESULTS+] |
 |
 |
For verification
evaluation of our method, a receiver operating characteristics
(ROC) curve has been plotted to show the probabilities
of authentic versus the probabilities of impostors.
From the following graph, it is clear that our optimized
tree achieved better results (blue line) than the
control test (red line). The probability of having
an authentic verification with zero probability of
having an impostor is about 83% for wavelet-domain
method and 67% for the standard filters.
As for classification
results, the error rates have been plotted for every
single class as shown in figure 5. There is a clear
reduction in classification error rate for the wavelet-domain
filters (red) compared to the standard correlation
filters. For class 4 where the error rate for the control test reaches 70%, it
is still hard for even the wavelet-domain filters to classify efficiently, even
though they yielded a better rate of 65%. However, for classes like 13 and 17
where the standard method had error in the order of 35% and 10% respectively,
the wavelet-domain method achieves a zero error rate. For the overall classification
rate, our wavelet-domain method yields 94.2% accuracy while the standard method
achieves 90%. |
| [+CONCLUSIONS+] |
| We have
discussed the basic elements of biometrics and wavelet
transforms, and how correlation filters may be used
to classify images within a biometric system. We
explored the advantage of using wavelet packet decomposition
for verification and classification and determined
how to best use our figures of merit to obtain an
optimal wavelet decomposition tree. The combined
wavelet tree performed better than the standard correlation
filters applied only in the image-intensity domain.
The results show that face images have some features
that remain more consistent in the wavelet sub spaces
than in the spatial domain. Future work may involve
designing different figure of merits that will be
tailored to specific datasets. |
Find the paper
to download below.
Paper |
