Proceedings of the 6th WSEAS International Conference on Multimedia Systems & Signal Processing, Hangzhou, China, April 16-18, 2006 (pp )

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1 The Application of onlinear Filtering in Reducing oise and Enhancing Radiographic Image Mingquan Wang, Yinong Liu, Li Zhang Department of Engineering Phsics Tsinghua Universit Beijing, China Abstract: - Real-time digital radiograph is an important developmental tendenc for radiographic inspection and diagnosis technique, and enhancement of image is the e to improve resolution and sensitivit of radiographic inspection. In this paper, the algorithm and character of Ran-Order filter is discussed with great emphasis. Ran-Order filter is one of nonlinear filter, All the methods are used to process radiographic image, and the result illustrate that linear filter can reduce noise but corrupt edge. Ran-Order filter can reduce noise as well as preserve the detail and has evidentl effect on improving image qualit. Ke-Words: - Radiographic Image Denoising; onlinear Filtering; Linear Filtering Introduction Real-time digital radiograph is a ver important means for DT.In the test sstem of real-time digital radiograph, because of the noise from quanta and gurgitation or a lot of an other reasons.which resulted in wea image signal,low SR,low definition,bad contrast, which also influencing the analsis and comments of the tested component b radiographic image. Enhancement of image technolog which based on the linear filtering has a lot of advantages, such as perfect theor foundation, simple mathematic algorithm, implemental hardware easil and so on, Linear filtering alwas pla an ver important role in the area of image filtering, but when it is used for processing the radiographic image. We can find that it will corrupt edge and lose the detail information of the image, and all of the above disadvantages are the side effect of reducing noise b using linear filtering. Rand-Order filtering not onl has the simple algorithm,good fleibilit,be prone to understand and realize but also has the function such as smoothing image,enhancing edge,restraining noise,saving detail etc [-9]. 2 Source of radiographic image noise Fig. shows the imaging sstem, which adopted b this paper, the sstem has a prominent character that can be fit for imaging test with different radiograph energ. D etect com ponent X-Ra Source Computer X -R a entoptic instrum ent From Fig. we can see that the noise of digital radiograph imaging sstem is caused from each part of the imaging sstem, the main noise comes from as following: quanta noise which is resulted from X-ra source, and mechanic noise which is resulted from asmmetr of transformation screen. 3 Linear processing approach of radiograph image noise Linear noise reduction includes neighborhood average in spatial domain and filtering process in frequenc domain, all of these methods are general called image smoothing processing. Smoothing is a common method in noise reduction of image processing, and in order to reduce noise b the average of the gra levels in the neighborhood piel, smoothing which is called neighborhood average in special domain, but called low-pass filtering in frequenc domain. Object of radiographic imaging testing is micro-structure (such as gaps,air hole), so linear smoothing will blur these information certainl. The Fig.2 can show slic processing. From the figure, f 0( is a ideal radiograph image. MTFO is the modulating transmission function of radiograph imaging sstem, g ( is the radiograph image, which is acquisition from imaging sstem. MTF is frequenc response function of smoothing processor and as a modulate transmission function of smoothing sstem, g ( is output which is processed b smoothing sstem. Fig. X-ra Digital Imaging Sstem Fig.2 the Smoothing Processing effect in the sstem

2 Either frequenc character of low-pass filters or modulating transmission function (MTF reflected the filtering performance in frequenc domain. Designing filters in frequenc domain can get ideal frequenc characteristic, and also can get good processing effect b frequenc domain processing. But frequenc domain processing has a great deal of operating data. Therefore, in real-time imaging testing, usuall adopt spatial domain smoothing process instead of frequenc domain filtering. Smooth processing methods in spatial domain are 2-D cross-integration procedure with proportional addition average of image and filter window arithmetic operators in spatial domain. From Fig.2 we can get that processed image is g (, window function is h (, output image is g (, hence g ( = g( * h( ( The Fourier transformation of above equation is G ω ) = G ω ) H ω ) (2) It is obvious that frequenc response function H ω ω ) of window function is modulating transmission function MTF of slic. Suppose the window width W (is odd number commonl of slic, proportion is, so the window function can be epressed as following equation: h ( n) = [ Λ,0,, 2 Λ 3,0, Λ ] (3) Therefore the point (n>w) of h(n) transformation can be epressed as j n H ( ) = h( n) e = e n= 0 2 W W n= 0 2 j n discrete 2 j W sin( W ) (4) e j ( W = = e 2 j -e sin( ) From equation (4) it indicates that H ) has different frequenc characteristic along with different window width. According sampling theorem, the ma frequenc resolution is / 2 for a sequence with the width is. if the image width is decided, then the influence of smooth filtering is certain. Common slics are rectangular window with size of 3 3,5 5,7 7, Slic is low-pass filter actuall, which not onl result in attenuation of high-frequenc element. Meanwhile but also result in much overla distortion in hi-frequenc part of the image because of truncation of window function.as for radiograph testing, whether how the width of image changing, Spatial sampling frequenc has been decided b image sampling, Image resolution is up to the number of image piel. Each piel of the image stands for effective size of actual image, the flaw with different width has different number of piel.supposing ideal flaw is a crac with the width of w piels, the unitar gra-level differential is. Fig.3 shows its crac has the form g ( n) = u( n (5) W Fig.3 Ideal Crac Signal The Discrete ourierransform of its points is sin( W G( ) = (6) sin( ) The main petal width of crac signal frequenc chart can be fied via sin( W = 0,amel = (7) W Or unitar bandwidth is B 0 = (8) W From (7) and (8), we can confirm the window width of slic or bandwidth of low-pass. Therefore, when choosing smoothing filter or linear low-pass processing the noise radiograph image, the bandwidth of filter should be more than main petal width of least resolution flaw size. This shows, smooth filtering can decrease noise and enhance image effectivel, but, if window width of smooth filter is chosen improperl. Which will induce flaw information losing of radiograph image and decreasing the testing sensitivit of real-time digital radiograph imaging sstem.. So smooth filter design must be combined with the MTF characteristic and frequenc characteristic of testing object in radiograph digital imaging testing, especiall in application of the automatic quantitative testing. 4 on-linear Filtering approach of radiograph image 2

3 Although the linear filter can attenuate the noise of the signal average affect a lot. But also corrupt edge and lose image details at the same time. The emphasis of radiograph image processing is that the flaw can be shown clearl in image, flaw (air hole,crac etc) onl has the width of several piels commonl in the whole image. In this wa, the eeping edge characteristic of linear filter result to corrupt edge and lose flaw details indeed. Ran-Order filter is one ind of on-linear filter, Ran-Order filter not onl has simple arithmetic,good fleibilit,can be understood and realized easil; but also has man functions, such as can smoothing image,enhancing edge,restraining noise and saving details,so can get the most ideal combination. Following will discuss some inds Rand-Order filter. 4. Median filtering Median Filtering [] is a slic window which include odd points. Use the median gra-level of the piels in the window replace the gra-level of the center piel. Supposing some piel gra-level is f( in the image, the neighboring region of which is a rectangular window with the size of ( 2 + (2l +,then through Median filtering,the gra-level of the piel is: Hereb, l + i= j= l g( = Med Med[ f ( + i, j) Med and (9) Med stand for the median value of horizontal direction and vertical direction respectivel. The window form and size design of the Median Filtering has a great influence on the filtering effect. Different image content has different application requirement, generall adopt different window form and size. The window form of the 2-D Median Filtering has linear.,ectangular,circular, cross-shaped and ring-shaped in common use. Generall speaing, we often adopt rectangular window or circular window for the image with long contour line object, and adopt cross-shaped window for the image with sharp-angled object. But the window size should be less than the size of the least available object in the image. The most noticeable thing during using the 2-D Median Filtering is eeping the available filament object in image. Median Filtering has following characteristics: the Median Filtering output has invariabilit for some input signal; the impulse response is zero, which decided Median Filtering has the character of eliminating impulse interference; Invariable signal response decided Median Filtering has the character of eeping edge. Therefore, adopt the Median Filtering into image processing, can restrain impulse interference and eep edge. 4.2 Contrast-Select Filtering Contrast-Select Filtering enhances image grads in the situation of unnown noise transcendent information. Such arithmetic is a self-adaptation sequence statistic filter, which not onl has simple arithmetic, but also eliminating noise at the same time of doing edge enhancement. Such filter arithmetic will introduce as following. At the time, the output Y of contrast-choice filter which with parameter J can be shown as: ( + J ) if M Y = X, µ ( + + J) (0) X, if µ < M The window size introduced here is 2 +. X,..., X,... X + are the sample (i) value in the window. X is sorted from small to big in the window. µ and M are sample average value and median respectivel, integer J meets J. Contrast-Select Filter has the performance of enhancing the edge grads. In addition, which is not sensitive to noise. Actuall,it can cut impulse noise and some non-impulse noise, such as Gauss noise,addition white noise. Generall speaing, it ll has preferable noise attenuation feature if J is small [0]. 4.3 Lower -Upper-Middle Filtering LUM Filter [], which is a sort of filters with good fleibilit and can achieve the ideal combination of noise smoothing and eeping signal detail, both of them are opposite. And LUM also avoids a lot of defects, which is eistent in multi-linear edge enhancement filter. LUM Filter, wh call it such a name, because of its output is received b lower and upper statistic of data, which has been sorted, and b comparing the filter window middle sample. LUM Filter is composed of LUM Slic and LUM Sharpener. Smoothing parameter controls smoothing character of which. The variet smoothing parameter also can adjust from non-smooth to smooth. That is to sa, if the parameter is chosen as a ver little smooth, then a lot of useful information will be saved and eliminate noise. Sharpening character is controlled b its parameter. In the past, edge enhancement is implemented b linear technolog commonl, these 3

4 linear technolog include Winner filtering,high-pass filtering and non-sharpening blind age. Linear Sharpener can get good effect in most cases, however, a lot of functions can not be achieved b Linear Sharpener Such as Linear Sharpener overdoing so as to can t achieve the epectation effect. Consequentl brought edge dithering or magnified bacground noise. But Sharpener can avoid these disadvantages. Especiall, it is not sensitive to Gauss noise and eliminating impulse noise effectivel. At the same time it also enhancing edge [2]. Following will discuss the arithmetic of LUM Filter. Supposing sample-point. The center element of which is, for the 2-D signal, the rectangular sample of window, which with the size of ( 2m + (2m + = can be written as following after sorting 2)... ) ( Center sample output is. LUM Filter, which consists of LUM Slic and LUM Sharpener. The definition of which is as follows: ), if < ) l), if l) < tl = l+, if tl < < l+ +, if + < others (2) Hereb l ( + / 2. LUM Filter show different features through change the value of and l. 5. Eperimental results and Analsis Using the sstem(x-ra source voltage is 60KeV,current is 0.3mA, focus diameter is 0.5mm) as Fig.4 shows do digital imaging for some aluminum compoment.fig.4(a) is the original image, the rest images are processed through the approach which introduced above, window size is 5 5 and window form is rectangular. (b) is the image which is processed b neighboring average filtering; (c),(d),(e) are the images which are processed b median filtering. the window form are rectangular,cross-shaped,rows and cols respectivel;(f) is contrast-select filtering, window form of which is rectangular;(g),(h),(i)are the images processed b LUM filtering, window form of which are rectangular,cross-shaped,rows and cols respectivel. From the processed results shows that: neighboring average filtering corrupting edge at the same time of eliminating image noise, and this ind of filter has no good effect for impulse noise; Median Filtering eep the edge information at the same time of eliminating image impulse noise, the effect of range separable median filtering is better than above approach for this eperimental image. Contrast-Select filtering enhancing the edge at the same time of eliminating the noise; LUM filter which is a ver fleible filter, as long as select adequate smoothing parameter and sharpening parameter l, LUM filter made noise smoothing,eeping and enhancing edge information these two conflicts into a ideal combination. This paper selected =3 l =3, for this image, the effect of range separable LUM Filtering is the best. (a) (b) (c) (d) (e) (f) 4

5 (g) (h) (i) Fig.4 Original and Processed Image [7] Fitch J.P., Cole E.J. et al, Root properties and convergence root median filters, IEEE Trans. ASSP-33, Feb.985: [8] Pomalaza C.A. et al, An adaptive nonlinear edge-preserving filter, IEEE Trans.ASSP-32, Jan.984: [9] X.Z. et al, Adaptive schemes for noise filtering and edge detection b using local statistics, IEEE Trans. CAS-35, Jan.988: 57-69, [0]Arec and R.E.Foster Detail preserving raned-order based filters for image processing, IEEE Trans. Signal Processing, 987,37(7) []Hardie and C.G.Boncelet, et all, LUM filters: A class ran order based filters for smoothing and sharpening, IEEE Trans. Signal Processing, Vol. 4, o.3mar Conclusion In the sstem of radiograph digital imaging, because the influence of the quanta noise, quantitive noise,dispersion noise,sstem heat noise etc, resulted in what output image submerged into noise, much important detail and edge can t be distinguished clearl. Linear Filtering corrupted edge at the same time of smoothing image noise. Order Filtering ept and enhanced detail at the same time of decreasing image noise. In the test sstem of industr radiograph digital imaging sstem. Because of the component s flaw (e.g. crac,air hole) has little edge information, so order filtering can get good effect for radiograph image processing. References: [] W. Tueonlinear Method for Smoothing data, In Conf. Rec., EASO [2] A.C.BoviT.S.Huang et al A generalization of median filtering using linear combinations of order statistics IEEE Trans.Vol. ASSP.3, Dec [3] JB. Beder, T.L.Watt, Alpha-trimmed means and their relationship to the media filtering, I EEE Trans.Vol. ASSP.32, Feb [4] eiminen A. and Heimonen P. et al, Median-tpe filter with adaptive substructure, IEEE Trans. CAS-34, Jul [5] Gallagher.C. and Wise G., A theoretical analsis of properties of median filters, IEEE Trans. ASSP-29, Dec.98: 36-4 [6] odes A.. and Gallagher.C., Median filter: some modification and their properties, IEEE Trans. Vol.ASSP-30 Oct.982: