![](bg3.png)
where Th represents a threshold value.
In ε-filter, ε is an essential parameter to reduce the
noise appropriately. If ε is set to an excessively large
value, the ε-filter becomes the same as linear filter.
On the other hand, if ε is set to 0, it does nothing to
reduce the noise anymore, that is, the filter output be-
comes the input image itself. Hence, SQF is a subset
of SQEF. When we take into account the design of
SQF, numerator in Eq.4 should become similar to the
original image, while denominator in Eq.4 should be-
come an smoothed image.
By setting ε adequately, we can effectively reduce
small amplitude noise while preserving shape and tex-
ture information. Hence, the optimized ε value is uti-
lized as numerator in Eq.4. It should be noted that the
optimized ε can be obtained automatically by using
signal-noise decorrelation criterion (Matsumoto and
Hashimoto, 2009). On the other hand, a sufficient
large ε should be used as the denominator in Eq.4 to
emphasize the feature of the image.
When we apply SQEF to impulse noise corrupted
image, it is considered that both ε-filters in SQEF
keep the impulse noise in the image unlike when two
smoothed filters are employed. Hence, when one fil-
ter output in SQEF is divided by the other filter in
SQEF, the impulse noise effect is reduced by the self-
quotient effects.
3 EXPERIMENTS
To evaluate the filter characteristics of SQEF, we con-
ducted the evaluation experiments using various types
of facial images. Some facial images are selected
from Yale image database (Georghiades et al., 2001)
and facial parts are cut from them. The image size is
256 pixels × 256 pixels. We added 10%, 20% and
30% impulse noise to images, respectively. Through-
out the experiments, the filter coefficient a
i
is set to
1/(2K + 1)
2
to make it uniform weight. To test the
robustness of the the proposed method concerning the
window size, the window size was changed from 3 ×
3 to 9 × 9. We show the results when the window size
was set to 5 × 5 as examples. Similar results could be
obtained throughout all the experiments regardless of
the window size.
Figures 2, 3, and 4 show the experimental results
when we used the image with impulse noise whose
percentage was 10%, 20% and 30%, respectively.
Figures 2(a), 3(a) and 4(a) show the original image
for comparison.
Figs.2(b), 3(b) and 4(b) show the input image with
impulse noise whose percentage is 10%, 20% and
30%, respectively. Figs. 2(c), 3(c), and 4(c) show the
(a) Original image (b) Image with 10% im-
pulse noise.
(c) Filter outputs when
SQF was used.
(d) Filter outputs when
SQEF was used.
Figure 2: Experimental results when 10% impulse noise is
added.
(a) Original image (b) Image with 20% im-
pulse noise.
(c) Filter outputs when
SQF was used.
(d) Filter outputs when
SQEF was used.
Figure 3: Experimental results when 20% impulse noise is
added.
filter outputs of SQF when we used the input image
with noise whose percentage is 10%, 20% and 30%,
respectively. Figs. 2(d), 3(d), and 4(d) show the fil-
ter outputs of SQEF when we used the input image
with noise whose percentage is 10%, 20% and 30%,
respectively. As shown in Figs.2, 3 and 4, SQEF can
extract the shape and texture information with reduc-
ing the noise, while SQF can not extract the feature
clearly.
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