Computerized Cephalometric Line Tracing Technique on X-ray Images

Size: px

Start display at page:

Download "Computerized Cephalometric Line Tracing Technique on X-ray Images"

Hope Barber
6 years ago
Views:

1 Computerized Cephalometric Line Tracing Technique on X-ray Images C. Sinthanayothin National Electronics and Computer Technology Center, National Science and Technology Development Agency, Pathumthani, Thailand Abstract Cephalometric radiography analysis is an important diagnostic tool in orthodontics and craniomaxillofacial surgery. Conventionally, cephalometric variables are measured manually on X-ray film. The clinician need to trace all the lines to sho skull, teeth and ja structures by themselves, hich is inconvenient and time consuming. D cephalometric analysis can analyze in both lateral and frontal (PA) x-ray images. Therefore, this paper presents the method on producing the digital cephalometric tracing lines on x-ray images. The cephalometric tracing lines can lead to the measurement of the skull both in lateral and PA vies in both bones and soft tissue sections and also can lead to the diagnostic of abnormalities of skull, face and teeth as ell. Especially, PA vie can use for analysis on symmetry of the skull. The computerized cephalometric lines tracing method combines ith 4 steps. Firstly, the x-ray images are processed via adaptive, local, contrast enhancement. Secondly, the landmarks are defined by the dentists on both lateral and PA x-ray images. Next the cephalometric tracing lines are automatic generated by using the deformable template registration and cubic spline fitting techniques. Finally, the tracing lines are smoothed by put all lines into bitmap data hich an interpolation technique is applied hen the tracing lines are zooming. In this study, 0 laterals and 0 PA x-ray images are tested by this technique and the result shos very ell draing comparing to the manual method. Also the tracing lines are satisfied by the clinicians as a smoothed lines and curves. The cephalometric tracing lines ill aid the future orthodontic and orthognathic analysis, diagnostic and planning in the next step. Keyords Cephalometric Line Tracing, Lateral, PA I. INTRODUCTION Cephalometric analysis has been applied as tools in orthodontic diagnoses as ell as cranio-maxillofacial surgery. The measurement of skull, ja and soft tissue is simply called Cephalometric analysis here cephalo means head and metric comes from measurement. The cephalometric measurement in x-ray film can be done by locating the standard landmarks hich is orld ide ell kno for many years and continue developing for diagnostic for more than 50 abnormalities. To-dimensional cephalometric measurements from lateral and/or frontal cephalograms ere idely studied for diagnostic of abnormalities of skull bone and tissue and could be a tool that leads to an appropriated treatment planning by clinician. Currently, dentists perform orthodontic planning by initially taking the X-ray pictures of lateral and PA and then draing the structure of surface, jas, and teeth. At the same time the distance and angles are measured and calculated by using the stationary hich taking a large amount of ork and time. Hoever, the softare for cephalometric analysis are available such as Oris- Ceph Rx3 [], OnyxCeph [], Dolphine [3], Quick Ceph [4], Dr.Ceph (FYI) [5] and etc. [6-8]. Also group of researcher in Thailand have developed the softare for cephalometric analysis called CephSmile [9] as ell. Also many researchers are developed an automatic draing of the cephalometric line tracing such as the revie ork by Leonardi [0] that the systems described in the literature are not accurate enough to allo their use for clinical purposes as errors in landmark detection ere greater than those expected ith manual tracing. Therefore, this paper proposes the technique on producing the digital cephalometric tracing lines on x-ray images. The method combines ith 4 steps. First, contrast the x-ray images by local contrast enhancement technique. Second, define the landmarks by the dentists. Next dra the cephalometric line tracing hich can be done by using the deformable template and cubic spline fitting. Finally, the tracing lines are smoothed. The cephalometric tracing lines can be use for both orthodontic and orthognathic planning in the next step. II. METHODOLOGY The method on producing the digital cephalometric tracing lines on x-ray images can lead to the measurement of the skull both in lateral and PA vies in both bones and soft tissue sections and also can lead to the diagnostic of abnormalities of skull, face and teeth as ell. Especially, PA vie can use for analysis on symmetry of the skull. The method combines ith 4 steps are as follo: A. Radiographic Image Enhancement using Local Contrast Enhancement technique. Most of x-ray images in this ork are loss of detail and create of artifacts especially the digital image that taken from the x-ray film that placed on the vie box or scanned as can be seen in figure. Therefore x-ray image is necessary pre-processed in order to perform the clearer image, Chee Teck Lim, James C.H. Goh (Eds.): ICBME 008, Proceedings 3, pp , 009.springerlink.com

66 C. Sinthanayothin Fig : Original x-ray images of PA and Lateral vies. hich the local contrast enhancement technique has been applied in this paper [].

Consider a subimage of size M M centered on (i, j), in this paper M=49. Denote the mean and standard deviation of the intensity ithin W by <f> W and W (f) respectively.

The implicit assumption is that W is large enough to contain a statistically representative distribution of the local variation of grey levels, yet small enough to be unaffected by the gradual change

2 66 C. Sinthanayothin Fig : Original x-ray images of PA and Lateral vies. hich the local contrast enhancement technique has been applied in this paper []. For the local contrast enhancement technique, let the intensity, f, of the picture elements (pixels) of an N N digital image be indexed by (i,j) i, j N. Consider a subimage of size M M centered on (i, j), in this paper M=49. Denote the mean and standard deviation of the intensity ithin W by <f> W and W (f) respectively. The objectivity for this method is to define a point transformation dependent on W such that the distribution is localized around the mean of the intensity and covers the entire intensity range. The implicit assumption is that W is large enough to contain a statistically representative distribution of the local variation of grey levels, yet small enough to be unaffected by the gradual change of contrast beteen the centre and the periphery of the x-ray image. The adaptive contrast enhancement transformation is defined by [ ψ( f) ψ ( fmin )] f( i, j) g( i, j) = 55 () ψ ( f ) ψ ( f ) [ ] max min Fig : X-ray images ith local contrast enhancement. B. Cephalometric Landmarks on Lateral and PA Vies. The method in this paper could be able to dra the cephalometric line tracing of skull and face in both bones and soft surface sections on both lateral and PA images by using the landmarks defined by the dentists. Therefore, the landmarks need to be located by the clinician folloing the guideline in a step by step, 79 reference points for lateral vie and 57 reference points for PA vie as shon in figure 3. Some landmarks can be generated automatically or the ruler can appeared as a guideline for locating the reference point. The program also provides tools that allo users to mark the correct points ith ease as ell. Where the sigmoidal function as < f > f ψ ( f ) = + exp σ While f max and f min are the maximum and minimum values of intensity ithin the hole image ith W(, i j) M ( kl, ) W( i, j) () < f > = f( k, l) (3) σw( f) = f( k, l) < f > M ( ) (4) ( kl, ) ( i, j) The result of local contrast enhancement technique can be seen in figure. Fig 3: Reference points: 57 points for PA and 79 points for Lateral Vie. C. Cephalometric Line Tracing on Lateral and PA Vies In this paper, there are methods for cephalometric line tracing on lateral and PA vies. Firstly, cephalometric line tracing using deformable template is described. Secondly, the cephalometric line tracing using cubic spline technique is explained. One technique ill be applied at a time depends on the characteristic of the reference points.

Computerized Cephalometric Line Tracing Technique on X-ray Images 67 C.

This specific shape line can be matched ith a fe reference points. Therefore, the template of specific shape must be prepared as can be seen in figure 4. Fig 4: Templates ith difference shapes.

In this paper shos the example of tooth template matching ith reference points on x-ray image as shon in figure 5.

3 Computerized Cephalometric Line Tracing Technique on X-ray Images 67 C.Cephalometric Line Tracing using Deformable Template Cephalometric line tracing using deformable template can be applied hen the tracing line has a unique shape such as tooth, circle and etc. This specific shape line can be matched ith a fe reference points. Therefore, the template of specific shape must be prepared as can be seen in figure 4. Fig 4: Templates ith difference shapes. Once the templates have been prepared, then the template is fitted to a fe reference points. In this paper shos the example of tooth template matching ith reference points on x-ray image as shon in figure 5. The template matching can be done by determine the vector of to reference points on template and x-ray image respectively. Then the angle beteen to vectors has been calculated using dot product for template rotation. Next the distance of each vector indicates the size of template on x-ray image. Last the middle of the vector on x-ray image indicates the position that the template needs to be translated. Fig 5: Tooth template matching ith reference points on x-ray image. Equation 5, 6 and 7 shos the translation, rotation and scaling matrixes of template s coordinates on x-ray image. x' x d x = y + dy x ' cosθ sinθx = sinθ cosθ y x' sx 0 x = 0 s y y (5) (6) (7) C. Cephalometric Line Tracing using Cubic Spline Cubic spline technique is used for draing curve along the reference points. The spline is obtained by calculating the second derivatives of the interpolating function at the tabulated points based on the formulation given in Numerical Recipes in C. [] One dimensional cubic spline fitting can be explained as in Eq. (8) Eq.(3). With this method, a series of unique cubic polynomials is fitted beteen each of the data points ith the condition that the curve obtained be continuous and appears smooth. This spline consists of eights attached to a flat surface at the points to be connected. A flexible line is then bent across each of these eights, resulting in a smooth curve. g( x) if x x< x g( x) if x x< x3 Gx ( ) = (8) gn ( x) if xn x< xn Where g i is a 3 rd degree polynomial defined by 3 gi( x) = ai( x xi) + bi( x xi) + ci( x xi) + d (9) i for i =,,, n-. Since the pieceise function G(x) ill interpolate all of the data points, e can conclude that Gx ( i ) = y i (0) for i =,,, n-. Since x x, x, y = g ( x ) [ ] i i i+ i i i The coefficients a i, b i, c i, and d i in (9) are determined from the first and second derivatives of the n- equations of g i (x). ' " The routine must ensure that gi( x), gi( x)and gi ( x) are equal at the interior node points for adjacent segments. '' Substituting a variable S i for the gi ( xi) and y i for s i (x i ) ill reduce the number of equations and simplify the tasks. Given the spacing beteen successive data points is hi = xi xi () Finally, the variables a i, b i, c i and d i in (9), or termed the eights of each n- equations, ill be Si+ Si ai = 6h Si bi = yi+ yi Si+ + Si c () i = ( ) h h 6 di = yi When substituting these eights in (9), its st and nd derivatives, and including the condition of natural spline here nd derivative is equal to zero at the endpoints (S = Sn = 0), the system can be determined in matrix equation as follos

68 C. Sinthanayothin 4 0 0 0 0 S y y + y3 4 0 0 0 S 3 y y3 + y 4 0 4 0 0 0 S4 y3 y4 + y 5 6 = h 0 0 0 4 0 Sn 3 yn 4 yn 3 + y n 0 0 0 4 Sn yn 3 yn + yn 0 0 0 0 4 S n yn yn + y n (3) Therefore, Eq.

The result of fitting the cephalometric line ith cubic-spline interpolation can be seen as in figure 6. III.

This method has been tested on 0 PA and 0 Lateral x-ray images and found that cephalometric lines shoed the similar result depends on the coordinate of reference points.

Cephalometric Line Smoothening Cephalometric tracing lines are automatic generated by using the deformable template registration and cubic spline fitting techniques as mention above.

Therefore cephalometric line smoothening technique has been proposed by transform the indo/canvas coordinates of the tracing lines into bitmap coordinates.

The result of cephalometric line smoothening technique shos as figure 7(B) hich the user zooms into the specific area. IV.

4 68 C. Sinthanayothin S y y + y S 3 y y3 + y S4 y3 y4 + y 5 6 = h Sn 3 yn 4 yn 3 + y n Sn yn 3 yn + yn S n yn yn + y n (3) Therefore, Eq. (3)[3] is used to find the interpolation values in all dimensions. In this paper, a data point is equivalent to the number of reference points. The result of fitting the cephalometric line ith cubic-spline interpolation can be seen as in figure 6. III. RESULT The result of cephalometric line tracing on both PA and Lateral x-ray images can be displayed as figure 8(A) and 8(B) respectively. This method has been tested on 0 PA and 0 Lateral x-ray images and found that cephalometric lines shoed the similar result depends on the coordinate of reference points. (A) PA Vie (B) Lateral Vie Fig 8: Cephalometric line tracing result. Fig 6: Tracing cephalometric line ith cubic spline. D. Cephalometric Line Smoothening Cephalometric tracing lines are automatic generated by using the deformable template registration and cubic spline fitting techniques as mention above. Hoever, the lines are not smooth hen zoom into specific area as can be seen in figure 7(A). Therefore cephalometric line smoothening technique has been proposed by transform the indo/canvas coordinates of the tracing lines into bitmap coordinates. Then the program ill dra lines on bitmap instead of canvas and apply image interpolation hen the user zooms into the specific area of x-ray image. The result of cephalometric line smoothening technique shos as figure 7(B) hich the user zooms into the specific area. IV. CONCLUSION The result of the computerized cephalometric line tracing technique on x-ray images is reasonable and acceptable by collaboration clinicians. Since the tracing lines from computerized are similar to a hand draing but more convenient and less time consuming. Therefore, this method can perform automatic draing of the significant traces of face, skull, and teeth by using the reference points. The cephalometric analysis ith different types of analysis, such as Mahidol Analysis, Don Analysis, Steiner Analysis, Teed Analysis, Jaraback Analysis, Harvold Analysis, Rickette Analysis, and McNamara Analysis can be performed in the near future in order to sho the structural problems on skulls, face, and teeth. ACKNOWLEDGMENT This project is a part of CephSmile V..0. Thanks to National Electronics and Computer Technology center (NECTEC) for grant supporting. Special thanks to the orthodontics team from Mahidol University for their advices. (A) On Canvas (B) On bitmap plus interpolation Fig 7: Cephalometric lines. REFERENCES. OrisCeph Rx3, Ref: OnyxCeph, by OnyxCeph Inc. Ref:

5 Computerized Cephalometric Line Tracing Technique on X-ray Images Dolphin Imaging 0, by Dolphin Imaging System Inc. Ref: 4. QuickCeph 000, by QuickCeph System Inc, Ref: 5. Dr.Ceph (FYI), Ref: 6. Dental Softare VWorks, CyberMed, Ref: 7. Dental Softare VCeph, by CyberMed, Ref: 8. Cephalometric AtoZ v8.0e Ref: 9. CephSmile Ref:.typo3hub.com/chanjira/CephSmileV/cephsmileVEng.html 0. Leonardi R, Giordano D, Maiorana F, Spampinatod C. Automatic Cephalometric Analysis. The Angle Orthodontist: Vol. 78, No., pp Sinthanayothin C, Boyce JF, Cook HL, Williamson TH. Automated localisation of the optic disc, fovea, and retinal blood vessels from digital colour fundus images. British Journal Ophthalmology (BJO) 999;83: Press W.H.. et. al., Cubic Spline Interpolation, Numerical Recipes in C: The Art of Scientific Computing, Cambridge, UK: Cambridge University Press, (988). 3. McKinley S, Levine M. Cubic Spline Interpolation. Ref: redoods.cc.ca.us/instruct/darnold/laproj/fall98/skymeg/proj.pdf Author: Chanjira Sinthanayothin Institute: National Electronics and Computer Technology Center Street: Thailand Science Park, Phahonyothin Rd. City: Pathumthani Country: Thailand

SIMULATION OF ELASTIC SOFT TISSUE DEFORMATION IN ORTHODONTICS BY MASS-SPRING SYSTEM

SIMULATION OF ELASTIC SOFT TISSUE DEFORMATION IN ORTHODONTICS BY MASS-SPRING SYSTEM Pathomphong Phannurat 1, Wichit Tharanon 1, Chanjira Sinthanayothin 2 1 Advanced Dental Technology Center (ADTEC) 2 National