Restoration of Color Image Corrupted by
Gaussian Noise
J.Harikiran1, R.UshaRani2, Prof P.V.Lakshmi3, Reddi Kiran Kumar4
1,2,3 Department of Information Technology ,GIT, GITAM University, Vizag 4Assistant Professor, Department of Computer Science, Krishna University, Machilipatnam
Abstract:
A new approach to the restoration of color images corrupted by Gaussian noise is presented. The proposed technique is based on a simple non-linear algorithm for detail preserving smoothing of noisy data whose filtering behavior depends on only one parameter. The parameter is estimated by a new step-by-step procedure that takes into consideration the progressive mean square error (∆MSE) between subsequent pairs of processed images. This method does not require any “a priori” knowledge about the amount of noise corruption. In-order to better appraise the noise cancellation behavior of our filter from the point of view of human perception we perform edge detection using canny filter. Experimental results show that the filtering performance of the proposed approach is very satisfactory.
Keywords: Gaussian noise, image enhancement, nonlinear filter, image restoration, image processing Section I: Introduction
Image noise is the random variation of brightness or color information in images produced by the sensor and circuitry of a scanner or digital camera. The development of techniques for noise removal is of paramount importance for image-based measurement systems [1]. In-order to smooth out from noise many filtering architectures have been proposed in the literature [2]. The goal of the filtering action is to cancel noise while preserving the integrity of edge and detail information, non linear approaches [3] generally provide more satisfactory results than linear techniques. However, a common drawback of the practical use of these methods is the fact that they usually require some “a priori” knowledge about the amount of noise corruption. Unfortunately such information is not available in real time applications.
In this paper, a new approach to estimation and filtering of Gaussian noise in color images is presented. The color image is processed by first converting it from RGB to YIQ domain. Then, the filter is applied only to the chrominance (I and Q) component of YIQ domain and the filtered image is converted from YIQ into RGB domain. The filtering behavior of the proposed nonlinear algorithm depends on one parameter p only. An estimate of the optimal parameter value can be obtained without any “a priori” information about the variance of Gaussian noise. The images generated by our method have been obtained without taking into account the original uncorrupted data, in order to simulate a real application where only noise data is available. This is the key advantage of the proposed method. This paper is organized as follows. Section II presents conversion of color image from RGB to YIQ domain. Section III presents new filtering architecture. Section IV presents the method for parameter estimation, Section V discusses the experimental results and finally Section VI reports conclusions.
Section II: Conversion from RGB to YIQ domain:
leaving the luminance component. In our work, the YIQ system is used to process color image. The conversion from RGB to YIQ and YIQ to RGB is given as follow:
Y 0.299 0.587 0.114 R I = 0.596 -0.274 -0.322 G Q 0.211 -0.523 0.312 B
Figure: 1 Conversion from RGB to YIQ
R 1 0.9563 0.6210 Y G = 1 -0.2721 -0.6474 I B 1 -1.1070 1.7046 Q
Figure: 2 Conversion from YIQ to RGB
Section III: Proposed filter.
The filter, we are using in our approach is called “zed filter” [7]. Let us suppose we deal with digitized images having L levels (color images). Let x(n) be the pixel luminance at location n=[n1,n2] in the noisy image. Let x1(n),
x2(n) ……, xN(n) be the group of N=8 neighboring pixels that belong to a 3X3 window around x(n) shown in figure
3. The output y(n) of the filter is defined by the following relationship : y(n) = x(n) +
N
1
Ni1
(
xi(n), x(n)) (1)Where
u – v |u – v|
p
(u,v)= 2| |
3p uv sgm(u-v) p<|u-v|
3p0 |u-v|>3p
(2)
and p is an integer ( 0<p<L). The filtering mechanism takes into account the pixel luminances in the neighborhood. According to (2), this mechanism aims at gradually excluding pixel values that are very different from the central element, in order to avoid blurring the image details during noise removal.
Figure 3: 3X3 Window
The conditions in (2) can be described as follows:
1. Let the luminance of the neighbours be very close to the value of the central pixel, then |xi(n)–x(n)|
p i=1,2,…,N (3) In this case,y(n) =
N
1
N
i 1
xi(n) (5)
2. Let the luminance of the neighboring values be very different from the central element, then |xi(n)–x(n)|>3p i=1,2,…,N (6)
In this case
(xi(n),x(n)) = 0 (7) The zed filter behaves as the identity filter, thus performing the maximum detail preservation. y(n)=x(n) (8)3. In the last case, the luminance of a neighboring pixel is not very close to the value of the central pixel, and not very far from this value, according to the following expression:
p<|xi(n)–x(n)|
3p i=1,2,…,N (9)
In this case, (2) can gradually reduce the importance of such neighboring pixels, as the luminance difference |xi(n)–
x(n)| becomes large. The filter behavior depends on the value of parameter p only. Large values produce a strong smoothing action. Small values, on the contrary, better preserve fine details and textures. The optimal choice of p depends on the amount of noise corruption in the input image and represents the value that would yield the minimum mean square error (MSE) between the filtered image and the original noise-free data.
Section IV: Method for parameter (p) estimation [7]:
The method for estimating the optimal parameter value is done, when only noisy data are available and the amount of noise corruption is unknown. Our method takes the progressive mean square error (∆MSE) between subsequent pairs of processed images. Let y(k)(n) represent the output of the filter when p=k. The progressive mean
square error (∆MSE) between the noisy filtered with p=k and the same image filtered with p=k-1 is defined as follows
∆MSE= (
M
1
)
F n
(y(k)(n) – y(k-1)(n))2 (10)
Where F denotes the set of M processed pixels. The procedure operates as follows:
1. A color image corrupted by Gaussian noise with unknown variance is assumed as input data.
2. Convert the color image to YIQ domain using Fig 1 and apply the below steps (3) - (8) to I and Q (color) components of the image separately leaving luminance Y component shown in figure 4.
3. By varying the value of parameter p from a minimum (p=2) to a maximum (p=L/4), a collection of filtered images is obtained. At each step (p=k), the ∆MSE(k) is evaluated. Let k1 be the value that corresponding to
the maximum ∆MSE(k1) = MAX{∆MSE(k)}.
4. A heuristic estimate of the optimal value of parameter p is given by: p1=2(k1-2). Thus the input
data are processed by setting p = p 1.
5. The resulting image is assumed as input data in order to (possibly) perform a second filtering action. 6. Again, by varying the value of parameter p, a collection of filtered images is obtained. Let k2 be the value
that corresponding to the maximum.
∆MSE(k2)=MAX{∆MSE(k)}.
7. If k2< k1 proceed to the next step, otherwise stop the procedure and consider the previous resulting image
as the output data.
8. A second pass filtering is performed by choosing p = p 2=2(k2-2).
9. The result represents the output image in I and Q components. 10. Convert the output image in YIQ to RGB domain using figure 2.
Figure 4: Transformation in YIQ color systems
Section V: Experimental Results
This section presents the simulation results illustrating the performance of the proposed filter. The test image employed here is the true color image “parrot” with 290×290 pixels. For the addition of noise, the source image was corrupted by additive Gaussian noise with standard deviation σ =10, 20,30 and 40. The noise model was computer simulated. The performance of the zed filter is compared with the traditional mean filter shown in Table (1). All filters considered operate using 3×3 processing window. The performance of filters was evaluated by computing the mean square error (MSE) between the original image and filtered image as follow:
MSE= (
M
1
)
F n
(I(x,y) – I1(x,y))2 (11)
Where F denotes the set of M processed pixels, I(x,y) denotes the vector pixel value in the original image and I1(x,y)
denotes the vector pixel value in the filtered image.
Fig 5 shows the results of filtering the color image parrot which is corrupted by Gaussian noise with σ=10. First the color image is converted from RGB to YIQ domain. The proposed filter is applied for the removal of noise in I and Q components and the resultant image is converted from YIQ to RGBdomain.
Figure: 5) a, b, c, d take in clock-wise direction from the first figure
5a) Original noise free color image with 290×290 pixels 5b) Noise image with σ=10 5c) filtered image obtained by using mean filter 5d) Resultant noise free obtained by using proposed method.
Noise Image
RGB To YIQ
Filter
Filter YIQ
To RGB
Noise Free Image Y
I
Edges define the boundaries between regions in an image, which helps with segmentation and object recognition. In order to better appraise the noise cancellation behavior of our filter from the point of view of human perception, we perform edge detection mechanism for the filtered image. We used canny filter [8] for detection of edges in our “parrot” image. Fig 6 shows that our filter significantly reduces Gaussian noise and the image details have been satisfactorily preserved.
mean square error(MSE)
σ=10 σ=20 σ=30 σ=40
Noise Image
39.113 39.5747 39.6598 39.6865 Mean
Filter 26.125 26.235 26.578 26.789
Proposed Filter
18.5163 18.3276 18.2927 18.2806
Table 1: Experimental results
(a)
(b) (c)
Figure 6. (Edge detection using canny filter)a)Original noise free image b) Noise image c) Resultant image by our method
Section VI: Conclusion
A new technique for the restoration of color images degraded by Gaussian noise has been presented. The proposed approach is a simple and effective algorithm for noise cancellation and a method for parameter estimation is done without any “a priori” information about the amount of Gaussian noise. This restoration of image data is very likely to find potential applications in a number of different areas such as electromagnetic imaging of objects, medical diagnostics, remote sensing, robotics, etc. Experimental results show that the proposed method yields very satisfactory results.
References:
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