Image registration is one of the image processing methods which is widely used in computer vision, pattern recognition, and medical imaging. In digital subtraction radiography, image registration is one of the important prerequisites to match the reference and subsequent images. In this paper, we propose an automatic non-rigid registration method namely curvature-based registration that relies on a curvature based penalizing term and its application on dental radiography. The regularizing term of this intensity-based registration approach provides affine linear transformation so that pre-registration step is no longer necessary. This leads to faster and more reliable solutions. The implementation of this approach is based on the numerical solution of the underlying Euler-Lagrange equations. In addition, a comparison between this algorithm and Linear Alignment Method (LAM) with 20 image pairs is presented. © 2005 IEEE.published_or_final_versio

Leung, CC

Tsui, WK

Yiu, KL

Zee, KY

C.C. Leung

K.L. Yiu

W.K. Tsui

K.Y. Zee

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Image Registration in Intra-oral Radiography

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Title Image registration in intra-oral radiographyAuthor(s) Leung, CC; Yiu, KL; Zee, KY; Tsui, WKCitationAnnual International Conference Of The Ieee Engineering InMedicine And Biology - Proceedings, 2005, v. 7 VOLS, p. 3206-3209Issued Date 2005URL http://hdl.handle.net/10722/45857Rights Creative Commons: Attribution 3.0 Hong Kong LicenseImage Registration in Intra-oral Radiography C.C. Leung1, K.L. Yiu1, K.Y. Zee2, and W.K. Tsui11Department of Electrical & Electronic Engineering, The University of Hong Kong; 2Faculty of Dentistry, The University of Hong KongAbstract: Image registration is one of the image processing methods which is widely used in computer vision, pattern recognition, and medical imaging. In digital subtraction radiography, image registration is one of the important prerequisites to match the reference and subsequent images. In this paper, we propose an automatic non-rigid registration method namely curvature-based registration that relies on a curvature based penalizing term and its application on dental radiography. The regularizing term of this intensity-based registration approach provides affine linear transformation so that pre-registration step is no longer necessary. This leads to faster and more reliable solutions. The implementation of this approach is based on the numerical solution of the underlying Euler-Lagrange equations. In addition, a comparison between this algorithm and Linear Alignment Method (LAM) with 20 image pairs is presented. Keywords: Image registration, digital subtraction radiography, Euler-Lagrange equations.I.  Introduction Image registration is a useful technique in image processing applied in the areas such as geophysics, computer vision and medical image analysis [1,4-5]. Particularly in medical imaging, it is very important for a large number of applications such as clinical diagnostic, planning treatment, guiding surgery and studying disease progression. In this paper, we focus on medical image registration and specifically on dental application.  Digital subtraction radiography (DSR) is a useful technique introduced by Ruttimann el al. [6-7] for diagnosing subtle changes in radiographic density by longitudinal evaluation of serial radiographs of the same anatomical region. DSR has become important for early detection of disease and for measurement of disease progression. It has been used for the diagnosis of dental caries, destructive periodontal diseases and alveolar bone changes. Visual interpretation of intra-oral radiographs has been shown to be of limited diagnostic value for the early detection of subtle bone changes. With advances in the development of computer technology, DSR is developed into practical approach in dentistry to assess the differences between intra-oral radiographs. Image registration is one of the crucial prerequisites for DSR in order to obtain an accurate subtracted image. However, misalignments and bending mismatches easily arises in image alignment which will affect the accuracy of the subtracted image and diagnosis [10]. Most of DSR methods currently used are based on manual registration techniques.  The landmarks or reference points are marked manually on both images undergo registration or only one of them in these manual registration methods. Therefore, the result and quality of the registration is affected by the degree of precision in positioning landmarks and the observer experience placing the landmarks [8]. In this paper, we approach a new non-rigid intensity-based image registration method called curvature registrationwhich was developed by Fishcher et al [1-3]. This method is fully automatic and accurate without using the manual selection of reference points. The key of image matching in this method is minimized a suitable distance measure subject to a curvature-based constraint, and the computation of displacement is dependent on the intensity of image pairs. II. Theory of Curvature Registration It is given two images called reference image R and a template image T. The objective of image registration is to determine a transformation of T onto R such that the template image T aligns onto the reference image R absolutely. For a particular spatial point x ???? on T, the value T(x) is the intensity at x. It is determined a displacement field u: ??? ? such that ))(( xuxT ?  is very similar to )(xR  or ideally )())(( xRxuxT ?? . The problem is how to find this displacement field u, in two dimensions, (u1, u2) to obtain a satisfactory registration result.  In order to find the desired displacement u, we need to minimize the following function shown in equation (1). [ ] [ , ; ] [ ]curvu D R T u S u?? ? ? (1) where ????? dxxRxuxTuTRD 2))())(((21];,[           (2) dxuuSdll?????12curv )(21][                (3) D[R, T; u] represents the sum of square difference (SSD) distance measure and Scurv[u] determines the smoothness of the displacement u. The second term Scurv[u] is important since it can solve the problems during transformation such as cracks, foldings or other useless deformations. One of the reasons for choosing Scurv[u] is that it has a non-trivial kernel containing affine linear transformations. The parameter ? may be used to control the strength of the smoothness of the displacement versus the similarity of the images. Proceedings of the 2005 IEEEEngineering in Medicine and Biology 27th Annual ConferenceShanghai, China, September 1-4, 20050-7803-8740-6/05/$20.00 ©2005 IEEE. 3206The minimization of equation (1) is characterized by the following Euler-Lagrange equations 2( , ( )) 0,f x u x u?? ? ? ??x       (4) where           ))(()))(()(())(,( xuxTxuxTxRxuxf ?????? ))(,( xuxfis the force field which is the Gateaux derivative of the distance measure D and ?2u is the Gateaux derivative of the regularizing term Scurv. In equation (4), a suitable value of displacement u can be achieved.  Introducing an artificial time t, making the displacement utime dependent, u = u(x,t) and setting uk(x)=u(x,k?), where ? denotes a fixed time-step, a semi-implicit method for the time-dependent PDE is shown in equation (5). ))(,()(),( 121 xuxfxutxu kkkt ?????? ?       (5) To apply a finite different discrimination adapted to the geometry of the domain ?, this approach results in a system of linear equations, 2 1( ) k k kNI U U F?? ??? ? ? ?               (6) where N denotes the number of pixel, IN is the unit matrix, ?is the time step (?t) and Uk and Fk represent the values of displacement u and force f respectively. Uk+1 represents the displacement on the grid in the next step.  Eigendecomposition is then used to solve for Uk+1 and the eigenvalue ? of?2 is found to be 2)2cos(cos4 ??bxax ?? .Uk+1 can immediately be computed by obtaining the eigenvalue ? and performing the discrete cosine transformation (DCT). Uk+1can be found by the three steps shown as follows: 1. Find the DCT of FU k ?? , such that G = DCT FU k ??2. Divide G by )1( ????  pointwise, such that H = G1)( ?????NI3. Do inverse DCT on H, such that Uk+1 = iDCT(H) III. Results and Discussion 1. Experiments on Intra-oral radiographThe performance of the curvature registration is evaluated using a pair of Intra-oral radiographs. Figure 1 (a) and (c) show the reference R and the template T respectively, and it can be observed that there is bending error existed in the images. The mismatched area between R and T is shown in Figure 1 (d). Due to the bending error, ? should be set to a small value so as to allow template to undergo a large deformation and then align on the reference. Here, ? is chosen to be 10 while ? is set to 2, to keep the time step low and to prevent the deformation from vacillating too vigorously. With 250 iterations, the satisfactory registration result is shown in Figure 1 (b) whereas the difference |R-T250| is shown in Figure 1 (e). Figure 1 (f) shows the relative error of the two dental radiographs decreased to approximately less than 25%, that means over 75% of mismatched area has been eliminated.  2. Comparison of curvature registration and LAM Linear alignment method (LAM) is first present by Leung et al [10-11] which is a semi-automatic image alignment algorithm using linear transformation. The disadvantage of this method is limited to linear transformation only. In this section, our approach and LAM is evaluated based on 20 set of intra-oral radiographs. Intra-oral radiographs are taken from the same lower molar region in a human dry skull with each of three exposure times (0.16s, 0.18s, 0.22s) [6]. In order to have standardized periapical radiographs for subtraction, a custom-made acrylic bite block attached to a Rinn XCP film holder was made. The X-ray machine’s long cone was modified so as to produce a rigid attachment of the bite block to the cone. Hence, the angulations between the X-ray source, the object and the film could be reproducible. All periapical radiographs were taken using the paralleling technique with the same X-ray machine at the same setting, 70kV, 15mV. All films were developed with an automatic developing machine and in a batch to reduce variability during the development process.  Twenty pairs of images are selected for this experiment. One is to be the reference R and the other is the template T for each pair, which is shown in Figure 2. Then, curvature-based registration method is performed on these twenty sets of images so twenty registered template Tcurv are produced. Then three regions of interest (ROIs), refer to Figure 3, are selected and the computer-assisted densitometric image analysis (CADIA) [9] values are calculated to determine correlations between the CADIA values and the actual bone mass change. Since R and T are taken from the same human dry skull at the same time, so that the bone mass of the two radiographs should be the same. In the subtraction radiography, CADIA value should be a zero or below the threshold respectively as there is no bone change.Figure 4 (a) and (b) are shown the result of the subtraction radiography using LAM and curvature registration respectively. The bottom right hand corner of (a) and (b) reveal the difference between the pixel values of two images. The green color denotes no change in pixel values that means the net change in bone mass is zero. The positive pixels in red and negative pixels in blue represent bone gain and bone loss respectively.  In order to investigate whether the error percentage of curvature registration is significantly lower than that of linear alignment method, a t-test is conducted for the three regions. For Cadia1, the derived t value from the statistics is 3.983, exceeds the tabled critical t value of 2.093 at level of significance = 0.05 with df=19. Thus, the mean of percentage error by using the curvature registration is significantly lower than the mean of percentage error by using the LAM in this region. Similarly, the derived t values of Cadia2 and Cadia3 are 4.105 and 5.214respectively. From the above consistent statistical results, the derived t values of the three regions all exceed the tabled critical t 3207value of 2.093. Thus, this experiment demonstrates that the percentage error of radiography subtraction making use of curvature registration method is significantly lower than that of linear alignment method. In other words, the curvature registration method appears to work more effectively than LAM.  In this experiment, due to the radiographs were taken from a human dry skull, less force is exerted by the musculature of the oral cavity, many of the radiographic image pairs have only a small degree of bending error and it can be used the linear transformation to obtain the good result. However, in real-life, bending error has been existed too significant in intra-oral radiographs. Linear alignment method cannot satisfy to align this kind of images. For example, in Figure 5 (a), the template image has been moved to match with the reference image but it is impossible to eliminate the mismatched area using the linear alignment method. In such cases, curvature registration method is very useful, ? can be set to a small value to allow the template to undergo a non-linear deformation so as to align well on the reference image. The subtracted image of the reference R and the registered template T150 is shown in Figure 5 (b). IV. Conclusion The curvature image registration method has been presented in this paper. It shows that it is very efficient and reliable for automatic registration of different Intra-oral radiographs. Also, from the comparison with LAM, our approach obtains lower percentage error than the LAM.  References [1] Jan Modersitzki, Numerical Methods for Image Registration,Oxford University Press, 2004 [2] B. Fischer & J. Modersitzki, A unified approach to fast image registration and a new curvature based registration technique, Institute of Mathematics, Medical University of Lubeck, 2004 [3] B. Fischer & J. Modersitzki, Curvature based image registration, Institute of Mathematics, Medical University of Lubeck, 2003. [4] Van den Elsen, P.A., Pol, E.-J.D. and Viergever, M.A., Medical image matching-a review with classification,Engineering in Medicine and Biology Magazine, IEEE, Volume 12, Issue 1, March 1993, pp. 26 – 39 [5] J. B. Antoine Maintz and Max A. Viergever, A survey of medical image registration, Medical Image Analysis (1998) volume 2, number 1, pp 1–36 [6] B. M. S. woo, K. Y. Zee, F. H. Y. Chan and E. F. Corbet, In vitro calibration and validation of a digital subtraction radiography system using scanned images, Journal of Clinical Peridontology 30, 114-118 [7] Ruttimann, U.E., Webber, R.L. and Schmidt, E., A robust digital method for film contrast correction in subtraction radiography. Journal of Periodontal Research 1986, 21, pp.486-495[8] W .J. Yi, M. S. Heo, S. S. Lee, S. C. Choi, S. B. Lee and K. H. Huh, Automatic noise robust registration of radiographs for subtraction using strategic local correlation: an application to radiographs of dental implants, Computers in Biology and Medicine 35, 2005, pp 247-258 [9] Bragger, U., Litch, J., Pasquali, L. and Kornman, K.S., Computer assisted densitometric image analysis for the quantitation of radiographic alveolar bone changes, Journal of Peridontal Research, 1987, 22, pp.227-229 [10] Leung Chung-Chu, Digital Subtraction Radiography using Generalized Fuzzy Operator, Ph. D. Thesis, The University of Hong Kong. [11] C.C. Leung, P.C.K. Kwok, K.Y. Zee, and F.H.Y. Chan, Minimizing the bending error in intra-oral radiographs using point-by-point linear interpolation with image scaling,Proceedings of EMBEC’99, Part II, pp.1050-1051, 1999. (a) Reference R (b) Registered Template T250 (c) Template T (d) |R-T| (e) |R-T250| (f) |R-Tk|/|R-T| Figure 1. Curvature registration of human teeth X-ray images, ?=10, ?=2, 250 iterations: (a) reference R, (b) registered template T250, (c) template T, (d) difference |R-T|, (e) difference |R-T250| and (f) |R-Tk|/|R-T| against number of iterations 250 3208(a) Reference R  (b) Template T  Figure 2 (a) Reference R, (b) template T Figure 3 Three regions of interest: cadia1, cadia2 and cadia3 Linear Alignment Method(a) After normalization, LEFT TOP: reference R, RIGHT TOP: aligned template TLAM, BOTTOM: subtracted image of R and TLAMCurvature Registration(b) After normalization, LEFT TOP: reference R, RIGHT TOP: registered template Tcurv, BOTTOM: subtracted image of R and TcurvFigure 4 Comparison results between LAM and curvature registration (a) Subtracted image |R-TLAM|(b) Subtracted image |R-Tcurv|Figure 5. Subtracted images of implantation teethCadia3Cadia1Cadia2 3209

Image registration in intra-oral radiography

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Image registration in intra-oral radiography

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