Analysis on Digital Image Processing using Based on Matrix Analysis.doc

Analysis on Digital Image Processing using Method Based on Matrix Analysis Abstract. Image processing, image analysis and image understanding are three research levels of image engineering. And image processing is the basic theory part of the main body. This paper com 1. Image Processing 1.1 Image Graying In the RGB model, R,G,B value of each pixel is 0-255. When R=G=B, the multicolor represents a gray color, where R=G=B value is gray value, so the gray value range of gray image is 0-255. For conducting the gray processing of the RGB mode image, there are the following several methods. (1)Component Method RGB image has R, G, B of three components. According to requirement, we can choose any one of the components as the gray value of gray image. For example: f1(i,j)=R(i,j)，f2(i,j)=G(i,j)，f3(i,j)=B(I,j),where fk(i,j)(k=1,2,3) is gray value of gray image at(i,j) after conversion. (2)Maximum Method Using the maximum value of three component brightness in the colorful image as the gray value of gray image. f(i,j)=max(R(i,j),G(i,j),B(i,j) （1） (3)Average Value Method Using the three component brightness of the colorful image to obtain a gray image on average. f(i,j)=(R(i,j)+G(i,j)+B(i,j)/3 （2） (4)Weighted Average Method The weighted average method is to make R,G,B three components to use different weight values for conducting weighted average. Because the human eyes are most sensitive to green color and least sensitive to blue color. Thus, according to the following equation, conducting weighted average of the RGB three components can obtain reasonable gray image. f(i,j)=0.30R(i,j)+0.59G(i,j)+0.11B(i,j) （3） In Matlab, the RGB image is transferred into function of gray value image: rgb2gray, and the default method is weighted average method. Through the above mentioned gray method comparison, the effect of weighted average method is better, which can conform to the requirement of this research in the paper. 1.2 The Histogram of Gray Image For an image, its gray value is 0-255, making statistics of each gray value containing pixel quantity. Making the gray value as the abscissa axis of the axis, and the pixel quantity of the gray value as the ordinate, drawing the gray valuepixel quantity graphics, abbreviated as histogram. Through the histogram, it can obtain the pixel quantity of various gray values, so as to judge the gray distribution situation of the whole image and brightness and darkness comparison situation. Generally, the dark image gray value is smaller, corresponding to the left side of histogram. The gray value of bright image is greater, corresponding to the right side of histogram. The image of lower comparison degree should correspond to the narrow histogram and concentrates to the middle part of gray level. The image of high comparison degree should correspond to the wide range of histogram distribution, and the distribution is even. Thus, the histogram reflects the clarity degree of image. When the histogram distribution is even, the image is the clearest. The histogram in the image processing has a wide range of application. In image segmentation, it can segment ideal goal image. In image enhancement, it can change the distribution situation of gray image in histogram, so as to change the comparison degree of original image. Through the histogram, it can find the gray value change and distribution situation of the whole image. And through the histogram, it determines a threshold, providing basis for the two values and image segmentation. 2. The Digital Image Processing Technology Based on Matrix Analysis The digital image technology based on matrix analysis was first proposed by J. W. Jukey and used in one-dimensional signal processing technology (time sequence analysis). Later, it was used in two-dimensional image smooth processing technology, and the median filter is a nonlinear smoothing technology. Under certain conditions, the median filter can effectively overcome many linear filters, such as the image detail feature fuzziness caused by average value filter and Gauss filter. And it especially has the best restriction effect on the noise and filtering pulse suppression interference caused by image scanning. However, in the actual calculation process, it doesnt need to use the statistics feature of image, and this makes the calculation of median filtering very convenient. The basic principle of median filter is to regard the corresponding point of maximum and minimum value in the filtering window as the noise point, making the value of image or sequence center point position use the median in this field to replace, with calculating rapid, simple and good noise-removing effect. The median filtering technology is the most typical nonlinear filtering technology. Because of imperfect imaging equipment, recording equipment and transmission equipment, the image is polluted by all kinds of interference noise, such as the electromagnetic wave (external noise) produced by sky objects electronics and electrical equipment and various joints causing noise and the circuit of the inner system causing the noise (inner noise), etc. The possibility of image system may come from many aspects, such as the thermal noise generated by grain noise junction transistor, the heated noise generated by the resistance, the noise caused by camera tube and the electric fluctuation noise of photoelectric tube. Some noise can often form relatively obvious lonely pixel points in the image. The noise production has unpredictability in theory. However, because of the noise existence, it makes many features of image restricted by some degree of distortion (brightness, dark point interference). For the unpredicted distortion in the image, it greatly reduces image quality, which normally influences the reliability and validity of the follow-up work, such as the image segmentation, feature extraction and image recognition, etc. So in the image processing technology, how to reduce the image noise interference is an important technology. So, the image filter technology is an indispensable technology in image processing. Image filtering (also called image smoothing) technology refers to highlighting low frequency component, main part, wide area or suppressing image noise and interfering high frequency part of the image, so as to make the image brightness gentle gradient and improve the image processing technology of the image quality. The technology index of image filtering technology not only can retain the image detail characteristics (for example, the shape, size and special topology of goal image), recovering the real picture, but also can effectively restrict the image noise. It needs to use the noise reduction filter to conduct the image data. People have a long history of research on image noise-removal technology. According to the actual feature of image, image formation environment and image noise statistics feature and spectral distribution law, studying the various types of noise removal methods. Some common methods are : neighborhood average method, Gauss filtering method and median filtering method. And the neighborhood average filtering method is the most simple image filtering method. Table 1 The relationship of pixel f(i,j) and its neighborhood field It can be seen that in calculating the average value, the obtained neighborhood pixel points are more, and the filtering effect is better, but this will make image more blurred. The commonly used neighborhood model in the neighborhood average method has: 3x3 mean filter, NxN mean filter, etc. By taking 3x3 mean filter as an example, its calculation is as follows: set f(i,j) as containing the noise image pixel point gray, through simple field average process, the pixel point gray is g(i,j). The mathematical expression is : (4) In the equation (4), S is the coordinates of the pixel of neighborhood field, and M is containing neighborhood pixel number. On f(i,j), for each pixel, it can select fixed size neighborhood, to determine M value, and using the equation (1) to calculate the obtained the average gray value of neighborhood pixel in the obtained neighborhood field to replace this pixel, after processing all the pixels, it can obtain pixel function g(x,y). But actually, the each neighborhood pixel point in the neighborhood area has different influence degree on the center pixel point, that is to say, if all the neighborhood point pixel simply for average, then the image filter effect is not ideal. Generally speaking, the influence of the point on the closer point is greater. Then, we can introduce the weighted coefficient to improve the filtering effect. The algorithm is as follows: set the image gray as f(i,j), the noise gray is h(i,j), containing noise image gray is f(i,j)+g(i,j), then the image gray of conducting neighborhood weighted average is g(i,j), the calculation formula is as seen in formula(5): （5） This weighted for average value method can effectively restrict the noise, but it still can not avoid making some neighborhood field selection in the image have different templates, as follows: In order to maintain image gray average value unchanged after filter processing, the total of various elements in the template is 1. The third template is template of weighted average value. This filtering method is in the condition of its adjacent pixel gray value and its own gray value having great difference, using the adjacent pixel average value to replace its gray value. It can obviously restrict the noise point, so as to achieve good noise restriction effect, making its adjacent pixel average value close to even, playing the role of smooth gray. Through this linear filter, it is equal to that the image is going through a two dimensional low-pass filters. Although it reduces the noise, also it fuzzes the edge feature and detail feature of image, and this is the inevitable defects of this type of filter. 3. Conclusion The author introduces the traditional image processing into matrix analysis, proposing the