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 show skull, teeth and jaw structures by themselves, which is inconvenient and time consuming. 2D 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 views in both bones and soft tissue sections and also can lead to the diagnostic of abnormalities of skull, face and teeth as well. Especially, PA view can use for analysis on symmetry of the skull. The computerized cephalometric lines tracing method combines with 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 which an interpolation technique is applied when the tracing lines are zooming. In this study, 10 laterals and 10 PA x-ray images are tested by this technique and the result shows very well drawing comparing to the manual method. Also the tracing lines are satisfied by the clinicians as a smoothed lines and curves. The cephalometric tracing lines will aid the future orthodontic and orthognathic analysis, diagnostic and planning in the next step.
orthodontic planning by initially taking the X-ray pictures of lateral and PA and then drawing the structure of surface, jaws, and teeth. At the same time the distance and angles are measured and calculated by using the stationary which taking a large amount of work and time. However, the software for cephalometric analysis are available such as OrisCeph Rx3 [1], OnyxCeph [2], Dolphine [3], Quick Ceph [4], Dr.Ceph (FYI) [5] and etc. [6-8]. Also group of researcher in Thailand have developed the software for cephalometric analysis called CephSmile [9] as well. Also many researchers are developed an automatic drawing of the cephalometric line tracing such as the review work by Leonardi [10] that the systems described in the literature are not accurate enough to allow their use for clinical purposes as errors in landmark detection were greater than those expected with manual tracing. Therefore, this paper proposes the technique on producing the digital cephalometric tracing lines on x-ray images. The method combines with 4 steps. First, contrast the x-ray images by local contrast enhancement technique. Second, define the landmarks by the dentists. Next draw the cephalometric line tracing which 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
Keywords — Cephalometric Line Tracing, Lateral, PA
I. INTRODUCTION Cephalometric analysis has been applied as tools in orthodontic diagnoses as well as cranio-maxillofacial surgery. The measurement of skull, jaw and soft tissue is simply called Cephalometric analysis where “cephalo” means head and “metric” comes from measurement. The cephalometric measurement in x-ray film can be done by locating the standard landmarks which is world wide well know for many years and continue developing for diagnostic for more than 50 abnormalities. Two-dimensional cephalometric measurements from lateral and/or frontal cephalograms were widely 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
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 views in both bones and soft tissue sections and also can lead to the diagnostic of abnormalities of skull, face and teeth as well. Especially, PA view can use for analysis on symmetry of the skull. The method combines with 4 steps are as follow: A. Radiographic Image Enhancement using “Local Contrast Enhancement” technique. Most of x-ray images in this work are loss of detail and create of artifacts especially the digital image that taken from the x-ray film that placed on the view box or scanned as can be seen in figure 1. Therefore x-ray image is necessary pre-processed in order to perform the clearer image,
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Fig 1: Original x-ray images of PA and Lateral views.
Fig 2: X-ray images with local contrast enhancement.
which the local contrast enhancement technique has been applied in this paper [11]. 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) 1 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 within W by 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 between the centre and the periphery of the x-ray image. The adaptive contrast enhancement transformation is defined by
[ψ w ( f ) −ψ w ( f min )]
f (i, j ) → g (i, j ) = 255
[ψ w ( f max ) −ψ w ( f min )]
B. Cephalometric Landmarks on Lateral and PA Views. The method in this paper could be able to draw 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 following the guideline in a step by step, 79 reference points for lateral view and 57 reference points for PA view as shown 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 allow users to mark the correct points with ease as well.
(1)
Where the sigmoidal function was ª
ª < f >w − f º º »» σw ¬ ¼¼
−1
(2)
ψ w ( f ) = «1 + exp « ¬
While fmax and fmin are the maximum and minimum values of intensity within the whole image with
< f >W (i , j ) = 1 σ (f)= 2 M 2 W
1 M2
¦
(3)
f (k , l )
( k ,l )∈W ( i , j )
Fig 3: Reference points: 57 points for PA
¦ ( f (k , l )− < f > ) w
2
and 79 points for Lateral View.
(4)
( k ,l )∈( i , j )
The result of local contrast enhancement technique can be seen in figure 2.
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C. Cephalometric Line Tracing on Lateral and PA Views In this paper, there are 2 methods for cephalometric line tracing on lateral and PA views. Firstly, cephalometric line tracing using deformable template is described. Secondly, the cephalometric line tracing using cubic spline technique is explained. One technique will be applied at a time depends on the characteristic of the reference points.
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C.1Cephalometric Line Tracing using Deformable Template
C.2 Cephalometric Line Tracing using Cubic Spline
Cephalometric line tracing using deformable template can be applied when the tracing line has a unique shape such as tooth, circle and etc. This specific shape line can be matched with a few reference points. Therefore, the template of specific shape must be prepared as can be seen in figure 4.
Cubic spline technique is used for drawing 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”. [12] One dimensional cubic spline fitting can be explained as in Eq. (8) – Eq.(13). With this method, a series of unique cubic polynomials is fitted between each of the data points with the condition that the curve obtained be continuous and appears smooth. This spline consists of weights attached to a flat surface at the points to be connected. A flexible line is then bent across each of these weights, resulting in a smooth curve.
Fig 4: Templates with difference shapes.
Once the templates have been prepared, then the template is fitted to a few reference points. In this paper shows the example of tooth template matching with 2 reference points on x-ray image as shown in figure 5. The template matching can be done by determine the vector of two reference points on template and x-ray image respectively. Then the angle between two 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 with 2 reference points on x-ray image.
if g1 ( x) ° g ( x) if ° 2 G ( x) = ® # ° °¯ g n −1 ( x) if
ª x ' º ªcos θ − sin θ º ª x º « y ' » = « sin θ cos θ » « y » ¬ ¼ ¬ ¼¬ ¼ ª x ' º ª sx 0 º ª x º « y '» = « 0 s » « y » y¼¬ ¼ ¬ ¼ ¬
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(7)
xn −1 ≤ x < xn
Where gi is a 3 degree polynomial defined by (9) g i ( x ) = ai ( x − xi )3 + bi ( x − xi ) 2 + ci ( x − xi ) + d i for i = 1, 2, …, n-1. Since the piecewise function G(x) will interpolate all of the data points, we can conclude that G ( xi ) = yi (10) for i = 1, 2, …, n-1. Since xi ∈ [ xi , xi +1 ] , yi = gi ( xi ) The coefficients ai, bi, ci, and di in (9) are determined from the first and second derivatives of the n-1 equations of gi(x). g i ( x ), g i' ( x ) and g "i ( x ) The routine must ensure that are equal at the interior node points for adjacent segments. '' Substituting a variable Si for the g i ( xi ) and yi for si(xi) will reduce the number of equations and simplify the tasks. Given the spacing between successive data points is (11) hi = xi − xi −1 Finally, the variables ai, bi, ci and di in (9), or termed the weights of each n-1 equations, will be Si +1 − Si 6h Si bi = 2 yi +1 − yi S + 2 Si )h ci = − ( i +1 6 h d i = yi ai =
(5) (6)
(8)
rd
Equation 5, 6 and 7 shows the translation, rotation and scaling matrixes of template’s coordinates on x-ray image. ª x ' º ª x º ª dx º « y '» = « y » + « d » ¬ ¼ ¬ ¼ «¬ y »¼
x1 ≤ x < x2 x2 ≤ x < x3
(12)
When substituting these weights in (9), its 1st and 2nd derivatives, and including the condition of natural spline where 2nd derivative is equal to zero at the endpoints (S1 = Sn = 0), the system can be determined in matrix equation as follows
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C. Sinthanayothin ª4 « «1 «0 « «# «0 « «0 «0 ¬
1
0 "
0
0
4 1 # 0 0
1 4 # 0 0
" " % " "
0 0 # 4 1
0 0 # 1 4
0
0 "
0
1
0 º ª S2 º ª y1 − 2 y2 + y3 º « » 0 »» «« S3 »» « y2 − 2 y3 + y4 » « y3 − 2 y4 + y5 » 0 » « S4 » 6 « » » »« # # »« # » = 2 « » h « « » » y − 2 yn − 3 + yn − 2 » 0 Sn −3 » « n−4 » »« 1 » « Sn − 2 » « yn −3 − 2 yn − 2 + yn −1 » « y − 2y + y » 4 »¼ «¬ S n −1 »¼ n −1 n ¼ ¬ n−2
III. RESULT
(13)
Therefore, Eq. (13)[13] 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 with cubic-spline interpolation can be seen as in figure 6.
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 10 PA and 10 Lateral x-ray images and found that cephalometric lines showed the similar result depends on the coordinate of reference points.
(A) PA View
(B) Lateral View
Fig 8: Cephalometric line tracing result.
IV. CONCLUSION
Fig 6: Tracing cephalometric line with 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. However, the lines are not smooth when zoom into specific area as can be seen in figure 7(A). Therefore cephalometric line smoothening technique has been proposed by transform the window/canvas coordinates of the tracing lines into bitmap coordinates. Then the program will draw lines on bitmap instead of canvas and apply image interpolation when the user zooms into the specific area of x-ray image. The result of cephalometric line smoothening technique shows as figure 7(B) which the user zooms into the specific area.
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 drawing but more convenient and less time consuming. Therefore, this method can perform automatic drawing of the significant traces of face, skull, and teeth by using the reference points. The cephalometric analysis with different types of analysis, such as Mahidol Analysis, Down Analysis, Steiner Analysis, Tweed Analysis, Jaraback Analysis, Harvold Analysis, Rickette Analysis, and McNamara Analysis can be performed in the near future in order to show the structural problems on skulls, face, and teeth.
ACKNOWLEDGMENT This project is a part of CephSmile V.2.0. 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
REFERENCES
(B) On bitmap plus interpolation
Fig 7: Cephalometric lines.
1. 2.
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OrisCeph Rx3, Ref: http://www.orisline.com/en/orisceph/pricelist.aspx OnyxCeph, by OnyxCeph Inc. Ref: http://www.onyx-ceph.de/i_functionality.html
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Dolphin Imaging 10, by Dolphin Imaging System Inc. Ref: http://www.dolphinimaging.com/new_site/imaging10.html 4. QuickCeph 2000, by QuickCeph System Inc, Ref: http://www.quickceph.com/qc2000_index.html 5. Dr.Ceph (FYI), Ref: http://www.fyitek.com/software/comparison.shtml 6. Dental Software VWorks, CyberMed, Ref: http://www.cybermed.co.kr/e_pro_dental_vworks.html 7. Dental Software VCeph, by CyberMed, Ref: http://www.cybermed.co.kr/e_pro_dental_vceph.html 8. Cephalometric AtoZ v8.0E Ref: http://www.yasunaga.co.jp/CephaloM1.html 9. CephSmile Ref: www.typo3hub.com/chanjira/CephSmileV2/cephsmileV2Eng.html 10. Leonardi R, Giordano D, Maiorana F, Spampinatod C. Automatic Cephalometric Analysis. The Angle Orthodontist: Vol. 78, No. 1, pp. 145–151.
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269 11. 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) 1999;83:902-910. 12. Press W.H.. et. al., “Cubic Spline Interpolation, Numerical Recipes in C: The Art of Scientific Computing”, Cambridge, UK: Cambridge University Press, (1988). 13. McKinley S, Levine M. Cubic Spline Interpolation. Ref: http://online. redwoods.cc.ca.us/instruct/darnold/laproj/Fall98/SkyMeg/proj.pdf
Author: Institute: Street: City: Country: Email:
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Chanjira Sinthanayothin National Electronics and Computer Technology Center 112 Thailand Science Park, Phahonyothin Rd. Pathumthani Thailand
[email protected]
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