![](bg2.png)
truth by a specialist. In general, evaluation with only
3 images is not sufficient. However, in a Wnt-3a
image, many light spots are included as shown in
Figure 4. Thus, we consider that the evaluation is
sufficient. The accuracy of our method achieves
85.28%. This is much better than ImageJ
(
http://rsbweb.nih.gov/ij/) which is used in cell
biology.
Section 2 explains the light spots detection by
robust statistics (Huber, 1981). In section 3,
experimental results one shown. Conclusions and
future works are described in section 4.
2 LIGHT SPOT DETECTION AND
NOISE REDUCTION
First, we estimate a background image from only an
input image, and we perform background subtraction
to emphasize the Wnt-3a. The Wnt-3a is detected
from the difference image by using the robust
statistics. However, since there are many noises
which are similar to Wnt-3a, noises are also detected
as Wnt-3a. Thus, it is difficult to detect the light
spots by only one step and by Otsu's binarized
method after candidates of light spots are detected
by background subtraction.
In the following sections, we explain the details
of our method.
2.1 Background Estimation
It is the best that we prepare the background image
without foreground in advance. However, in Wnt-3a
images, the background regions are also changed
and we can not prepare the background image in
advance. We can not use the sequential information
too. Therefore, we make a background image from
only one test image by median filter. In experiments,
we apply a median filter with the size of 9 x 9 to the
test image to estimate the background.
Foreground such as light spots are emphasized
by subtracting the estimated background image from
the test image. To classify the foreground and
background, good threshold value is required.
However, adequate threshold value is changed for
every image. Therefore, the threshold is determined
by Least Median of Squares (LMedS) which is one
of robust statistics. Since the area of background is
larger than that of foreground, the inlier becomes
background and outlier becomes foreground.
2.2 Light Spot Detection using Robust
Statistics
We use LMedS (Rousseeuw, 1984) to classify
foreground and background. LMedS is more robust
to outlier than least squares. In LMedS, the
estimation result does not so change if the ratio of
outlier is below 50 percents.
Next, we describe how to use LMedS criteria.
We calculate difference image between test image
and the estimated background image. Next, we
calculate the median d
medd
in the
difference image. The standard deviation of error
distribution is computed by using the median as
σ
1.48261
5
M1
d
,
(1)
where M is number of pixels in the image, and
1.4826 is a coefficient which error distribution
normal distribution is in accordance with normal
distribution. 5/(M-1) is a correction term for small
number samples. We determined outlier (light spot
candidates) as d
2.5σ.
2.3 Noise Reduction
There are a lot of noises in images of Wnt-3a. Since
only background subtraction can not classify noises
and light spots, we distinguish the noises and light
spots by Otsu’s binarized method (Otsu, 1979) after
LMedS. However, there are noises with higher
intensity than light spot. Therefore, if we use Otsu’s
binarized method instead of LMedS, light spots are
not detected well. Since there are small light spots
with 1 pixel. We can not use the morphological
operation. To classify noise and Wnt-3a, we pay
attention to the neighboring intensities because noise
is always the spike and the intensities of neighboring
region is not large. Figure 1 shows the noise and
light spot. Figure shows the neighboring pixels of
noise have low intensity. Therefore, we compute
average intensity of a local 3 x 3 region whose
center is the point detected by background
subtraction. The average intensities in 3 x 3 pixels
are fed into Otsu's binarized method, and we detect
light spots with unsupervised manner.
Figure 1: Comparison between around noise and light spot.
(a) noise. (b) light spot.
(a) (b)
UnsupervisedLightSpotDetectionusingBackgroundSubtraction
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