PHOTOGRAMMETRIC MEASUREMENT OF LINEAR OBJECTS WITH CCD CAMERAS SUPER-ELASTIC WIRES IN ORTHODONTICS AS AN EXAMPLE

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1 PHOTOGRAMMETRIC MEASUREMENT OF LINEAR OBJECTS WITH CCD CAMERAS SUPER-ELASTIC WIRES IN ORTHODONTICS AS AN EAMPLE Tim SUTHAU, Matthias HEMMLEB, Dietmar URAN, Paul-Georg JOST-BRINKMANN Technical Universit of Berlin, German Department for Photogrammetr an Cartograph Charité, Meical Facult of the Humbolt Universit of Berlin, German School of Dentistr, Department of Orthoontics an Dentofacial Orthopeics Working Group V/ KE WORDS: Calibration, CCD, Meicine, Object recognition, Orthoontics, Photogrammetr, Recognition ABSTRACT This paper escribes the evelopment of an approach for nearl automatic recognition of the shape of linear objects on the eample of super-elastic wires in orthoontics. This is mae possible b the integration of known parameters which escribe the general shape of the objects concerne. Such parameters are erive from the prouction process of these objects. A igital photogrammetric 3D measurement sstem shoul give a touchless measurement of the wires. The images were taken with two CCD cameras. The goal was to fin specific algorithms for object recognition an to appl them to the measurement of the wires. The algorithm shoul guarantee an automatic etraction of eges of a linear object b moel base proceures in the image. In this case, a 3D moel shoul be erive from the parameters controlling the prouction process. It shoul be introuce into the algorithm as a base of knowlege. As a result we get new 3D coorinates of the vertices of the wires. The ege lengths an the bening an torsion angles between the vertices coul be erive from these coorinates. Afterwars the results were compare with the parameters of the bening machine, an the accurac of the photogrammetric proceure was evaluate. INTRODUCTION For man ears photogrammetric proceures have significantl contribute to the touchless measurement of objects of all kin. Especiall the introuction of igital image processing techniques has opene new fiels of applications for photogrammetr. Digital image processing is an efficient tool to erive geometrical information from igital imager in a fast an economic wa. In recent ears versifie approaches for object recognition as well as was for etraction of geometrical information were evelope for ver ifferent applications. This paper escribes the evelopment of an approach for nearl automatic recognition of the shape of linear objects. This is mae possible b the integration of known parameters which escribe the general shape of the objects concerne. Such parameters are erive from the prouction process of these objects. The proceure was teste b appling it to the measurement of angulations in super-elastic wires. These memor-niti-wires to be eamine are use uring orthoontic treatments. A bening sstem which controls a bening machine via a CNC batch file is use for shaping the wires. The memor-form is programme into the wires b a special heat treatment, so that, at a specific temperature, the wires somewhat return into their initial configuration. The use proceure ought to check the setting values at the bening machine. A igital photogrammetric 3D measurement sstem was applie for image acquisition. The images were taken with two CCD cameras which were connecte to a workstation via a vieo boar. Program moules for the photogrammetric restitution, e.g. for calibration an for point etermination, were available. The goal was to fin specific algorithms for object recognition an to appl them to the measurement of the wires. The algorithm shoul guarantee an automatic etraction of eges of a linear object b moel base proceures in the image. In this case, a 3D moel has to be erive from the parameters controlling the prouction process. It shoul be introuce into the algorithm as a base of knowlege. As a result new 3D coorinates of the vertices of the wires are obtaine. The ege lengths an the bening an torsion angles between the vertices can be erive from these coorinates. Afterwars the results were compare to the parameters of the bening machine. 78 International Archives of Photogrammetr an Remote Sensing. Vol. III, Part B5. Amsteram.

2 From investigations on the accurac of the proceure it is possible to evaluate the applicabilit of the approach. One has to istinguish between the accurac of the calibration of the cameras, the accurac of the algorithm for the location of the eges an vertices, an the absolute accurac of the overall sstem. The assignment is to verif the angles, accoringl the relative accurac is to be eamine. Furthermore, the applicabilit of this proceure to similar tasks must be consiere. In general, linear objects of ever kin e.g. wires of ever size, pipes, etc. or objects with linear eges concrete slabs can be treate if moel ata e.g. in the form of a CAD are available. IMAGE DATA ACQUISITION AND THE CONFIGURATION OF THE SSTEM. Image ata acquisition In this work, two commonl available CCD cameras of the tpe SON C 77CE were emploe, which where connecte over a frame grabber. The technical ata of the cameras are liste in Table. Tpe of the camera Number of piels Signal transfer Piel size Lens SON C 77CE 756 columns, 58 rows Analogue composite vieo-signal CCIR,, µm focal length 6 mm Table. Technical ata of the camera A CCD camera can be unerstoo as a metric camera because of its soli CCD matri. It is assume that the lens is stabl interconnecte with the camera bo an the focal length is fie. The interior orientation of the cameras must either be available or has to be calculate together with the eterior orientation uring the calibration of the cameras.. Configuration of the sstem The configuration of the measurement correspons to the case of aerophotogrammetr Figure. The efinition of the rotation that is necessar to escribe the position of the cameras, is shown in Figure. For the etermination of an appropriate configuration an the calculation of the camera parameters the following input was use: - object size, - principal istance an - the size of the igital image. The istance between object an camera was fie on 3 cm, because the focal length is on the nearest position stopposition. With this configuration the photogrammetric restitution of objects with a size of approimatel 6 cm is possible. The epth of focus amounts 5 cm. Figure. Definition of rotation Figure : Camera configuration International Archives of Photogrammetr an Remote Sensing. Vol. III, Part B5. Amsteram. 78

3 3 PHOTOGRAMMETRIC PROCESSING 3. Calibration Due to the configuration of the sstem Figure, the calibration object consists of a base-plate cm with 6 control points an an attache cube 553 cm 3 with 9 control points Figure 3 Figure 3: Calibration object A bunle ajustment was applie for calibration of the CCD camera. Thus we etermine the parameters of the interior orientation of the cameras an the calibration of the whole sstem incluing the eterior orientation in one step. For the central perspective conition, the following equations were emploe: c k H c k H For the istortion moel, the following equations were emploe: k 5 3 k 6 with, - image coorinates,, - coorinates of object points i - rotation matri c k, h, h,, - interior orientation for each camera,,, ϕ, ω, κ - eterior orientation for each image k,k - parameters for raial lens istortion In the eperiment, the calibration object was taken at a istance of approimatel 3 cm an at the principal istance of 5,3 mm from the CCD camera from 9 ifferent irections an positions, in such a wa that the images coul be overlappe %. In orer to test the absolute accurac of the configuration, we calculate the bunle ajustment with etermination of the calibration points as new points. The achieve accurac of the 3D measurement is, mm in - an -irection an,4 mm in. In orer to attain a better accurac it woul be necessar to enhance the istortion parameters an to use a calibration object with more accurate calibration points. Suthau, Tim International Archives of Photogrammetr an Remote Sensing. Vol. III, Part B5. Amsteram. 78

4 3. Photogrammetric processing moel The photogrammetric calibration elivers the orientation parameters of the cameras an the whole sstem. With the application of these parameters an the measurements in the images of the represente object it is possible to erive 3D coorinates of this object. The measurement of image coorinates took place with methos of igital image processing. It was a combination between ifferent image processing operations, like ege etraction an vectorisation. A sstem overview is illustrate in Figure 4. Figure 4. Sstem overview 3.3 Evaluation of the object The task was to surve super elastic wires. As mentione above, these memor-niti-wires to be eamine are use uring orthoontic treatments. A bening sstem which controls a bening machine via CNC batch file is use for shaping the wires. The input ata for shaping the wires are the ege lengths an the bening an torsion angles between the vertices. These values shoul be checke. In orer to achieve the comparison between the parameters of the bening machine an the actuall eisting values of the wire all the steps illustrate in Figure 5 were necessar Proviing moel coorinates In the first step a 3D moel has to be erive from the parameters controlling the prouction process. The CNC batch file contains the ege length between the vertices istance s [, the bening angles from it the azimuth t [ anthe torsion angles. From these parameters the coorinates of the moel were calculate: [ i [ i s s cos t sin t In this work onl wires without torsion were eamine. If it is intene to measure wires with torsions the equation has to be enhance. In orer to etermine the searche vertices a backprojection of the moel coorinates in the images is necessar. In accorance with the evaluation plan of the object Figure 5, base on the information about the interconnection of points, a new enhance ege ata file was generate incluing azimuth an the istance of the ege. 7, 8 International Archives of Photogrammetr an Remote Sensing. Vol. III, Part B5. Amsteram. 783

5 Figure 5. Flow chart for ata processing 3.3. Ege etraction Further eperiments achieve reasonable results on the basis of the cann operator. The accurac of the measure vertices an calculate angles epens on the qualit of the cann operator an on the following vectorisation chapter The result of the cann operator epens on the use threshol metho an on the image acquisition conitions. The ascertainment of the threshol occurre on screen. The suitable threshol is use as a efinite value for all wires, which were measure uner the same conitions. Figure 6. Original image of a wire Figure 7. Ege image from Figure 6 Therefore, the prerequisite is given for an automation of the measurement. The image acquisition conitions of the wires coul be optimise on the basis of the structure of the wires. We put wires on a light table an we achieve a ver goo contrast between the object an the surrouning area. Also shaow an shine effect, that appear with metallic workpieces otherwise, coul be prevente this wa. This high brightness ifference is optimal for the ege etraction. The original image an the corresponing ege image are illustrate in Figure 6 an International Archives of Photogrammetr an Remote Sensing. Vol. III, Part B5. Amsteram.

6 3.3.3 Vectorisation An algorithm was evelope for the etermination of the vertices. A searching area, in which the vertices, that escribe the object, are suspecte, coul be calculate with the help of the moel ata. All eges in this searching area were etecte an use for the calculation of a regression straight line. The intersection of these straight lines elivers the esire coorinates of the vertices as result. This metho has the avantage that eges with a certain thickness are reuce to a central ais. Figure 8. Searching area for the vectorisation Figure 9. Ege image with the points after the vectorisation Figure. Original image with the points after the vectorisation Determination of object coorinates After the etection of vertices in the images of both cameras, these vertices coul be transforme into the object area on the basis of the bunle ajustment with the help of orientation parameters. There was no problem with the assignment of homologous points because the new vertices coul be name after their corresponing moel points Derivation of istances, bening an torsion angles from object coorinates The space istance, bening an torsion angles were calculate from the given object coorinates as follows: Space istance The space istance s[ between two points P i : s [ [ i [ [ i ] z[ z[ i 9 Bening angle The bening angle between straight lines in the 3D case is escribe as an angle between two vectors represente through three points P, P. First, the azimuth-cosine of vectors angle between the coorinate ais was [ i ] calculate: International Archives of Photogrammetr an Remote Sensing. Vol. III, Part B5. Amsteram. 785

7 Vector P i : cosα cos β cosγ z z / / / z z z z z z - Likewise Vector P i was calculate. The esire angle δ[ between the vectors is δ arccoscosα cosα cos β cos β cosγ cos γ 3 3 Torsion angle The torsion angle is escribe as an angle between two planes represente b three points. At the wires, two points of the first plane are ientical with two points of the other plane. The first plane is escribe b P i, the secon plane through P i i ]. Parameters of the first plane are A C B z z [ i [ i [ i z z z z z z [ i [ i [ i 4-6 Likewise the secon plane was calculate. Stanarisation of both planes: A B C N A B C N 7 8 As result the angle between the planes: τ arccos A A B B C C / N N 9 Bronstein, 993 The calculation of the torsion angles is of interest for the measurement of the wires onl in the respect that eviations from the plane can be prove. 4 EVALUATION SAMPLES 4. Practical application measurement of super-elastic wires After the camera was calibrate successfull an the moel ata were prepare, the moel coorinates coul be projecte into the respective original image. As well, the eges were etracte in the image b the cann operator. The vectorisation of the vertices of the wires took place uner ai of the projecte moel coorinates. The search areas of the vectorisation an the result are represente in Figures 8-. The calculation of the object coorinates was achieve with a bunle ajustment. The results are ocumente in Table. It shoul be notice that the final points, on the basis of the application of straight-cuts, coul not be etermine again. point [mm] [mm] z [mm] m [mm] m [mm] mz [mm] Table. Values of the object coorinates 786 International Archives of Photogrammetr an Remote Sensing. Vol. III, Part B5. Amsteram.

8 The accurac achieve of the as well as coorinates is about ±,8 mm, the accurac of z coorinates is about ±,7 mm. The new spatial istances an bening angles were calculate with the help of the object coorinates with formulas 9-9. A comparison between the values of the moel an the real values is ocumente in Table 3. Distance from point to3 3to4 4to5 5to6 6to7 Moel istance [mm],,,,, Object istance [mm] Angle between point,3 an 4 3,4 an 5 4,5 an 6 5,6 an 7 Angle in moel [egrees] 3, 5, 5, 3, Angle on object [egrees] 8,86 3,94 4,58 3,46 Table 3. Comparison between the results an the moel ata 4. Evaluation of results an accurac With the presente algorithm goo results coul be achieve concerning the ege etraction an vectorisation. The achieve accurac of the calibration is ±, mm in plane an ±,4 mm in height. The accurac of the measurement of a wire achieve about ±,8 mm in the as well as in coorinate an about ±,7 mm in the z coorinate. This precision epens on the length of the etecte straight lines an the image acquisition conitions. This accurac is most important for the comparison of the parameters of the bening machine an the real values. The appointe accurac correspons to the angle accurac ±,5 egrees m, ±,8 mm, s mm an ±,86 egrees m z ±,7 mm, s mm. The inner accurac was teste b a comparison between the represente algorithm an a software for automatic measurement of image coorinates. The achieve accurac of the whole sstem is estimate ±, mm in plane an ±,5 mm in height. An epansion of the bunle ajustment using further istortion parameters an a better etermine calibration object woul improve the accurac. 5 CONCLUSIONS In the presente paper, an approach for nearl automatic recognition of the shape of super-elastic wires has been introuce. For inustrial use, the separate program components have to be summarise an optimise. An improvement of the calibration e.g. the etension of the istortion parameters woul lea to an increasing precision. A surveing of other objects is possible, if the pre-conition bounar of the object through straight-pieces an eistence of moel coorinates is fulfille. The size of the object plas no role with it, but must be consiere regaring the resolution an the accurac however. Also a transfer of the sstem on other objects is possible. An aaptation of the vectorising algorithm woul be necessar. With the presente paper it coul be shown that the utilisation of CCD cameras an suitable software enables an effective surveing of objects in the fiel of close-range photogrammetr. ACKNOWLEDGEMENTS The autors like to thank Volker Roehorst TU Berlin for his implementation of the Cann operator an his suggestions in the fiel of image processing. REFERENCES Bronstein, I. N., Semenjajew, K. A., Musiol, G., Mühlig, H., 993. Taschenbuch er Mathematik..Auflage, Verlag Harri Deutsch, Thun, Frankfurt am Main. Drescher, D., Bourauel, Ch., Thier, M., 98. Materialtechnische Besonerheiten orthoontischer Nickel-Titan-Drähte. Fortschritt Kieferorthopäie 6 5, pp Marr, D., 98. Vision A Computational Investigation into the Human Representation an Processing of Visual Information. W.H. Freeman & Co., San Francisco. Roehorst, V Architectural Image Segmentation Using Digital Watershes. In: Proc. Of the 7 th Int. Conf. For Computer Analsis of Images an Patterns CAIP 97, Lecture Notes in Computer Science 96, Eitors: Sommer, G., Daniiliis, K., Pauli, J. Kiel, pp Vieweg, A., Carlsohn, M.F., 99. Moellgesteuerte Konturverfolgung zur vollstänigen Segmentierung von Bilern. Mustererkennung 99, Springer Verlag Berlin Heielberg. International Archives of Photogrammetr an Remote Sensing. Vol. III, Part B5. Amsteram. 787