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A simple method for the correction of distorted digital angiographic images for stereotactic target localization
Cancer/Ijadiother 0 1999 Editions
1999 ; 3 : 489-93 scientifiques et mCdicales Elsevier
SAS. Tous droits r&xv&
Technical note
A simple method for the correction of distorted digital angiographic for stereotactic target localization
images
K. Theodorou 1,J.C. Rosenwaldz, D. Siamplis 3, D. Karnabatidis 3, C. Kappas 1 ’ Medical Physics Department, University of Patras, 26500 Parras; 2Medical Physics Department, Institute Curie, 26, rue d’lllm, Paris, France; 3 Department of Radiology, University qf Patras, 26500 Part-as, Greece Corresponding
Author:
(Received
the 2 November
SUMMARY The most commonly used imaging modality for the diagnosis and localization of arteriovenous malformations (AVMs) treated with stereotactic radiotherapy is traditional angiography, but it would be desirable to also use digital subtraction angiography (DSA). However, DSA images are distorted due to the electron-optical characteristics of the X-ray image intensifier. For that reason, we have developed a method for the correction of the image distortion. The ISIS II Treatment Planning System (ISIS II TPS), developed at the Curie Institute, has been used for image acquisition and stereotactic localization. A grid phantom has been constructed for determining the distortion of the DSA images. The software developed for the correction has been implemented into the TPS and is based on a correction vector produced by matching the distorted and corrected grid points. The method has been tested for its ability to correct the position of all grid points as well as its effectiveness in real cases as compared to traditional angiography. The maximum displacement of the corrected grid points compared with their original position is measured to be 0.1 mm. The accuracy of the target localization using the corrected DSA images is comparable with traditional angiography localization and falls inside acceptable accuracy limits. In conclusion, this method offers the possibility of using DSA images for stereotactic localization without limiting the requested accuracy. 0 1999 Editions scientifiques et medicales Elsevier SAS digital subtraction localization
angiography
/ distortion
/ stereotactic
1998; accepted the 17 March
1999)
RiSUMi Correction des images angiographiques numbriques en stkrkotaxie. L’angiographie classique est la methode la plus simple et la plus repandue pour le diagnostic et la localisation des malformations arterioveineuses (MAV) trait&es par irradiation stereotaxique. II est souvent souhaitable d’utiliser aussi I’angiographie numerique (DSA) qui est maintenant tres repandue, bien que la distorsion des images DSA (due aux caracteristiques electroniques et optiques de I’intensificateur d’images) pose un probleme majeur. Nous avons done mis au point une methode de correction de la distorsion de I’image. Le systeme de calcul de dose ISIS-II (ISIS-II TPS) developpe a I’institut Curie a ete utilise pour I’acquisition de I’image et la localisation stereotaxique. Un fantome constitue d’une grille a et6 construit pour la quantification de la distorsion de I’image DSA. Le logiciel de correction a et6 implement6 dans le systeme de calcul de dose. Ce logiciel est base sur une matrice de correction obtenue a partir du decalage entre les points de la grille obtenue (ayant subie une distorsion) et ceux de grille originale dont la position est connue. La m&ode proposee a ete testee en etudiant sa capacite de corriger la position de tous les points de la grille, ainsi que son efficacite dans des cas reels ou il est possible de faire une comparaison avec I’angiographie classique. Le decalage maxrmal entre les points de la grille recalcules apres correction de I’image et les points originaux de la grille est de 0,3 mm. La precision de la localisation de la cible en utilisant les images DSA corrigees est du meme ordre et comparable avec la precision de la localisation de I’angiographie classique. Elle se trouve done a I’interieur des limites de precision
K. Theodorou
490
acceptable. Cette m6thode offre la possibilite d’utiliser des images DSA pour des localisations stkkotaxiques saris compromettre la prkcision exigke. 0 1999 iditions scientifiques et mkdicales Elsevier SAS angiographie st6rCotaxique
par soustraction
/ distorsion
/ localisation
In recent years, stereotactic radiotherapy has become a viable alternative for the treatment of inoperable or residual cerebral arteriovenous malformations. Planning radiosurgical treatment requires accurate localization of the nidus. Angiography is the most common diagnostic procedure, as this image modality is best for visualizing the blood vessels. In the majority of the cases, traditional angiography is used for the exact target localization, but it would be desirable to use digital subtraction angiography (DSA) as well. Nevertheless, DSA images are distorted due to the electron-optical characteristics of the Xray image intensifier, so they cannot be directly used for stereotactic target localization. Several methods have been proposed for the correction of the DSA images’distortion [l-4]. Some of them are based on correction vectors against a rectilinear grid and others are based on analytical functions, which could correct some of the characteristics of the distortion. As the distortion is a function of several parameters (electron-optical characteristics of the X-ray image intensifier chain, gravity, magnetic field, etc.), a complete correction is difficult to perform. In stereotactic treatment of arteriovenous malformations, the calculation of the target coordinates is based on the exact determination of the stereotactic localizers, which appear as points on the anterior-posterior and lateral angiographic images [5]. This work proposes a simple method for the correction of the distorted localizers’position and in consequence the correct determination of the target position, applied directly to the treatment planning system.
METHODS
AND MATERIALS
The Treatment Planning System (TPS) used was the ISIS Treatment Planning System (ISIS TPS), developed at the Curie Institute in Paris. A phantom has been constructed for the correction of image distortion. It is made out of Plexiglas and its dimensions are 36 cm x 36 cm x 1 cm, adequate for the complete coverage of the image intensifier. Inside the Plexiglas plate, a rectilinear grid of steel balls was embedded. The steel balls are 1 mm in diameter and the distance between them is 5 mm. The phantom is placed directly on
et al.
top of the image intensifier in order to avoid magnification, as well as to have the maximum number of points possible appear on the grid image. Once the grid phantom has been placed on the image intensifier, an image is captured and printed on a film. The software for the correction of the image distortion is implemented into the ISIS TPS and is divided into two parts: an independent algorithm for the introduction of the distorted image of the grid, and an algorithm incorporated to the target localization program of ISIS for the correction of the distortion of the target localizers on DSA images.
Introduction of the grid The introduction of the grid image to the TPS is done via digitizer. The distortion presented on digital images acquired from an image intensifier is mainly due to the curvature of the upper surface of the detector. Thus, the photons, which are perpendicular to the center of the image intensifier, are less distorted than the ones found on other parts of the detector. In the present study, the central part of the intensifier is assumed as having no distortion. For the production of the theoretical undistorted grid, the user has to introduce nine central points of the grid image. The digital angiographer scales the image using an arbitrary scaling factor. Knowing that the real distance between two grid points is by construction 5 mm. the program calculates the scaling factor of the image and then automatically produces the theoretical, undistorted grid. The distorted grid points are then acquired via the digitizer and the program verifies that all points have been introduced. The distorted positions of all grid points are kept on record.
Correction of the distortion The method for the distortion correction is based on the displacement of each grid point in the digital image in respect to its original position. The algorithm begins from the center of the image, where there is not supposed to be any distortion, and moves in steps of 5 mm (equal to the distance between the grid points) in the four directions. In this neighborhood it searches for the next point (taking into account that the displacement could not be bigger than the diagonal formed by four grid points), and corrects its position. This procedure is repeated for all points and a record of all the displacements is kept as a function of the point distance from the center. In the case of target localization from two projected orthogonal angiographic images, the system requires the four localization points, the contour of the target as seen in each projection and the target’s center 151. When digital images are used, the algorithm executes the following steps for each image on the above points: - calculates the radial distance between the image center and the point of interest; - searches and finds from the file with the distorted grid points the four points, which surround the point of interest;
Correction of DSA images for stereotactic localization
491
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. ........... ..........
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:::::::::::::: ........... .... ...........
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:::
Corrected grid.
Figure 1. Distorted grid with a sixth-degree polynomial distortion, symmetrical in all directions, applied to all grid points.
- corrects the point’s position, applying a weighted displacement according to the distance of the point from the surrounding grid points. The above procedure is followed for all points required by the localization program. Finally, the localization is performed using the corrected positions of the localizers. RESULTS The above method has been tested for its ability to correct the position of all grid points as well as for its effectiveness in real cases, as compared with traditional angiography. In the first case, we have applied to the grid points an extreme, fifth-degree polynomial distortion, symmetrical in all directions: r=r+dxr3+exr5
where: r is the radial distance of the point from the image center, d = 0.00021, e = 0.0000031. This kind of polynomial distortion often appears in several digital imaging systems. The choice of the parameters d and e have been made so the resultant distortion would be of several orders of magnitude for the more distal, from the center, points (figure I).
After applying the correction algorithm to all grid points, the maximum displacement of the corrected grid points compared to their original position is measured to be 0.1 mm. The result is shown in figure
2.
The accuracy assessmentof the target localization using corrected DSA images was done by a homemade head phantom, which was able to be accurately repositioned to the immobilization frame [6]. The phantom was made from Plexiglas and could accommodate different target’sizes and shapesas well a number of dosimeters (films, TLDs, chromic films, ionization chamber), and has been used for dosimetric measurements as well as for verification purposes(figure 3). The’targets,‘with known positions, were spaced in different radial distances from the center of the image intensifier. In total, we have used six target positions. For each target we acquired a set of traditional angiographic images and a set of DSA images. The localization for all targets has been performed using the traditional images, the distorted DSA images and the corrected DSA images, and the resulting target stereotactic coordinates have been compared with their true values (figure 4). The maximum deviation between the corrected image localization and the true ta.rget position was measured to be 1.l mm, while the deviation between classical localization and the corrected DSA was 0.3 mm.
492
K. Theodorou
et al
DISCUSSION
AND
CONCLUSION
One of the major prerequisites for stereotactic radiotherapy is the accurate delineation of the target volume for treatment planning. In this framework, DSA images could be used in the case of arteriovenous malformations treatment, as they provide more information than traditional angiography and help the physicians to determine targets accurately. The proposed method is able to provide equally accurate target localization with traditional angiography and at the same time keep all the advantages of a digital image. This method is simple, not time-consuming as it does not apply the correction to the whole image, and directly applicable to the treatment planning system. Nevertheless, some difficulties exist since the whole grid image has to be introduced manually to the treatment planning system via digitizer. This means that, for the moment, the user is obliged to digitize 5,000 grid points and also to verify that all points have been introduced. Improvements on the method, including image transfer via network connection and automatic pattern recognition for the grid points, are under development.
Figure 3. The homemade head phantom. which is able to accommodate different’target’siaes and shapes as well as a number of dosimeters (films, TLDs, chromic films. ionization chamber).
3
2.5
. . .
. .
. i
0
m A
2
A
4
6 Radial
Figure 4. Deviation of the lesion stereotactic coordinates three localization means: (a) through classic angiographic
Distance
a
10
12
(cm)
as a function of the radial distance from the center of the intensifier. images, (b) through uncorrected DSA images and (c) through corrected
We have considered DSA images.
Correction
of DSA images for stereotactic
This will make the method more efficient and less timeconsuming for the user. ACKNOWLEDGEMENTS The authors are indebted to Dimitris Pelekoudas for his valuable advice in the computer application of the method. This project was supported by the Bodosakis Foundation.
REFERENCES 1 Bergstrom M, Greitz T, Ribbe T. A method of stereotactic localization adopted for conventional and digital radiography. Neuroradiology 1986 ; 28 : 100-4.
localization
493
2 Chakraborty DP. Image intensifier distortion correction. Med Phys 1987 ; 14 : 249-52. 3 Gronenschild E. The accuracy and reproducibility of a global method to correct the geometric image distortion in the x-ray image chain. Med Phys 1997 ; 24 : 1875-88. 4 Kappas C, Theodorou K, Kardamakis D, Maraziotis T, Dimopou10s I, Papadakis I, et al. Design, construction and installation of a new stereotactic system for single dose and fractionated radiotherapy. Physica Medica 1997 ; 13: 123-8. 5 Rubin S, Bednarek DR. Wong R. Accurate characterization of image intensifier distortion. Med Phys 1991 ; 18 : 1145-51. 6 Schad LR, Ehricke HH, Wowra B, Layer G, Engenhart R, Kauczor HU, et al. Correction of spatial distortion in magnetic resonance angiography for radiosurgical treatment planning of cerebral arteriovenous malformations. Magn Reson Imaging 1992 ; 10 : 609-21.
1999 ; 3 : 489-93 scientifiques et mCdicales Elsevier
SAS. Tous droits r&xv&
Technical note
A simple method for the correction of distorted digital angiographic for stereotactic target localization
images
K. Theodorou 1,J.C. Rosenwaldz, D. Siamplis 3, D. Karnabatidis 3, C. Kappas 1 ’ Medical Physics Department, University of Patras, 26500 Parras; 2Medical Physics Department, Institute Curie, 26, rue d’lllm, Paris, France; 3 Department of Radiology, University qf Patras, 26500 Part-as, Greece Corresponding
Author:
(Received
the 2 November
SUMMARY The most commonly used imaging modality for the diagnosis and localization of arteriovenous malformations (AVMs) treated with stereotactic radiotherapy is traditional angiography, but it would be desirable to also use digital subtraction angiography (DSA). However, DSA images are distorted due to the electron-optical characteristics of the X-ray image intensifier. For that reason, we have developed a method for the correction of the image distortion. The ISIS II Treatment Planning System (ISIS II TPS), developed at the Curie Institute, has been used for image acquisition and stereotactic localization. A grid phantom has been constructed for determining the distortion of the DSA images. The software developed for the correction has been implemented into the TPS and is based on a correction vector produced by matching the distorted and corrected grid points. The method has been tested for its ability to correct the position of all grid points as well as its effectiveness in real cases as compared to traditional angiography. The maximum displacement of the corrected grid points compared with their original position is measured to be 0.1 mm. The accuracy of the target localization using the corrected DSA images is comparable with traditional angiography localization and falls inside acceptable accuracy limits. In conclusion, this method offers the possibility of using DSA images for stereotactic localization without limiting the requested accuracy. 0 1999 Editions scientifiques et medicales Elsevier SAS digital subtraction localization
angiography
/ distortion
/ stereotactic
1998; accepted the 17 March
1999)
RiSUMi Correction des images angiographiques numbriques en stkrkotaxie. L’angiographie classique est la methode la plus simple et la plus repandue pour le diagnostic et la localisation des malformations arterioveineuses (MAV) trait&es par irradiation stereotaxique. II est souvent souhaitable d’utiliser aussi I’angiographie numerique (DSA) qui est maintenant tres repandue, bien que la distorsion des images DSA (due aux caracteristiques electroniques et optiques de I’intensificateur d’images) pose un probleme majeur. Nous avons done mis au point une methode de correction de la distorsion de I’image. Le systeme de calcul de dose ISIS-II (ISIS-II TPS) developpe a I’institut Curie a ete utilise pour I’acquisition de I’image et la localisation stereotaxique. Un fantome constitue d’une grille a et6 construit pour la quantification de la distorsion de I’image DSA. Le logiciel de correction a et6 implement6 dans le systeme de calcul de dose. Ce logiciel est base sur une matrice de correction obtenue a partir du decalage entre les points de la grille obtenue (ayant subie une distorsion) et ceux de grille originale dont la position est connue. La m&ode proposee a ete testee en etudiant sa capacite de corriger la position de tous les points de la grille, ainsi que son efficacite dans des cas reels ou il est possible de faire une comparaison avec I’angiographie classique. Le decalage maxrmal entre les points de la grille recalcules apres correction de I’image et les points originaux de la grille est de 0,3 mm. La precision de la localisation de la cible en utilisant les images DSA corrigees est du meme ordre et comparable avec la precision de la localisation de I’angiographie classique. Elle se trouve done a I’interieur des limites de precision
K. Theodorou
490
acceptable. Cette m6thode offre la possibilite d’utiliser des images DSA pour des localisations stkkotaxiques saris compromettre la prkcision exigke. 0 1999 iditions scientifiques et mkdicales Elsevier SAS angiographie st6rCotaxique
par soustraction
/ distorsion
/ localisation
In recent years, stereotactic radiotherapy has become a viable alternative for the treatment of inoperable or residual cerebral arteriovenous malformations. Planning radiosurgical treatment requires accurate localization of the nidus. Angiography is the most common diagnostic procedure, as this image modality is best for visualizing the blood vessels. In the majority of the cases, traditional angiography is used for the exact target localization, but it would be desirable to use digital subtraction angiography (DSA) as well. Nevertheless, DSA images are distorted due to the electron-optical characteristics of the Xray image intensifier, so they cannot be directly used for stereotactic target localization. Several methods have been proposed for the correction of the DSA images’distortion [l-4]. Some of them are based on correction vectors against a rectilinear grid and others are based on analytical functions, which could correct some of the characteristics of the distortion. As the distortion is a function of several parameters (electron-optical characteristics of the X-ray image intensifier chain, gravity, magnetic field, etc.), a complete correction is difficult to perform. In stereotactic treatment of arteriovenous malformations, the calculation of the target coordinates is based on the exact determination of the stereotactic localizers, which appear as points on the anterior-posterior and lateral angiographic images [5]. This work proposes a simple method for the correction of the distorted localizers’position and in consequence the correct determination of the target position, applied directly to the treatment planning system.
METHODS
AND MATERIALS
The Treatment Planning System (TPS) used was the ISIS Treatment Planning System (ISIS TPS), developed at the Curie Institute in Paris. A phantom has been constructed for the correction of image distortion. It is made out of Plexiglas and its dimensions are 36 cm x 36 cm x 1 cm, adequate for the complete coverage of the image intensifier. Inside the Plexiglas plate, a rectilinear grid of steel balls was embedded. The steel balls are 1 mm in diameter and the distance between them is 5 mm. The phantom is placed directly on
et al.
top of the image intensifier in order to avoid magnification, as well as to have the maximum number of points possible appear on the grid image. Once the grid phantom has been placed on the image intensifier, an image is captured and printed on a film. The software for the correction of the image distortion is implemented into the ISIS TPS and is divided into two parts: an independent algorithm for the introduction of the distorted image of the grid, and an algorithm incorporated to the target localization program of ISIS for the correction of the distortion of the target localizers on DSA images.
Introduction of the grid The introduction of the grid image to the TPS is done via digitizer. The distortion presented on digital images acquired from an image intensifier is mainly due to the curvature of the upper surface of the detector. Thus, the photons, which are perpendicular to the center of the image intensifier, are less distorted than the ones found on other parts of the detector. In the present study, the central part of the intensifier is assumed as having no distortion. For the production of the theoretical undistorted grid, the user has to introduce nine central points of the grid image. The digital angiographer scales the image using an arbitrary scaling factor. Knowing that the real distance between two grid points is by construction 5 mm. the program calculates the scaling factor of the image and then automatically produces the theoretical, undistorted grid. The distorted grid points are then acquired via the digitizer and the program verifies that all points have been introduced. The distorted positions of all grid points are kept on record.
Correction of the distortion The method for the distortion correction is based on the displacement of each grid point in the digital image in respect to its original position. The algorithm begins from the center of the image, where there is not supposed to be any distortion, and moves in steps of 5 mm (equal to the distance between the grid points) in the four directions. In this neighborhood it searches for the next point (taking into account that the displacement could not be bigger than the diagonal formed by four grid points), and corrects its position. This procedure is repeated for all points and a record of all the displacements is kept as a function of the point distance from the center. In the case of target localization from two projected orthogonal angiographic images, the system requires the four localization points, the contour of the target as seen in each projection and the target’s center 151. When digital images are used, the algorithm executes the following steps for each image on the above points: - calculates the radial distance between the image center and the point of interest; - searches and finds from the file with the distorted grid points the four points, which surround the point of interest;
Correction of DSA images for stereotactic localization
491
................... ......... :.::::::::::: ......... ................... ....... ......... ............. ................... ................... .............. ............. .... ................... .... ............. ............. ...... :.:: .:: .... .......... ............. .... ................... :................... .::. ........... :: ............. ::.:::. .......... :: ............. :: .............. :.::::::::::, .... ...........
.......... ............... ................. ................. ......... ........ ........... ............ ............. ...
.................
...........
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........... :::: .......... ........ I.:: ............... .... ....... ..... .... .... ............. ....... ......
..........
..........
....... :.::.: ......... ............. .... ........ ....... ............. Figure
. ........... ..........
2.
::,
................... ......... : ........ ....... ......... .......... :.:.:: .......... :.:. ............ ......... ........
:.:.:.:“‘I:::
...................
....
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:.::.
....
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.....
...... ...... ....... :....... : ......... ..... ... ......... ......... ......... ......... ......... ......... ........
................... ...::.............. :... : ........ ..... .: ::........ ::jjj:: ..:.:,::,:::: ......... ........ i ................ ......... ... ......... :.......... ......... ......... ............. ................. ................. :: .:.
:::::::::::::: ........... .... ...........
..:::
:::
Corrected grid.
Figure 1. Distorted grid with a sixth-degree polynomial distortion, symmetrical in all directions, applied to all grid points.
- corrects the point’s position, applying a weighted displacement according to the distance of the point from the surrounding grid points. The above procedure is followed for all points required by the localization program. Finally, the localization is performed using the corrected positions of the localizers. RESULTS The above method has been tested for its ability to correct the position of all grid points as well as for its effectiveness in real cases, as compared with traditional angiography. In the first case, we have applied to the grid points an extreme, fifth-degree polynomial distortion, symmetrical in all directions: r=r+dxr3+exr5
where: r is the radial distance of the point from the image center, d = 0.00021, e = 0.0000031. This kind of polynomial distortion often appears in several digital imaging systems. The choice of the parameters d and e have been made so the resultant distortion would be of several orders of magnitude for the more distal, from the center, points (figure I).
After applying the correction algorithm to all grid points, the maximum displacement of the corrected grid points compared to their original position is measured to be 0.1 mm. The result is shown in figure
2.
The accuracy assessmentof the target localization using corrected DSA images was done by a homemade head phantom, which was able to be accurately repositioned to the immobilization frame [6]. The phantom was made from Plexiglas and could accommodate different target’sizes and shapesas well a number of dosimeters (films, TLDs, chromic films, ionization chamber), and has been used for dosimetric measurements as well as for verification purposes(figure 3). The’targets,‘with known positions, were spaced in different radial distances from the center of the image intensifier. In total, we have used six target positions. For each target we acquired a set of traditional angiographic images and a set of DSA images. The localization for all targets has been performed using the traditional images, the distorted DSA images and the corrected DSA images, and the resulting target stereotactic coordinates have been compared with their true values (figure 4). The maximum deviation between the corrected image localization and the true ta.rget position was measured to be 1.l mm, while the deviation between classical localization and the corrected DSA was 0.3 mm.
492
K. Theodorou
et al
DISCUSSION
AND
CONCLUSION
One of the major prerequisites for stereotactic radiotherapy is the accurate delineation of the target volume for treatment planning. In this framework, DSA images could be used in the case of arteriovenous malformations treatment, as they provide more information than traditional angiography and help the physicians to determine targets accurately. The proposed method is able to provide equally accurate target localization with traditional angiography and at the same time keep all the advantages of a digital image. This method is simple, not time-consuming as it does not apply the correction to the whole image, and directly applicable to the treatment planning system. Nevertheless, some difficulties exist since the whole grid image has to be introduced manually to the treatment planning system via digitizer. This means that, for the moment, the user is obliged to digitize 5,000 grid points and also to verify that all points have been introduced. Improvements on the method, including image transfer via network connection and automatic pattern recognition for the grid points, are under development.
Figure 3. The homemade head phantom. which is able to accommodate different’target’siaes and shapes as well as a number of dosimeters (films, TLDs, chromic films. ionization chamber).
3
2.5
. . .
. .
. i
0
m A
2
A
4
6 Radial
Figure 4. Deviation of the lesion stereotactic coordinates three localization means: (a) through classic angiographic
Distance
a
10
12
(cm)
as a function of the radial distance from the center of the intensifier. images, (b) through uncorrected DSA images and (c) through corrected
We have considered DSA images.
Correction
of DSA images for stereotactic
This will make the method more efficient and less timeconsuming for the user. ACKNOWLEDGEMENTS The authors are indebted to Dimitris Pelekoudas for his valuable advice in the computer application of the method. This project was supported by the Bodosakis Foundation.
REFERENCES 1 Bergstrom M, Greitz T, Ribbe T. A method of stereotactic localization adopted for conventional and digital radiography. Neuroradiology 1986 ; 28 : 100-4.
localization
493
2 Chakraborty DP. Image intensifier distortion correction. Med Phys 1987 ; 14 : 249-52. 3 Gronenschild E. The accuracy and reproducibility of a global method to correct the geometric image distortion in the x-ray image chain. Med Phys 1997 ; 24 : 1875-88. 4 Kappas C, Theodorou K, Kardamakis D, Maraziotis T, Dimopou10s I, Papadakis I, et al. Design, construction and installation of a new stereotactic system for single dose and fractionated radiotherapy. Physica Medica 1997 ; 13: 123-8. 5 Rubin S, Bednarek DR. Wong R. Accurate characterization of image intensifier distortion. Med Phys 1991 ; 18 : 1145-51. 6 Schad LR, Ehricke HH, Wowra B, Layer G, Engenhart R, Kauczor HU, et al. Correction of spatial distortion in magnetic resonance angiography for radiosurgical treatment planning of cerebral arteriovenous malformations. Magn Reson Imaging 1992 ; 10 : 609-21.