In using line scan camera to acquire the cotton fiber image, it is often to produce stripe noises, which affects the
extraction and recognition of the foreign fiber . Today there are many methods to remove the stripe noises.
The traditional method of denoising can be divided into the frequency domain and the spatial domain. Fre-
quency domain denoising depends that the noise frequency is different larger with the image frequency, and
therefore with the noise of the image is converted from the spatial domain to the frequency domain, to change
the transforming coefficient of the noise, as far as possible to retain the transforming coefficients of the image
information, and then inversing transform image to reducing image noises. But the denoising process tends to
lose the part detail information of the image, resulting in blurred images. Commonly used methods are Wavelet
transform  and Fourier transform . Spatial denoising is mainly through calculating the image gray values, and
using the normal pixel gray value as a reference to correct the noise pixel gray value, so as to reduce the influence
of noise pixels. Typical methods are median filter , histogram equalization   and the moment matching .
Using rough set theory  in multi threshold image segmentation has a good effect. If using statistical color
replacement the color of segmentation region, it will realize the target image denoising. The distribution and in-
tensity of stripe noise in the cotton fiber image is not uniform, in order to ensure the clarity of the image, the
multi threshold segmentation of rough set is used to remove the noise.
Since 1982 Poland scholar Z. Pawlak proposed the rough set theory, it has been a hot research topic in the field
of artificial intelligence, and has been widely applied machine learning, data mining, process control and image
Definition 1: information systems can be represented as a four tuple, the formalized definition is:
in which U: finite set of objects;
: finite set off properties; :
V is p attribute domain;
UA V is general function, makes
for each ,
U is a subset of individuals on the global, PA. The lower approximation and the
upper approximation of the X are respectively
PX is the confirmed largest defined set contained within the X, PX is the smallest defined set contained
Therefore, the boundary region can’t be clearly defined as:
BndXPX PX (3)
The larger the boundary area is, the more the set X can’t express. The uncertainty of the set X can be ex-
pressed by the roughness of rough sets, the formula is as follows:
is [0, 1], the greater the value is, the more uncertainty the set X is.
The core idea of rough set denoising is that the color of a segmentation region can be replaced by a same color,
so as to achieve the purpose of noise removal. Therefore, how to determine the region is a core problem. The li-
near scanning image of the cotton fiber is a color image, and the information contained in the RGB color image
is often more than the gray image, and it is more consistent with the human visual sense. If only gray level his-
togram is used to distinguish different gray areas, the approximate relationship between pixels in color image
cannot be reflected.
The histogram can be used to express the number of pixels in each gray level, so the basic histogram can be
used as the lower approximation of the region. The histon histogram considered the color difference between the
pixels in the neighborhood, and the uncertain information is described. So the histon histogram is used as the
Let f for a RGB color image of M × N, which is decomposed into fr, fg and fb in R, G, B three color channels.
The basic histogram and histon histogram are defined respectively:
Definition 3: basic histogram
The σ is an impulse function; the value L is 256, representing the number of gray level of images; fi repre-
sents a gray image; (,, )
mn f is the gray value of pixel (,)
Definition 4: histon histogram
mn is a matrix of M × N, which indicates that the difference of the neighborhood pixel color, can be
obtained by the following Equation (7):
Xmn oth er
where (,)Dmn represents the distance sum of between each pixel and the center pixel point in the neighbor-
hood, and exp represents a threshold constant.
The process of removal of the stripe noise using rough sets is shown in Figure 1. Since the histogram is cal-
culated by the gray scale, it is necessary to decompose the RGB image from R, G and B three channels respec-
Roughness calculation: the calculating the basic image histogram and histon histogram, then get the rough-
ness images by Equation (4).
Bands calculation: due to many bands in the original image, in order to remove the noise information and
need to unite the less different band. Firstly, the position vector and the number N of all the peaks in the image
are obtained according to the roughness, Height threshold Th of the peaks can be calculate by Equation (8):
Which Mp is mean of the maximum and minimum peak value, Pi is the peak point. The experimental results
show that the best of the width threshold Tw of the peak is 10. Then the peaks of less than Th are abandoned,
and the width of the peaks of less than Tw is united.
The minimum value between two peaks is the valley value, the gray level between the two valleys is a band.
Band’s colors calculation: a band using a replace gray color, the color of band [k1, k2] can be calculated by
The h(i) is the number of pixels in the gray level i of the basic histogram, SH is the sum of the number of pix-
els between [k1, k2], can be calculate by the Equation (10):
A new composed gray color can be used to represent the color of the band.
In the R, G and B channels, the band information and band colors are calculated respectively, the color of
each band is replaced by the calculating the gray color, and then to synthesize a RGB color image.
Figure 1. Rough set denoising process.
Experimental picture is the image obtained from the color line scan camera. The key of rough set denosing is to
determine the boundary of the color region, namely, the difference between the upper approximate histon his to
gram H(g) and the lower approximate basic histogram h(g), so as to determine the roughness of the image. If the
difference between the upper approximation and the lower approximation is obtained, that is the edge of the re-
gion, the roughness of the image can be calculated. Taking into account the image edge is the biggest difference
between the images, the use of edge operator and the direction of the image should be able to get the approxi-
mate effect, so compared respectively with the three methods of denoising effect.
Method 1: directional diagram. f(m, n) using the Equation (11) to calculate the distance between this point and
f(m − 1, n − 1) for the image f of
ColorDisabsfm nfmn (11)
and 1,1;mM nN
Method 2: using canny operator.
Method 3: using Sobel operator.
The experimental results are as follows:
Figure 2 is a cotton color image with a foreign fiber, among Figures 3-5, the (a) and (b) is the edge
difference image and the denoising image by using the directional diagram, Canny operator and Sobel operator
respectively. The experimental results show that the three methods do well in the strip noise removal. Compared
with directional diagram and Sobel operator method, Canny operator method for denoising retains more image
details, but some noise was also retained, so the denoising effects of the other two methods are better than its.
These three methods can enhance the distinction between foreign fiber and others in the image. The rough set
denosing not only realizes the removal of stripe noise, but also realizes the enhancement of the extraction region.
It can provide higher quality image for the next step of image segmentation, and is helpful to the extraction and
recognition of foreign fiber.
Figure 2. Color image of cotton.
Figure 3. Directional diagram method.
Figure 4. Canny operator method.
Figure 5. Sobel operator method.
The basic histogram and his ton histogram of the RGB color image is used as the lower approximation and the
upper approximation of the image, and the roughness of the image is obtained by them. The image is divided
into regions according to the roughness, and replaced the original color with statistical color within the region.
The experimental results show that the rough set algorithm can achieve the removal of stripe noise very well. In
the edge calculation of the image, the influences of the three methods are compared. Canny operator method has
retained the more details, and the results of the direction and Sobel operator method are much better. The for-
eign fiber region is enhanced, which makes the foreground and background more obvious, and provides a high
quality image for the following image segmentation.
The authors thank Hebei Natural Science Foundation (F2015201033), The Ministry of Science and Technology
of the People’s Republic of China (2013DFA11320), for their financial support.
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