![](bg6.png)
backgrounds. Figure 11 and Figure 12 show
parts of training and test images respectively. We
selected 10 images for training and 20 images
for test from the MSRC Object Category Im-
age Database v2
1
. Originally these images are
320 × 213 pixels and labeled roughly. In this ex-
periment, we reduced them to 100× 67 pixels and
labeled them precisely.
For comparison, we also applied four compara-
tive methods to the same tasks: the original FORCE,
Support Vector Machine (SVM) (Vapnik, 2000), C4.5
(Quinlan, 1993), and a graph cuts based segmentation
method (GC). GC is a method based on Interactive
Graph Cuts (Boykov and Jolly, 2001) which divide an
image into object and backgroundregionsusing graph
cuts to find globally optimal segmentation. Interac-
tive Graph Cuts use seeds marked pixels as object or
background by a user to provide hard constraints for
segmentation and to compute histogram for object or
background intensity distributions. GC does not use
seeds and computes the histogram from pixel values
of training images.
4.2 Experimental Settings
Input features used in the experiments are shown in
Table 2. The features were standard statistics com-
puted from pixel values in a local window of 5 × 5
pixel size, six FBs, and six rotation invariant pixel
values I
i
computed from neighbor pixel values us-
ing the same template as FBs. For color images, we
used L*a*b* color space, and the input features ex-
cept FBs are computed from each color component.
The “Groups” indicates the groups of input features
allowed to be compared each other in CFORCE. A
condition comparing input features x
1
i
and x
2
i
in dif-
ferent groups is changed to a condition comparing an
input feature x
1
i
and a constant c.
CFORCE and FORCE were tested six times with
different random seed in each experiment using the
following parameters: the number of generations was
10000, the population size was 50, the crossover rate
was 0.7, and the mutation rate was 0.02. Minimal
Generation Gap model [15] was used as a genera-
tion alternation model, and the number of children
was 30. The maximal number of nodes U for each
graph was 60. These parameters are based on the pre-
vious work. SVM and C4.5 were run using WEKA
(Hall et al., 2009). SVM employed RBF kernel,
and γ of the RBF kernel and the complexity parame-
ter C were selected from {2
n
|n = −7, −6, .., 1, 2} and
{2
n
|n = −2, −1, .., 6, 7} respectively by grid search in
1
http://research.microsoft.com/en-
us/projects/ObjectClassRecognition/
Table 2: Input features used in this work.
Groups Features
0 Max, Min, Mean, Median,
First quartile, Third quartile,
Six rotation invariant pixel values: I
i
1 Standard deviation
2 Range
3 Averaged edge magnitude
4 Skewness
5 Kurtosis
6 Six feedback features: FB
i
each task. The minNumObj and confidenceFactor
of C4.5 were also selected from {0, 1, 2, 3, 4, 5} and
{0.1, 0.2, 0.3, 0.4, 0.5} respectively by grid search.
For GC, we selected BIN# of histogram from
{16, 32, 64, 128, 256}, σ of boundarypenalty function
from {0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5} and λ a pa-
rameter for edge weights from {1, 2, 4, 8, 16, 32, 64}
to maximize F-measure for training images in each
task.
4.3 Results and Discussion
Accuracy results (F-measure) of the experiments are
summarized in Table 3. The values in parentheses
of FORCE and CFORCE are averaged results over
six runs, and the other values of them are results of
the elitist rules obtained in training. SVM and C4.5
processed the training images better than CFORCE in
coin and human extraction, but for the test images, the
elitist rules of CFORCE showed the most accurate re-
sults in all experiments. That is, CFORCE prevented
rules from overfitting the training images better than
SVM and C4.5. GC showed better results for the test
images in the coin and human extraction than SVM,
C4.5 and FORCE, although it hardly processed crack
extraction because the histogram based on gray level
is too simple to represent differences between cracks
and background.
The result images processed by each method are
shown in Figure 7-12. The feature of processing by
CFORCE is that extracted regions tend to be united
with little noises (small misclassified regions), al-
though boundaries between regions are likely impre-
cise a little. We consider this feature is caused by
FBs because results of FORCE without FBs do not
show such features, and some results of GC consid-
ering relationship between pixels have similarity to
those of CFORCE. SVM and C4.5 produced good
results with precise boundaries for the training im-
ages, but the test results of them have more noises
than those of CFORCE. Figure 13 illustrates an exam-
EvolutionaryFuzzyRuleConstructionforIterativeObjectSegmentation
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