Segmentation of Casting Defects in X-Ray Images Based on Fractal Dimension

Transcription

1 17th Wold Confeence on Nondestuctive Testing, Oct 2008, Shanghai, China Segmentation of Casting Defects in X-Ray Images Based on Factal Dimension Jue WANG 1, Xiaoqin HOU 2, Yufang CAI 3 ICT Reseach Cente, Chongqing Univesity, Chongqing , China Tel: , Fax: @163.com Abstact Consideing defect segmentation is the most impotant and hadest issue fo vaious defects ecognition and classification in the X-ay image, a segmentation algoithm based on factal dimension which is calculated by diffeential box-counting is investigated to locate defects in the gay-level images. The esults indicate that factal dimension can be a good altenative in defect-segmentation. Some compaative expeiments ae done and the esults demonstate that the algoithm is simple, and adapt to pecisely segmenting casting defects in X-ay images. Keywods: Casting Defects, X-Ray, Factal Dimension, NDT 1 Intoduction In the casting pocess, shinking pocesses occu duing the cooling of molten metal and they may lead to inhomogeneous egions within the wokpiece such as cavity, cacks, gas, inclusion [1]. In ode to insue the safety of conductions, especially those pats elevant to vehicle safety like ailway casts, wheel ims, a contol of thei quality is equied. Among seveal nondestuctive testing (NDT) methods used to detect and estimate quality-level, X-ay inspection is an established technique fo identification and evaluation of intenal defects, which has been applied to a wide ange of industies such as casting, welded seams and heavy steel stuctues that ae moe than 100 mm thick. Unfotunately, the visual esult evaluation of X-ay images is adopted by most X-ay inspection systems. The inspection quality depends on opeato expeience, and the inspection pocess itself is time-consuming and inefficient. Moeove, human inspecto is not able to make quantitive analysis fo the size and classes of defects. With the development of moden poduction technology, moe complicated wokpieces need to be tested and much moe X-ay

2 images need to be evaluated, such manual inspection method has lagged behind moden poduction. In ode to make the inspection efficient and all testing esults objectivity and epoducibility, the eseach of automatic detection of casting defects has become moe and moe valuable. An automated X-ay inspection system is typically composed of five pats: a manipulato, an X-ay souce, an image sensos, a CCD camea and an image pocesso fo the automatic classification of the test piece as satisfactoy o defective by digital image pocessing [2,8,10]. And an image pocesso is consist of fou pats: image pepocessing which includes noise eduction and enhancement, defect extaction, defect classification, the statistic esult output and defect display, and defect-segmentation is the most impotant and difficult pat. Diffeent methods fo extaction of casting defects using image pocessing can be found in liteatue within the past twenty yeas. And geneally these methods can be classified two classes: one is diect extaction, and the othe is indiect [3]. The indiect class of appoaches geneally poceeds by identifying the significant diffeence between a test image and the efeence image to classify the test piece as defective [2]. In ode to use efeence image, the distibution of gay values in the image must coelate to the cuent image. This equies a vey pecise positioning of the piece as well as vey stict fabication toleances and the epoducibility of the X-ay paametes duing imaging indispensable. Small vaiations in these vaiables may lead to geat diffeences between the two images [2]. In additionally, the efeence image of wokpiece which is not given peviously may be too difficult to get when wokpiece is too complex and the contolling of manipulato is not pecise enough. Thus the diect extaction of defects is applied in ou context. Yet simple pocess o specific filteing can not segment defects with any size and shape fom complex images. In this pape, a method of defect segmentation using factal dimension (FD) is poposed. 2 Factal theoy 2.1Factal dimension The factal dimension is an impotant chaacteistic of factal because it contains infomation about thei geometic stuctue. Usually we think that the dimension of a point is zeo; the dimension of a line is one; the dimension of a suface is two; and the body's is thee, and that the dimension of the object wouldn't change whateve the object does any tansfomation. This kind of dimension called as: topology dimension, defined as: d. Mandelbot, who intoduce the concept of factal and self-similaity to descibe ealistic objects, believe that, in the factal wold,

3 the dimension needn't be intege numbe. The dimension of factal geometic object (defined as D) is bigge than its topology dimension, so D d. Factal dimension pesents the iegula degee which equals an object s ability to occupy the space and then it can eflect the oughness degee of the object [4]. So we use factal dimension as a paamete to segment defects fom X-ay images. A basic pinciple to estimate factal dimension is based on the concept of self-similaity which can be explained as follows. Conside a bounded set A in Euclidean n-space. The set is said to be self-simila when A is the union of N distinct (nonovelapping) copies of itself each of which is simila to A scaled down by a atio. Factal dimension D of A can be deived fom the elation [5] D 1 = N o log( N ) D = (1) log(1/ ) Howeve, natual scenes pactically do not exhibit deteministic self-similaity. Instead, they exhibit some statistical self-similaity. Thus, if a scene is scaled down by a atio in all n dimensions, then it becomes statistically identical to the oigin one, so that (1) is satisfied. 2.2 Calculation of Gay Image Factal Dimension [5-7] Thee ae many diffeent methods to implement the factal dimension, and in which box-counting dimension o box dimension poposed by N.Saka is one of the most widely used dimension. Its populaity is lagely due to its elative ease of mathematical calculation and empiical estimation. Fist of all, the image is scanned by the window having the size M M pixels with the step a (if a=1 the window will be gliding, if a>1 it will be jumping ). Aftewads each step should be calculated and put into the matix D i,j, which is called factal dimension field(fdf) [9]. The calculation of factal dimension of evey sub-image is shown as follows. Conside that the sub-image of size M M pixels has been scaled down to a size s s whee M/2 s>1 and s is an intege. Then we have an estimate of = s / M. Now, as in pevious techniques, conside the image as a 3-D space whee two coodinates (x, y) epesent 2-D position and the thid (z) coodinate epesents gay level. N is counted as the following pocedue: 1) The (x, y) space is patitioned into gids of size s s. On each gid thee is a column of boxes of size s s s. If the total numbe of gay levels is G then [G/s ] = [M/s]. Fo example, see Fig. 1, whee s = s =3.

4 2) Assign numbes 1, 2, to the boxes as shown in Fig. 1. Let the minimum and maximum Fig. 1 Detemination of N gay level of the image in the (i, j)th gid fall in box numbe k and l, espectively. Then is the contibution of N, in (i, j)th gid. 3) Taking contibutions fom all gids, we have n ( i, j) = l k + 1 (2) N = n ( i, j) (3) i, j N is counted fo diffeent values of, i.e., diffeent values of s. Then using (1), we can estimate D, the factal dimension, fom the least squae linea fit of log (N ) against log (1 / ). Let y = mx + c be the fitted staight line, whee y denotes log (N ) and x denotes log (1 / ). Then eo of fit E can be expessed as the oot mean-squae distance of the points fom the fitted line. E = n i= 1 ( mx + c y ) i i 2 (1 + m ) n The eo povides a measue of fit so that the lowe the value of E, the bette is the fit. 2.3 The Chaacte of Gay Image Factal Dimension A. The factal dimension of the gay image has something to do with the size of the scanning window M, also have something to do with the box size s. The smalle s is, the moe pecise factal dimension is. In ou defect-segmentation system, M equals defect size. B. The factal dimension has nothing to do with which kind of logaithm we have taken in (1). 2 (4)

5 3 Expeiment Results In this section, we pesent the esults of defect segmentation using the poposed method and the othe two methods: viene filte & edge-detection, median filte & edge-detection. These esults demonstate the effectiveness of ou poposed method. We use 5 5 pixels scanning window, namely, M=5 and box counting algoithm fo FD calculation. In ode to save time fo building FDF, we make some changes to the box-counting method descibed in section 2.2. Fo a sub-image with size of M M pixels at the position ( i, j) in a wodpiece image, if its gay level is single, we set 0 to the coesponding position in FDF [9], namely D i,j =0. That is to say, if each pixel of the sub-image has the same gay value, we think that these aeas include nothing useful infomation about the stuctue of wokpiece and do nothing to it. So, we can use a theshold which equals to 0 to eliminate the backgound, and sometimes it may implement defect-segmentation at the same time. As Fig.2 show, Fig. (a) is a simulated image and Fig.(b) is the segmentation esult using factal dimension with theshold 0. Fo the same wokpiece image, diffeent aeas of factal dimension distinguish diffeent aea of the image, and which eflect diffeent stuctue infomation of wokpiece. Fo images of diffeent wokpieces, the same value-aea of factal dimension pesents diffeent infomation. So, we should adjust theshold-aea of defects to diffeent wokpieces. Additionally, since thee ae too much noise and atifact except defects in the eal industial X-ay image, pepocessing is equied befoe defect extaction. In fig. 3, Fig. (a) to Fig. (e) show the oiginal image, the pepocessing esult, the defect-extaction using the poposed method, the esult using viene filte & edge-detection, and the esult using median filte & edge-detection espectively. (a) (b)

6 Fig.2 simulating image with defects and its segmentation esult (a) (b) (c) (d) (e) Fig.3 (a) the oiginal image. (b) pepocessing esult. (c) esult using FD. (d) esult using viene filte & edge-detection (e) esult using median filte & edge-detection Fom Fig. 3(c), we can see all defects in Fig. (b) ae located based on factal dimension and little atifact is included in the esult, although thee is a poblem: the edge of defects is not close, and that is solved by defect-tack. Fom Fig. 3(c) and (d), it seems that using filte& edge-extaction also achieve this goal, but then you will find the esults include almost all edge: the edge of defects, the edge of wokpiece and too much edge of atifact, and no doubt that will make defect-tack too difficult to cay out. In a wod, the poposed method using factal dimension is effective to detect defects fom X-ay image. 4 Conclusion and futue wok In this pape, factal dimension is intoduced to defect-inspection and the esults demonstate that factal dimension can be a good paamete in defect-segmentation. In the futue, how to implement defect-tack with geat pefomance and how to design a classifie to identify the vaious defects will be the next impotant tasks to be tackled. Refeences [1] Romeu Ricado da Silva et al, Accuacy Estimation of Detection of Casting Defects in X-Ray Images Using Some Statistical Techniques, PSIVT 2007, LNCS 4872, p [2] Domingo Mey et al, A Review of Methods fo Automated Recognition of Casting Defects,

7 May 2002, [3] Veonique Rebuffel et al, Defect Detection Method in Digital Radiogaphy fo Poosity in Magnesium Castings, ECNDT 2006, we [4] Cao wen-lun et al, Taffic Image Classification Method Based On Factal Dimension Poc. 5 th IEEE Int. Conf. on Cognitive Infomation, 2006 [5] Niupam Saka et al, An Efficient Diffeential Box-Counting Appoach to Compute Factal Dimension of Image, IEEE Tansactions on System, Man, and Cybenetics, Vol. 24, No. 1, Jan [6] Jian Li et al, A New Box-Counting Method fo Estimation of Image Factal Dimension, IEEE Intenational Confeence on Infomation Pocessing, 2006 [7] Li Li et al, Detection of Cacks in Compute Tomogaphy Images of Logs Based on Factal Dimension, Poceeding of the IEEE Intenational Confeence on Automation and Logistics, Aug [8] Dawei Wi et al, Based on Computed Tomogaphy Multifactal Analysis of Wood Defect, IEEE Intenational Confeence on Contol and Automation, May, 2007 [9] V.K. Ivanov et al, Rada Remote Sensing Images Segmentation Using Factal Dimension Field, Poceeding of the 3th Euopean Rada Confeence, 2006 [10] Huang Qian et al, Computeized On-Line Inspection fo Inne Defects in Casing Poduct, Jounal of South China Univesity of Technology (Natual Science Edition), Vol. 30, No. 1, Jan. 2002