Image Noise Suppression Using Color Morphological Filter

Morphological filtering is a useful technique for processing and analyzing binary and grayscale images. These filters are effective in impulsive noise filtering, feature extracting


Introduction
Mathematical morphology is an ensembles theory used in image processing [1]. It provides an approach to digital images processing based on geometrical shape [2]. The original theory developed by Matheron and Serra was restricted to binary images, and later it was extended to grayscale morphology by Sternberg, Nakagawa and Rosenfeld [3]. The extension of the concepts of binary and grayscale morphology to color image is not a straightforward task. However, it is possible to extend some techniques to define morphological operators on color images [2].
The theory of morphology is built on two basic operators: the erosion and dilation [1], which are the base of most morphological operations such as opening and closing [4]. Generally, the morphological operators transform the original image into another image through the interaction with the other image of certain shape and size, which is known as the structure element. Geometric features of the image that are similar in shape and size to the structure element are preserved, while other features are suppressed [5].
Mathematical morphology is useful for the analysis of geometrical structures in images, the reduction of clutter in images, images enhancement and segmentation. It used widely in images analysis (i.e. edge detection, shape analysis, image coding, smoothing and thinning) [6].
The rest of this paper organized as follows: sections 1 and 2 begin with binary morphology that is based on set theory. The following grayscale morphology can be regarded as the extension of binary morphology as the three-dimensional space. In section 3, the part of color morphology is introduced. Section 4 explains morphological filtering approach. The experimental results are presented in section 5 finally; section 6 is dedicated to the conclusions.

Binary Morphology
The theoretical foundation of binary mathematical morphology is set theory. In binary images, those points in the set are called the 'foreground' and those in the complement set are called the 'background'. We need three general definitions that are used extensively to extend morphological operations [6]. Translation: it supposes that A is a set of pixels in binary image and ) , ( y x w= is a particular coordinate point. Then as in equation (1), A w is the set A "translated" in direction ) , ( y if A is set of pixels, then its reflection, denoted by Â, is obtained by reflecting A in the origin [7]. As shown in equation (2) (

Binary Morphological Operations
Dilation and erosion are the basic operations of morphology, in the sense that other operations are built on a combination of these two [7]. Dilation is the morphological translation that combines two sets by using vector addition of this element set's [3]. As shown in equations (3) & (4) dilation and erosion of a binary image A by structure element B, denoted by B A⊕ and B AΘ respectively [5].
Generally, dilation has an effect of expansion the object shape, fills gaps between objects and connects them together. Erosion shrinks the object in original image and eliminates small enough peaks [6].
Opening and closing operations may be considered as "second level" operations in that they build on the basic operations of dilation and erosion [7].
As shown in equation (5) in opening, the original image is first eroded by a structuring element and then dilated by the same one [6]. The opening of a binary image A by structuring element B, denoted by A○B [5].
Opening generally smoothes the contour object, breaks narrow isthmuses, and eliminates thin protrusions. Closing also tends to smooth sections of contours but is opposed to opening; it generally fuses narrow breaks and long thin gulfs, eliminates small holes and fills gaps in the contour [9].

Grayscale Morphology
In this section, binary morphology is extended to the grayscale case. Through the discussion below, we will see that the key issue is to use the 'maximum' and 'minimum' functions to define grayscale morphological operators [6].
When applied to a binary image, dilation and erosion operations cause an image to increase or decrease in spatial extent, respectively. To generalize these concepts to a grayscale image, it is assumed that the image contains visually distinct grayscale objects set against a gray background. In addition, it is assumed that the objects and background are both relatively spatially smooth [10].
The differences between binary and grayscale morphology results from the definitions of dilation and erosion because other operations depend on them [6].

Grayscale Morphological Operations
Grayscale erosion and dilation use 'min' and 'max' operators, respectively [3]. The minimum (min) operator will interrogate a neighborhood with a certain domain and select the smallest pixel value to become the output value. This has the effect of causing the bright areas of an image to shrink or erode. Similarly, grayscale dilation is performed by using the maximum (max) operator to select the greatest value in a neighborhood [6].
The dilation and erosion of grayscale image f(r,c) by a grayscale structure element g(r,c) are shown in equation (7) The grayscale dilation causes the brighter regions in an image to grow and causes regions darker than background to shrink. In contrast, grayscale erosion causes the darker regions to grow, and the brighter regions to shrink [3].
Grayscale closing realized by first performing grayscale dilation with grayscale structuring element, then grayscale erosion with the same structuring element. Similarly, grayscale opening is accomplished by grayscale erosion followed by grayscale dilation [10].
The effect of grayscale closing and opening is shown in figure 1. Both operations make an original image smooth along to the nature of minimum and maximum functions [6]. Note that opening decreases sizes of the small bright detail, with no appreciable effect on the darker gray levels, while the closing decreases sizes of the small dark details, with relatively little effect on bright features [9].

Color Morphology
After introducing binary and grayscale morphology, the task turns on dealing with the color image morphology. The application of mathematical morphology to color image is difficult, due to the vectorial nature of the color data [11]. In this paper, I deal with images in RGB color space. You can think of images in RGB color space as a three separate pixel images. Technically, these are three images in the grayscale mode that represent respectively, red, green and blue [12]. Each pixel in a color RGB image can be viewed as a three-component vector   [13]. In this paper, I introduce component-wise approach for color morphology.
In a component-wise approach, the grayscale morphological operator is applied to each channel of the color image separately. For example, component-wise color dilation of f(x,y)=[f R (x,y),f G (x,y),f B (x,y)] by the structure element h(x,y)=[h R (x,y),h G (x,y),h B (x,y)] in RGB color space is defined as in equation (9): Where the symbol C ⊕ represents component-wise dilation. Similarly component-wise color erosion defined in equation (10): Component-wise color opening, and closing can be defined in the same way [5]. The use of this approach in color image processing is the most straightforward [14].

Morphological Filtering Method
Morphological filter by reconstruction has the property of suppressing noise, preserving the contours of the remaining objects. The use of this filter in color image requires an ordering relationship among the pixels of the image [11]. Its basic idea is to probe an image with a structuring element (SE) and to quantify the manner in which the SE fits (or does not fit) within the image. The information probed depends on both the size and shape of the SE. If the size of the feature is smaller than the SE or the shape differs from the SE, the feature will be eliminated. As emphasis by Matheron, the nature of that information is therefore dependent on the choice of the structure element [3].
Morphological filter can be constructed using opening (erosion followed by dilation) operation followed by closing (dilation followed by erosion) operation. This filter can attenuate or completely eliminate positive, negative, or both positive and negative impulsive noise from an image [2]. The advantages of using this filter: first, it can be simply implemented. Second, it has geometric filtering property, which can filter out or preserve geometric features controlled by filter design. Furthermore, it can be easily implemented by simple hardware. The shortcoming of color morphological filter for de-noising is the opening followed by the closing operator cannot remove the noisy point at edge location.

Experimental Results
In this section, we present results of experiments involving noise suppression in color images. I see from the experiments that the shape and the pixel values of the structuring element that used play a very important role in morphological image filtering approach.
In this paper, several different objective measures utilized for performance comparison of noise suppression filter. These measures must show some degree of closeness between two images by exploiting the differences in statistical distributions of pixel values. Tables 1, and 2 Impulsive noise can appear during image capture, transmission or storage. Common sources of impulsive noise include lightening, industrial machines, faulty or dusty insulation of high-voltage power lines, and various unprotected electric switches [2]. I have used the Normalized Mean Square Error (NMSE) measure [10]. As in equation (11) Where f i,j , is the original image, and g i,j is the noisy image after filtering its components with the proposed method at (i,j) pixel. M and N denote the dimensions of f and g image pixels, respectively.
To measuring the restoration quality, the commonly used Peak Signal-to-Noise Ratio (PSNR) is used. It is a good measure of impulsive noise suppression efficiency [10]. The PSNR defined as in equation (12)  In figures 2, and 3, I have performed the proposed morphological filter using the color images of "Parrot", "Boys", and "Flower" for impulsive noise suppression purpose.

Conclusions
In this paper, I proposed color morphology filter for salt & pepper noise suppression from RGB color images. The combination of opening followed by closing techniques was applied to attenuate the noise component in noisy image. The proposed operators, like their grayscale counterparts, achieve detail preservation, it can be easily implemented by simple hardware, and it is simple to implement. A best elimination of noise can be obtained if the morphological elemental operations of the connected filters are made with a large structuring element, but the best conservation of structures and details in the image are achieved with a smaller structuring element.