An Algorithm of 3D Registration between Maxilla/Mandible and Dental Cast Apipon Visetvitsakul, Chanjira Sinthanayothin, Wisarut Bholsithi, Wichit Tharanon Advanced Dental T echnology Center National Science and T echnology Development Agency 111 Thailand Science Park, Phahol Yothin Road Klong Nueng Klong Luang, Pathumthani, 12120 T el: (02) 564-6960-1 Fax: (02) 564 - 6962 E-mail :
[email protected] Abstract - In the past, it requires dental experts to handle implant process since the experts know how to interpret x-ray data and place dental implant at the appropriated angles and positions. Currently, there are computer technologies that help dentists with little expertise on dental implanting process to place dental implant through custom made drill guide. This paper introduces a simple 3D image registration process to match the maxilla data rendered as STL data f rom DICOM data of I-CAT cone-beam CT scanner with corresponding dental cast data. The registration process starts f rom locating 3 corresponding pairs of landmarks on dental cast model and maxilla data. Next stepis to apply model registration techniques. The results f rom the experiments have shown that landmarks on 3D maxilla match with corresponding landmarks on the dental cast of the same patient. The results have shown potentials f or the application of placing custom-made drill guide and there are a f ew actual applications of this matching process to shorten the time f or dental implant surgery while keeping high accuracy f or placing dental implant.
I.
A. Preparing 3D Model Data of Maxilla and Dental Model into STL Files The first step fo r 3D data prep aration for Maxilla an d Dental Model into STL file is to prepare DICOM data tak en from a patient by Cone beam CT. Cone beam CT can take 323 x-ray photographs of 400 x 400 pixels shown in Figure 1.
INTRODUCTION
There are several senior citizens in Thailand who need dental implant services to substitute weak dental roots but there are few dental experts who can deal with dental implant. Furthermore, it takes long period to finish dental implant at each time due to the fact that dental experts need to make a guess from data in dental x-ray images which are prone to errors during the dental implant process. Computer technology and rapid prototype have been introduced and applied to produce custom made drill guide which helps dental experts to shorten the time spent for dental implant process while enhancing higher accuracy for dental implant placement. Dentists in Thailand have started applying such technologies to help on dental implant process, but high cost for importation of custom made drill guide has limited the application of dental implant treatment. There is a domestic research and development of custom made drill guide to cut down the cost for dental implant treatment and to get custom made drill guide that suits for each patient. Therefore, this paper is to introduce image registration which is one of critical processes for the production of custom made drill guide while taking errors in the model superimposition into account to ensure correct superimposed model with high accuracy. II. IMAGE R EGISTRATION IN 3D 3D image registration started from creating 3D model of both patient’s maxilla and the co rresponding dental model which can be described as follows.
Figure1: DICOM Files of Sku ll Taken from Cone Beam
The next step is to create 3D STL files o f maxilla and mandible section and dent al model from DICOM fil es by TM applying MIMICS from Materialise N.V. The thresholds fo r creating 3D model of maxilla and mandible are in between 800 and 3000 while the thresholds for creating dental model are in between 600 and 3000. After making a threshold, the result for maxilla threshold is shown in Figure 2(A) while the result for dent al model threshold [6] is shown in Figure 2(B).
(A) (B) Figure 2: Making Thresholds for 3D Model (A) Thresholds for Maxilla (B) Thresholds for Dental Model
During the threshold, users can edit and erase nois e on the images with thresholds to ensure smooth 3D rendering results. The 3D results aft er rend ering will b e stored as STL files [5 ] which consist o f triangles to from 3D image as shown in Figure 3(A) fo r maxilla and Figure 3(B) for dental model.
calculat e Normal Vector 1 from vectors o f reference landmarks and Normal Vector 2 from vector [2] i f movement landmarks as shown in Figure 5(B). The next calculation after normal vectors is to calculate the arbitrary axis from the matrix multiplication between Normal Vector 1 from reference s et and Normal vectors 2 from movement [3] set as shown in Figure 5(C) (A)
(A) (B) Figure 2: 3D Model in STL files (A) 3D Model for Maxilla (B) 3D Model for Dental Model
B. 3D Image Registration to fit Dental Model with Maxilla After p reparing 3D d ata o f m axilla and d ental model, the next step is to make 3D imag e registration between maxilla and dental model. This has been done by writing software for image registration by using Borland C++ Builder® and OpenGL Library to display image registration results in 3D. The procedure for 3D image registration started from identifying the positions to be matched on both m axilla and dental model. The next step is to rotate the dental model to fit with maxilla which has b een identi fied as referen ce. After dental model rotation, the countercheck for discrepancies Details for 3D image registration will be d escribed in the next sections. C. Position Identifications on Maxilla and Dental Model Position identification for referen ce positions will be execut ed on maxilla. After that, the position identification fo r movement will be done on dental model. There will be 3 positions for the reference set and movem ent set formed as a triangle as shown in Figure 4(A) and Figure 4(B) respectively.
r | u |=
u12 + u 22
(B)
(C) Figure 5: Vector Calculations to Fit Dental Model with Maxilla (A) Vector Calculation for Reference and Movement Set by Calculating Vector identical to a vector from P1 to P2 (B) Normal Vector Calculation for Reference Set (Normal Vector 1) and Movement Set (Normal Vector 2) by Py thagorean Theory (C) Arbitrary Axis Calculation from both Normal Vectors
After calculating Arbitrary Axis Vector, the next step is to substitute this vector into 4 x 4 matrix [1] in (1) and (2) to rotate dental model and superimpose into maxilla as shown in Figure 6 with (1) for writing into software that use DirectX to display 3D image and (2) for writing into software that use OpenGL to display 3D image.
Figure 4: Sets of Reference and Movement Landmarks (A) Reference Set of Landmark on Maxilla (B) Movement Set of Landmark on Dental Model
D. Dental Model Rotation to Fit with Maxilla by Vectors After identi fying the sets o f landm arks, the image registration of landm arks can be executed. The image registration process started from calculating vector of reference positions and movement positions as shown in Figure 5(A). Next step is to
⎡ (1 − cos θ ) x 2 + cos θ ⎢ ⎢ (1 − cos θ ) xy + z sin θ ⎢ (1 − cos θ ) xz − y sin θ ⎢ 0 ⎣⎢ ⎡ (1 − cos θ ) x 2 + cos θ ⎢ ⎢ (1 − cos θ ) xy − z sin θ ⎢ (1 − cos θ ) xz + y sin θ ⎢ 0 ⎢⎣
(1 − cos θ ) xy − z sin θ
(1 − cos θ )xy + y sin θ
(1 − cos θ ) y 2 + cos θ
(1 − cos θ ) yz − x sin θ
(1 − cos θ ) yz + x sin θ 0
(1 − cos θ ) z 2 + cos θ 0
(1 − cos θ ) xy + z sin θ
(1 − cos θ ) xy − z sin θ
(1 − cos θ ) y 2 + cos θ
(1 − cos θ ) yz − x sin θ
(1 − cos θ ) yz − x sin θ 0
(1 − cos θ ) z 2 + cos θ 0
0⎤ ⎥ 0⎥ 0⎥ ⎥ 1 ⎦⎥
(1)
0⎤ ⎥ 0⎥ 0⎥ ⎥ 1 ⎦⎥
( 2)
θ = Angle between Normal Vector 1 for Reference and Normal Vector 2 for Movement
x , y , z =Unit vector of Arbitrary Axis
III. R ESULTS Results from image registration experiments have been applied to treat 20 patients who need dental implant such as patient without teeth on the mandible as shown in Figure 8(A) and patient with very few teeth on the mandible as shown in Figure 8(B). The applied results match very closed to the results from computer model. Nevertheless, some cas es need to apply mouse to make readjustment functions of 3D image due to the incomplet e image registration. This image readjustment by mouse will facilitate the imag e registration process during actual implementation.
Figure6: Dental Model Rotation to Fit into Maxilla (A) Situation before Image Registration (B)Dental Model Movement (C) Dental Model (Shown as Texture) Fitted on Maxilla (Shown as Mesh)
E. Countercheck Process for Discrepancies For the countercheck for positioning dental implant, TM Simplant Master has been applied. Before using Simplant Master, it is necessary to measure the x, y, and z axis as shown in Figure 7(A) as the way to make final position for dental implant placement in 3D as shown in Figure 7(B). Repeat the process shown Figure 7(A) and Figure 7(B) to both before and after dent al implant placement for comparison as shown in Figure 7(C). This is a way to countercheck the result of image registration between m axilla and d ental model wh ether how much the discrepancy on image registration process during dental implant procedure.
(A) (B) Figure 8: Experiment Results (A) Registration on Patient without Teeth (B) Registration on Patient with Few Teeth
IV. CONCLUSIONS Results from imag e registration between maxilla and d ental model have shown that the calculat ed results have made a closed match with actual results. The discrepancies are due to the following 2 main factors: 1.
2.
Model movement slightly missed targeted positions due to noise around dental model even though the angular results match from actual implementation matched with calculated results. Human errors during dental implant process by manual due to the narrow mouth of patients which cause di fficulty to place the dental implants
The correction for these errors is to readjust the positions by mouse via moving readjustment functions, and then the dental model in 3D will go through the process for the production of custom made drill guide to be applied to patients later. ACKNOWLEDGMENT
(A) (B)
We appreciate for th e contribution from Dr. Kritkrai Sitthisereepratheep from MTEC fo r allowing authors to us e TM MIMICS to create 3D image o f maxilla and dental model in STL files fo r the experiment. R EFERENCES [1] [2] [3] [4]
(C) Figure 7: Experiment Results (A) Measurement of X Y, and Z Axis for Dental Implant Placement (B) Positioning for Dental Implant Placement in 3D (C) Comparison between Result before Actual Dental Implant Placement and Results after Actual Dental Implant Placement
[5] [6]
C. Thibualt, “Part III: Rotation About an Arbitrary Axis”, CProgramming .com, 2005, available online at www.cprogramming.com/tutorial/3d/rotation.html. N. Eua-Anant, “Vectors and Motion in Space”, Jan 10, 2004 available online at gear.kku.ac.th/~nawapak/math2/chapter09.ppt J. Tanthanuch, “Lines and Planes in Space”, October 2005, available online at math.sut.ac.th/~jessada/CALII/48-2/calII_5.ppt Hewlett-Packard Inc. Company and Silicon Graphic Inc., “Introduction to the Standard Template Library ”, 1994, available online at www.sgi.com/tech/stl/stl_introduction.html Marshall Burns, “The STL Format”, StereoLithography Interface Specification, 3D Sy stems, Inc., October 1989, available online at www.ennex.com/~fabbers/StL.asp S.Lobregt, J.J.Schillings, and E. Vuurberg, Dental Implant, Medical Mundi, Vol. 45, No. 4, November 2001, pp.30 – 35, available online at www.medical.philips.com/main/news/assets/docs/medicamundi/mm_vol 45_no4/MM_45-4_Dental.pdf
