New method for feature extraction based on fractal behavior - IDRBT

Y.Y. Tang et al. / Pattern Recognition 35 (2002) 1071–1081 1079
Fig. 5. Examples of signatures: (a) Six examples of A person’s signature, (b) Six examples of another B person’s signature.
(b) b 1 (x; y) is computedaccording to Eq. (8), i.e.
b 1 (x; y)
{
}
= min b 0 (x; y) − 1; min b 0 (i; j) ;
|(i;j)−(x;y)|61
(c) The volume Vol 1 of the blanket is computed
by Eq. (9), i.e.
Vol 1 = ∑ (u 1 (x; y) − b 1 (x; y));
x;y
Substep 3. Taking = 2 ,
(a) u 2 (x; y) is computedaccording to
u 2 (x; y)
{
= max u 1 (x; y)+1; max
|(i;j)−(x;y)|61
|(i;j)−(x;y)|61
}
u 1 (i; j) ;
(b) b 2 (x; y) is computedaccording to
b 2 (x; y)
{
}
= min b 1 (x; y)−1; min b 1 (i; j) ;
(c) The volume Vol 1 of the blanket is computed
by
Vol 2 = ∑ (u 2 (x; y) − b 2 (x; y));
x;y
Step 3. The sub fractal signature A k
Eq. (10), namely
A k = Vol 2
− Vol 1
:
2
is computedby
where k is a constant, andit is calledthe scale
of fractal signature.
Step 4. Combining sub fractal signatures A k , k =1; 2;
:::;n, into the whole fractal signature:
n⋃
A = A k ;
k=1
we can obtain the results of classication of two dierent
handwritten signatures from the fractal signature trend in
Fig. 6. We can see that the fractal signatures of the two
dierent handwritten signatures are clearly dierentiated
while the scale k¿4. In our experiments, 20 persons’
signatures were trainedandtested. These people’s signatures
are embodied six modes. Using this multiple-model,
the technique can oer better classication results. The
experimental results indicate that this <strong>method</strong> is eective
andreliable.
4. Conclusions
Pattern recognition requires the <strong>extraction</strong> of <strong>feature</strong>s
from regions of the image, andthe processing of these
<strong>feature</strong>s with a pattern recognition algorithm. In this
work, we presentedthe results which aimedat showing
that, within the eldof image analysis, it is possible to use
fractal <strong>feature</strong> <strong>based</strong>on the estimating fractal dimension
to extract in<strong>for</strong>mation that is relevant in object recognition
tasks. The motivation behindusing fractal trans<strong>for</strong>mation
is to develop a high-speed <strong>feature</strong> <strong>extraction</strong>
technique. A multiresolution family of the wavelets
is also usedto compute in<strong>for</strong>mation conserving
micro-<strong>feature</strong>s. Along the way, we have shown that