Computational Intelligence - February 2013 - 38

Cluster
1

Phase-One Filtering
Result

Geometric Histograms
yt = (t1 , g ,tN )
1
1
1

Cluster
15

object candidates, where
the non-object patterns are
filtered out in filtering
phase two.
B. Morphological
Operation and Final
Detection Process

f f
1
N
ty15 = (t 15, g ,t 15)

After the EGCD-based
FC-SSCSVM filtering, the
EGCD Values
center locations of the
15
1
H EGCD
H EGCD
f f
reserved object candidates
on all scaled images are
1
15
(H
, g ,H EGCD )
EGCD
rescaled to the original size
for a final object determiFC-SSCSVM
nation. Fig. 7(a) and (b)
Phase-Two Filtering
illustrate the test images
Result
and the distributions of all
of the object-candidate
Figure 6 The geometric distributions of the 15 clustered composing colors of a can and a non-can, ECGDcenters (from all scaled
based FC-SSCSVM filtering process, and the filtering result in phase two.
images) in each of them.
Most true objects are
detected at multiple nearby positions, whereas false alarms
(measuring w 1 # w 2 pixels) is divided into several non-overlapoften occur inconsistently. To find a connected region for each
ping sub-blocks, with each sub-block measuring s # s pixels,
candidate and eliminate some small noise, a morphological
where s is the window shift size defined in Section II-C. There
opening operation with two 5 # 5 dilation operations folare a total of N = (w 1 /s) # (w 2 /s) sub-blocks, where w 1 /s and
lowed by one 3 # 3 erosion operation is applied to the
w 2 /s are selected as integers. Among the Ti pixels belonging to
detected center pixels [29]. Figure 7(c) shows the connected
composing color (cluster) i, the total number of pixels located in
N
regions after the opening operation. The contour of each consub-block k is denoted as t ki , where / k = 1 t ki = Ti . The geonected region is found, based upon which a minimum enclosmetrical histogram yti that measures the geometric color distriing rectangle (MER) of each region is found, as shown in
bution of composing color i is thus given by yti = (t i1, f, t iN ),
Fig. 7(c). If the size of the MER of a region is greater than prei = 1, f, C max . To reduce the feature dimensions, an entropy
defined area i 2, then the MER is determined as an object;
value of this geometric color histogram is then computed. The
entropy value H iEGCD of composing color i is given as follows:
otherwise, it is deleted. This paper sets i 2 to 45 # 45 pixels
which
is the minimum size of the detected objects in the
N
k
k
H iEGCD =- / t i log 2 t i , i = 1, f, C max .
(7)
experiments.
Figure 7(d) shows the final detection result, where
Ti
Ti
k =1
the non-object with a small area is deleted.
The EGCD feature contains C max entropy values H 1EGCD, f,
max
H CEGCD
that encode the geometric distributions of the C max comIV. FC-SSCSVM for Object Filtering
posing colors. These C max values are fed to a classifier to filter
object candidates.This paper proposes the use of an FC-SSCSVM
A. Rules and Functions of FC-SSCSVM
as the classifier, the details of which are introduced in Section IV.
The FC-SSCSVM is composed of fuzzy if-then rules with a
To provide a quick glance at the detection process and the
fuzzy singleton in the consequent. In other words, each rule in
effect of the EGCD feature, Fig. 6 shows the filtering result in
the FC-SSCSVM has the following form:
phase two for the can described in Section II. The upper image
in this figure shows the generated object candidates in phase one.
Rule i : IF x 1 is A i1 And, f , And x n is A in Then yl is a i , (8)
Geometric distributions for each of the fifteen composing colors
of the two object candidates-one is an object and the other is a
where a i is a fuzzy singleton value and A ij is a fuzzy set. Each
non-object-are shown in this figure. These two candidates have
fuzzy set is employed with the following Gaussian membersimilar entropy values H ECC, but they differ in the geometric
ship function:
distributions of the fifteen composing colors. Based on these
(x j - m ij) 2
1,
(9)
M ij (x j) = exp ' geometric color distributions, geometric histograms followed by
2
vi
entropies H iEGCD are found. These fifteen entropies values,
H 1EGCD, f, H 15
where m ij and v i denote the center and width of the fuzzy set,
EGCD, are fed to an FC-SSCSVM for advanced
filtering. The lower image in this figure shows the remaining
respectively.The firing strength n i (xy) is obtained by implementing

IEEE ComputatIonal IntEllIgEnCE magazInE | FEbruary 2013

f f

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