Computational Intelligence - August 2012 - 31

The noisy test images used in the experiA pixel in a color image may be considered as a
ments are obtained by contaminating a given
test image with an impulse noise of given
point in the three dimensional R-G-B color space.
noise density. Three different noise densities
The contamination of this pixel by noise implies a
are considered. These are 25%, 50% and 75%
change in at least one of the three color components
representing the low, medium and high noise
densities, respectively.
(red, green, or blue) of this pixel, which corresponds
The performance enhancements obtained
to a shift of the location of the point that represents
by using the proposed impulse detector with
this pixel in the R-G-B color space. Hence, the filtering
a noise filter is evaluated by using it with
four representative impulse noise filters from
operation performed on this pixel by a noise filter
the literature. These are the standard median
may be thought of as an attempt to move the point
filter (SMF) [1], the edge-detecting median filter
representing this pixel back to its original location in
(EDMF) [6], the minimum-maximum exclusive
mean filter (MMEMF) [16] and the alphathe R-G-B color space.
trimmed mean-based filter (ATMBF) [17]. All
of  these impulse noise filters operate on a
original and the restored versions of a corrupted color test
minimal filtering window, which has a size of 3-by-3 pixels.
image respectively.
The improvement contributed by the proposed detector
Here s [l, c], y [l, c] is the vectorial (Euclidian) distance
to the performance of the noise filter is measured by using
between two points in the R-G-B color space defined as
the mean squared error (MSE) criterion, which is defined as
MSE = 1
LC

C

L

/ / ^s [l, c] - y [l, c]h2 ,

(9)

s [l, c], y [l, c] =

l=1 c=1

where s [l, c] and y [l, c] represent the luminance value of the
pixel at line l and column c of one of the three color bands of
the original and the restored versions of a corrupted test
image respectively.
It should be noted that this definition of MSE is valid for
gray level images only. Since the test images used in the filtering experiments reported in this section are color images, this
MSE computation is performed for three times, one for each
of the three color bands (red, green and blue), and the three
resulting MSE values are then averaged to obtain the representative MSE value for that image.
From a different point of view, a pixel in a color image may
be considered as a point in the three dimensional R-G-B color
space. The contamination of this pixel by noise implies a
change in at least one of the three color components (red,
green or blue) of this pixel, which corresponds to a shift of the
location of the point that represents this pixel in the R-G-B
color space. Hence, the filtering operation performed on this
pixel by a noise filter may be thought of as an attempt to move
the point representing this pixel back to its original location in
the R-G-B color space.
Based on these observations, we introduce a novel criterion
termed as the mean pixel distance as an alternative performance
measure that is better suited to color images. The MPD criterion can mathematically be defined as follows:
MPD = 1
LC

L

/

^s i [l, c] - yi [l, c] h2 .

(11)

i ! {R, G, B}

To the best of our knowledge, the MPD criterion described
above has not been proposed before.
Each individual filtering experiment represents a combination of a noise filter, a test image and a noise density. Hence, a
total of 48 individual filtering experiments are performed since
there are four different noise filters, four different test images
and three different noise densities included in the experiments.

(a)

(b)

(c)

(d)

C

//

s [l, c], y [l, c] ,

(10)

l=1 c=1

where s [l, c] and y [l, c] are vectorial quantities in the R-G-B
color space (i.e., s [l, c] = {s R [l, c], s G [l, c], s B [l, c]} ) and represent the color value of the pixel at line l and column c of the

FIGURE 6 The test images used in the experiments: (a) Baboon,
(b) House, (c) Lena, and (d) Peppers.

AUGUST 2012 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

31



Table of Contents for the Digital Edition of Computational Intelligence - August 2012

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