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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
respectively. The eigenvalues can be arranged in a descending
order (Al>A22>..2 Ad »0) with the highest eigenvalues
corresponding to the eigenvectors dimensions that has the
strongest correlation to the original image (Gonzalez et al, 2003).
The eigenvalues that are very small, whose corresponding
eigenvectors give insignificant contribution to represent the face
image samples are ignored. The eigenvectors with the highest
eigenvalues are projected into space and are known are eigenfaces
since these images are like faces. This projection results in a
vector represented by fewer dimensions (d<D) containing
coefficients [a,, ...aq4].
3. WAVELET DECOMPOSITION
Wavelet Transform has been a popular tool for multiresolution
image analysis for the past ten years (Mallat, 1989, Rioul,
1991, Daubechies, 1992, Chen et al, 2003). In this paper
wavelet is used to decompose the original image into wavelet
subbands each with different coefficients. An image, which is a
2D signal is decomposed using the 2D wavelet tree
decomposition algorithm [3].
> : LI
Di Ho[k E
» Hy [k] v Tg ®
>| Hi[k] LH
Original
Image
| >| Ho[k] -(9- HH
H[k] D
HL
—» Hk] 05
Figure 1: Wavelet Decomposition Algorithm
The original image is process along the x and y direction by Ho[k]
and H,[k] filterbank which, is the row representation of the
original image. It is decomposed row-wise for every row using 1D
decomposition algorithm to produce 2 levels of Low (L) and High
(H) components approximation. The term L and H refer to
whether the processing filter is lowpass or highpass. Because of
the downsampling operation that is perform on the L and H image
the resultant matrices are rectangular of size (N x N/2). These
matrices are then transposed and decomposed row-wise again to
obtain four N/2 x N/2 square matrices. The downsampling that is
then performs on these matrices will generate LL, LH, HH, HL
components. Each of these images corresponds to four different
wavelet subband [4]. The LL component (the approximation
function component) decomposed to obtain further details of the
image; the other wavelet component (LH, HH, HL) can also be
decomposed further. In this project the original images was
decomposed until (LLLL, LHLLL, HLLL, HHLL) where the
original image with a size 200X200 was decomposed into an
approximation image of 50X50. Figure 2 shows two wavelet
decomposition to one of training images.
781
Figure 2: Level 2 Wavelet Decomposition
4. FACE DATABASE CREATION
There are two face database used in the simulation. The first
database contains ten training images (frontal face). The Olivetti
and Oracle Research Laboratory (ORL) face database is used in
order to test our method in the presence of head pose variations.
There are ten different images of each of 40 distinct subjects. For
some subjects, the images were taken at different times, varying
lighting, facial expressions (open / closed eyes, smiling / not
smiling), facial details (glasses / no glasses) and head pose
(tilting and rotation up to 20 degrees). All the images were
taken against a dark homogeneous background. Figure 4.3
shows the whole set of 40 individuals 10 images per person
from the ORL database. These images are trained by performing
PCA in wavelet decomposition domain on them and their
eigenfaces are saved in eigenfaces database. The second database
consists of testing images. Each of these images has eight samples
of different face orientation so that the test should involve
matching of the same face with different facial expression and
orientation. The original size of each image is 112x92 pixels.
Figure.3 shows some of 40 individuals 10 images per person from
the ORL database.
5. IMPLEMENTATION AND RESULTS
The proposed algorithm was tested in order to determine the
performance and efficiency of the system. There were two stages
in the process: the first is the training stage, done to obtain
eigenfaces of the database images and second is testing stage,
done to test images of different orientations whether it match with
the database images.
In addition, both stages have three steps:
1. For each image presented above, wavelet decomposition was
performed according to level (level 1, 2 and 4) to reduce the size
of the original image and only the lowband wavelet was taken as
the approximation image.
2. Next, PCA was performed on this approximation image to
obtain its eigenfaces and were then stored in the database as
training images.
3. Eigenfaces of the testing and database images were compared to
find the best match.
System performance was measured in percentage considering the
accuracy of matching images with those in the database. The
accuracy of the system was measured based on the levels of the
wavelet decomposition and the number of eigenfaces that each
image has in the database.
Tables 1 to 3 shows sample of the results obtained. If the face
orientation of each sample image does not differ to much form its
