1. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),
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Volume 4, Issue 6, November - December (2013), pp. 121-126
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APPLICATION OF MEDIAN FILTER WITH THE THRESHOLD
TECHNIQUE TO REDUCE AND REMOVE GAUSSIAN NOISE ON THE
IMAGE EDGES PRODUCED BY SOBEL OPERATOR
H.A. Alshamarti1*,
Ali K. Hussein2,
B.A. Almayahi3
1
Department of Physics, College of Science, University of Kufa, Iraq
2
College of Dentistry, University of Kufa, Iraq
3
Department of Environment, College of Science, University of Kufa, Iraq
ABSTRACT
In this paper, a new method to remove Gaussian noise on the image edges produced by Sobel
operator is designed. The mean filter was used in literatures to removes or reduces Gaussian noise,
but this filter is not enough. Therefore, in this work median filter is added with the function of
threshold on the image edges, which it filtered by mean filter for clear the image using MATLAB
software. The comparison between the treatment image edges is conducted using Root Mean Square
Error (RMSE).
Keywords: Gaussian Noise, Sobel Operator, Edge Detection, Threshold Function.
1. INTRODUCTION
The process of image may generate images without quality due to mechanical problems, out
of focus blur, motion, illumination unsuitable, and noises. The different procedures related to the
types of noise are introduced to the image. There are many noises: Gaussian or White, Rayleigh,
Shot or Impulse, periodic, sinusoidal or coherent, uncorrelated, and granular (Gonzalez & Woods
2004). Image processing algorithms tend to perform worse when operating on images with noise.
Therefore, it is necessary to employ processing noise to reduction filters, which it product much of
the original image details (Azzam et al. 2008). This paper aims to removal of the Gaussian noise
presented on the image edges.
1.1. Noise Models
The principal source of noise in digital images arises during the image acquisition
(digitization) and transmission. The performance of image sensors is affected by a variety of factors
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2. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),
ISSN 0976 - 6375(Online), Volume 4, Issue 6, November - December (2013), © IAEME
such as environmental conditions during image acquisition and by the quality of the sensing
elements. In acquiring images with a CCD camera, light levels, and the sensor temperature are major
factors affect the noise in the image (Senthilkumarn & Rajesh 2009).
Removal of noise is important for most of the digital imaging applications (Gonzalez 2004).
Some of the noise removals algorithms are require prior knowledge about the noise in the image. The
standard noise types (Gaussian, speckle, salt, and paper) can be expressed in terms of noise variance
or standard noise deviation (Kutty & Ojha 2012).
1.2. Smooth Image
All in the case of Additive White Gaussian noise (AWGN) and all the image pixels deviate
from their original values following the Gaussian curve. The probability density function (PDF) for a
zero mean Gaussian distribution is (Gajanand 2011):
ܲீ ሺ‫ݖ‬ሻ ൌ
ଵ
√ଶ గ ఙ
݁
ି
ሺ೥షഋሻమ
మ഑మ
(1)
where z= represents gray level, µ= the mean of average value of z, and ߪ= standard deviation. The
standard deviation (ߪ 2)= the variance of z.
For each image pixel with intensity value Iij (1 ≤ i ≤ m, 1 ≤ j ≤ n; for the image (m * n)), the
corresponding pixel of the noisy image Nij is
Nij = Iij + Gij
(2)
where each noise value (G) is drawn from a zero-mean Gaussian distribution.
The main aim of image smoothing is to remove noise in digital images. It is a classical matter
in digital image processing to smooth image. It has been widely used in many fields, such as image
display, image transmission and image analysis,….etc. Image smoothing is a method of improving
the quality of images. Because image smoothing is a classical matter, many filters come into
practice based on the practical requirement and the development of related technology (Keiji 2001).
An averaging filter is useful for removing noise from an image. Because each pixel is set to the
average of the pixels in its neighborhood and local variations caused by grain are reduced (Yong &
Kassam 1985). Median filtering is similar the average filter, except that the value of an output pixel
is determined by the median of the neighborhood pixels, rather than the mean (Chen et al. 1999).
1.3. Mean and Median Filters
The Mean Filter is a linear filter, which it uses a mask over each pixel in the signal. Each of
the components of the pixels, which fall under the mask are averaged together with form a single.
The Mean filter is defined (Padmavathi et al. 2009):
Mean ϐilter ሺ ‫ܫ‬ଵ … … … … ‫ܫ‬ே ሻ ൌ
ଵ
ே
∑ே ‫ܫ‬௜
௜ୀଵ
(3)
where ሺ ‫ܫ‬ଵ … … … … ‫ܫ‬ே ሻ is the image pixel range.
The neighboring pixels are ranked according to brightness (intensity) and the middle value
(median value) becomes the new value for the central pixel. Its can do an good job of rejecting
certain types of noise, in particular, “shot” or impulse noise in which some individual pixels have
extreme values (Ko & Lee 1991).
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3. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),
ISSN 0976 - 6375(Online), Volume 4, Issue 6, November - December (2013), © IAEME
1.4. Edge Detectors Types
Edge detectors can be classified into two broad categories (Senthilkumarn & Rajesh 2009;
Ravi & Khan 2012; Alshamarti 2013):
1. First Derivative Operators
a. Roberts operator
b. Prewitt’s operator
c. Sobel’s operator
2. Second Derivative Operators
a. Laplacian of Gaussian Operator
b. Canny Edge Detector
1.5. Sobel Operator
The kernels can be applied to the input image to produce separately measurements of the
gradient component in each orientation (Sx and Sy). These can be combined to find the absolute
magnitude of the gradient at each point and the orientation of gradient. The masks used to convolute
Sobel operator are:
- - 1 2 1
0 0 0
0 1
1
0 2
2
0 1
1
Column Mask (Sy)
1 2 1
Row Mask (SX)
The Sobel operator is the magnitude of gradient and can be calculated (Maarten 2001):
ଶ
ଶ
M ൌ ඥܵ௫ ൅ ܵ௬
(4)
1.6. Threshold Technique
Threshold processing aims to remove fine fragments mixed with objects. Large lump ores in
original images are often mixed with fine sands and rocks, which have similar illumination reflection
and texture. It makes getting continue boundary of objects with very difficult ordinary edge detection
algorithms. Remove most of fine fragments as background and make edge detection algorithms focus
on objects (Maarten 2001). Threshold is one of the widely methods used for enhancement the image
edge. It is useful in discriminating foreground from the background. Select suitable threshold value
(T) and the image gray-level can be converted to binary image. The first binary image reduces the
complex of data and simplifies the process of recognition and classification. The common way to
convert an image gray-level to a binary image is to select a single threshold value (T). Then all the
gray-level values below T will be black (0) and above T will be white (1) (Salem et al. 2010). In this
paper the all gray level values below T will be classified as black (0) and above T will be white (z).
1.7. Algorithm
The fundamental steps in algorithm application are:
a. The smooth of Image: The application mean filter for primarily reduction of noise Gaussian.
b. Detection of edges: Local operations that select all the possible edges in the image and select the
true edges from the list of the possible edges using Sobel operator.
c. Final enhancement: It uses threshold technique and median filter, where there is a very well
removal of noise.
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4. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),
ISSN 0976 - 6375(Online), Volume 4, Issue 6, November - December (2013), © IAEME
2. RESULTS
The well-known Lenna image was used as shown in Fig. 1, the test image corrupted by
different amount of Gaussian noise and convolution by Sobel operator as shown in Fig. 2. The mean
filter and edge detection are used as shown in Fig. 3. The results of the enhancement image edge
after applying the threshold technique and median filter are shown in Fig. 4.
(a)
(b)
(c)
Figure 1. (a) original test image (b) with sobal operator (c) threshold technique
σ=0.004
σ=0,008
σ=0.012
σ=0.016
σ=0.02
RMSE =44.37 RMSE =58.40 RMSE =68.50 RMSE =77.04 RMSE = 82.36
Figure 2. Lenna images corrupted by different Gaussian noises with edge detection
(Sobal operator 3*3)
RMSE =27.88 RMSE =32.22 RMSE =36.14 RMSE =39.33 RMSE =41.86
Figure 3. Mean filter (Fig. 2) and down images represent edge detection using sobal operator 3*3
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5. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),
ISSN 0976 - 6375(Online), Volume 4, Issue 6, November - December (2013), © IAEME
RMSE =10.83 RMSE =11.75 RMSE =13.15 RMSE =14.82
RMSE =16.26
RMSE =12.94 RMSE =13.306 RMSE =13.81 RMSE =14.55 RMSE =14.89
Figure 4. Removal of Gaussian noise after applying median filter + threshold technique with T= 128
The RMSE for Gaussian noise at σ=0.02:0.004:0.04 as shown in Table 1.
Table 1. Mean square error with Gaussian for varies methods.
Sobel
Sobel and mean
Sobel+mean+threshold
Different noise
operator
filter
(SMT)
RMSE
74.523
35.603
28.563
(σ=0.02)
RMSE
80.269
38.334
30.240
(σ=0.024)
RMSE
84.614
41.035
31.790
(σ=0.028)
RMSE
88.978
42.685
33.021
(σ=0.032)
RMSE
92.390
44.889
34.737
(σ=0.036)
RMSE
94.112
46.355
35.961
(σ=0.04)
Median
(SMT)
28.580
29.240
30.053
30.239
31.282
31.995
3. CONCLUSION
Edge detector method using Sobal operator with mean filter failed to remove noise that has
different Gaussian noise amount for image edge. In this study concluded that the median filter with
threshold technique (threshold value =128) are very well for removal of Gaussian noise from image
edges.
4. ACKNOWLEDGMENT
Financial support was provided by the College of Science, University of Kufa.
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6. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),
ISSN 0976 - 6375(Online), Volume 4, Issue 6, November - December (2013), © IAEME
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