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Automatic noise robust registration of dental radiographs for implants using strategic local correlation
International Congress Series 1268 (2004) 1157 – 1161
www.ics-elsevier.com
Automatic noise robust registration of dental radiographs for implants using strategic local correlation Won-Jin Yi a,b,*, Min-Suk Heo a,b, Sam-Sun Lee a,b, Soon-Chul Choi a,b, Sun-Bok Lee a a
Department of Oral and Maxillofacial Radiology, BK21, College of Dentistry, Seoul National University, Seoul, South Korea b Dental Research Institute, College of Dentistry, Seoul National University, Seoul, South Korea
Abstract. We have developed an automatic registration method without using the manual selection of landmarks. By restricting a geometrical matching of images to a region of interest (ROI), we compare the cross-correlation coefficient only between the ROIs. The transform parameters satisfying maximum of cross-correlation between the local regions are searched iteratively by a fast searching strategy. The developed method can match the images corrupted by Gaussian noise with the same accuracy for the images without any transform simulation. The application of the developed method to radiographs of dental implants provides an automatic noise robust registration with high accuracy in almost real time. D 2004 CARS and Elsevier B.V. All rights reserved. Keywords: Digital subtraction radiography; Automatic registration for dental radiographs; Local correlation
1. Introduction Digital subtraction radiography (DSR) is a useful technique for diagnosing subtle changes in radiographic density by longitudinal evaluation of serial radiographs of the same anatomical region. Most of DSR methods currently used are based on manual registration techniques [1,2]. In these methods, the landmarks or reference points are marked manually in both images to be registered or in only one of them. Exquisite attention to detail is required during selecting reference points. Therefore, the quality of adjustment is affected by degree of precision in positioning landmarks. As a result, the registration depends on observer experience placing the landmarks. In this study, we have developed an automatic registration method without using the manual selection of reference points.
* Corresponding author. Department of Oral and Maxillofacial Radiology, BK21, College of Dentistry, Seoul National University, Seoul, South Korea. Tel.: +82-2-760-3049; fax: +82-2-744-3919. E-mail address: [email protected] (W.-J. Yi). 0531-5131/ D 2004 CARS and Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2004.03.060
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2. Materials and methods In DSR, reference point-based algorithms have been used affine or perspective (projective) transforms to achieve alignment between two intra-oral radiographs. All the components of tube, object, and sensor in intra-oral radiography may be moved and rotated between the acquisitions of two radiographs. Because the transforms are based on approximations of 18 displacements of the system [3], the transform parameters may be different in local areas of interest. To overcome these problems, we restricted a geometrical matching of images to a local region before alignment. A region of interest (ROI) was selected as a rectangle window in a baseline image or in a follow-up image. This allowed one to compare only the similarity measure between the ROIs of two radiographs. The measure used for comparing similarity between two local regions was cross-correlation coefficient (Eq. (1)). The transform parameters satisfying maximum of cross-correlation between local regions was selected finally. X
ðI2 ðx; yÞ I2 ÞðI1 ðx; yÞ I1 Þ
ðx;yÞaR
ffi ffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CðI1 ; I2 Þ ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X X ðI2 ðx; yÞ I2 Þ2 ðI1 ðx; yÞ I1 Þ2 ðx;yÞaR
ð1Þ
ðx;yÞaR
where I1: a reference image; I2: an unregistered image; R: a selected ROI; I1 ; I2: means of I1 and I2 in a ROI (R). The parameters were searched iteratively by a fast searching algorithm of ‘down hill simplex method’ [4]. When calculating the similarity measure between local regions, we reformatted only a local region from a follow-up image that corresponded to a ROI selected in a baseline image by reverse mapping. In this approach, every pixel in the follow-up image was not necessarily processed. Only pixels that appeared in the local output image were actually transformed. It could minimize the time required to transform the image in iterative searching of transform parameters considerably. In addition to this, the searching of transform parameters proceeded in two stages. First, transform parameters were searched on the 1/4 scale image coarsely and then, the fine registration was performed on the original scale image. The result of coarse registration was used as initial parameters for the following searching. This strategy also reduced the parameter searching time. The density histogram of a transformed image was matched to that of the other image using the method developed by Ruttimann et al. [5]. Then, the one image was subtracted from the other and 128 gray levels were added to the resultant image. The accuracy of image registration was measured as a standard deviation of the subtraction image (SDS). The accuracy measure should be zero for perfect registration of an image pair with only geometric variations. It was calculated over a sample region that included the pre-selected ROI for each image pair. The performance of the developed method was compared with the manual method.
W.-J. Yi et al. / International Congress Series 1268 (2004) 1157–1161
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3. Results Fig. 1 shows overall procedure for registration of dental implant radiographs using the developed method. A ROI as a rectangle window is selected in a follow-up image (Fig. 1(A)). The initial ROI in a baseline image is created automatically at the same position (Fig. 1(B)). The only area corresponding to the ROI is reformatted from the baseline image using the updated parameters at each iteration. The whole matched image is reformatted from the baseline image using the final parameters by a bilinear interpolation method (Fig. 1(C)). The follow-up image is subtracted from the reformatted image with contrast correction and 128 gray levels are added to all pixels (Fig. 1(D)). We can observe quantitative and qualitative changes of the bone at the alveolar ridge around the implant fixture from the subtraction image. The performance of the developed method was also analyzed using simulation images created from the in vivo implant images. The images were produced by transforming the original intra-oral image by a rotation-scale-translation (RST) transform in the presence of noise. The performance accuracy was evaluated using images with increasing noise levels. The noise level is quantified as a square root of noise variance. The accuracy between
Fig. 1. Overall procedure for registration of dental implant radiographs. (A) A ROI selected as a rectangle window in a follow-up image. (B) The initial ROI created automatically at the same position in a baseline image. (C) Whole matched image reformatted from the baseline image using the final parameters. (D) Subtraction image of the follow-up image from the reformatted image after contrast correction.
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Fig. 2. Mean SDS values over different simulations for 5 implant images with increasing noise variance.
original and registered images is measured over the ROI used for matching two images. The data in Fig. 2 represents the mean SDS values over different simulations for five implant images at each noise level. The horizontal axis indicates the SDS values from images without any transform simulation. It represents the amount of the noise added to the original image. The vertical axis indicates the mean SDS values over 100 simulation images at each noise level. There is no significant difference between two means of SDS with increasing the noise levels ( P>0.05, paired t-test). Generally, the developed method can register the images corrupted by Gaussian noise of large variances with success. Table 1 SDS values for 11 pairs of implant images by affine, perspective transform and manual methods Implant no.
Affine
Perspective
Manual 1
Manual 2
1 2 3 4 5 6 7 8 9 10 11 Mean
11.0 25.3 18.8 11.9 17.9 16.9 26.0 24.0 21.5 11.7 22.8 18.9
10.7 24.9 18.8 11.8 18.1 16.4 25.0 23.7 21.1 11.5 22.5 18.6
11.3 31.5 20.3 12.2 19.6 18.3 27.6 24.9 23.8 13.4 24.9 20.7
15.9 27.0 22.8 12.2 21.0 20.5 39.9 26.3 22.6 14.1 30.0 22.9
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Two dentists with clinical experiences in a department of oral and maxillofacilal radiology registered implant images manually. Table 1 lists the SDS values for 11 pairs of implant images by affine, perspective transform and manual methods. The results by affine and perspective methods show significant differences to those by manual methods ( P < 0.01, paired t-test). The perspective method provided higher accuracy than any other methods. Overall, the registration accuracy of the perspective method measured by SDS showed a 17% improvement over the manual method. 4. Discussion The registration based on a local ROI has several advantages. First, it can provide more accurate matching for the selected ROI than for any other areas in the radiographs. Because the transforms that have been used in DSR for intra-oral radiographs are based on geometrical approximations of the imaging system, the parameters representing transforms may be different according to the local areas of interest. Second, the ROI based method significantly decreases the processing time in iterative searching of transform parameters. It can considerably minimize the time required not only to calculate the similarity measure of cross-correlation, but also to reformat a region corresponding area by considering only the selected ROI. The parameter searching time can be further reduced by using the 1/4 scale images at the beginning of the searching. Third, the two ROIs selected in both images can provide initial parameters for approximate translation in searching. The difference of centers of mass for the ROI areas can be used as an initial translation of the two images. When one of the images is transformed with large translation value, this strategy can help to prevent the search from getting stuck in a local maximum and to find a global maximum faster. The developed method could register the images corrupted by Gaussian noise of large variances with the same accuracy for the images without any transform. The method was also independent of the observer because it did not use the manually selected landmarks. The developed method can be used in clinical applications for DSR without any special experiences or education with high accuracy. Therefore, the method for DSR can provide a useful diagnostic tool to be employed in such areas as dental implants for non-radiologists. References [1] J. Samarabandu, et al., Algorithm for the automated alignment of radiographs for image subtraction, Oral Surg. Oral Med. Oral Pathol. 77 (1994) 75 – 79. [2] V. Byrd, et al., Semiautomated image registration for digital subtraction radiography, Oral Surg. Oral Med. Oral Pathol. Oral Radiol. Endo. 85 (1998) 473 – 478. [3] T.M. Lehmann, H.G. Gro¨ndahl, D.K. Benn, Computer-based registration for digital subtraction in dental radiology, Dentomaxillofacacial Radiol. 29 (2000) 323 – 346. [4] W.H. Press, et al., Numerical Recipes in C, Cambridge Univ. Press, Cambridge, 1992, pp. 394 – 455. [5] U.E. Ruttiman, R.L. Webber, E. Schmidt, A robust digital method for film contrast correction in subtraction radiography, J. Periodontal Res. 21 (1986) 486 – 495.
www.ics-elsevier.com
Automatic noise robust registration of dental radiographs for implants using strategic local correlation Won-Jin Yi a,b,*, Min-Suk Heo a,b, Sam-Sun Lee a,b, Soon-Chul Choi a,b, Sun-Bok Lee a a
Department of Oral and Maxillofacial Radiology, BK21, College of Dentistry, Seoul National University, Seoul, South Korea b Dental Research Institute, College of Dentistry, Seoul National University, Seoul, South Korea
Abstract. We have developed an automatic registration method without using the manual selection of landmarks. By restricting a geometrical matching of images to a region of interest (ROI), we compare the cross-correlation coefficient only between the ROIs. The transform parameters satisfying maximum of cross-correlation between the local regions are searched iteratively by a fast searching strategy. The developed method can match the images corrupted by Gaussian noise with the same accuracy for the images without any transform simulation. The application of the developed method to radiographs of dental implants provides an automatic noise robust registration with high accuracy in almost real time. D 2004 CARS and Elsevier B.V. All rights reserved. Keywords: Digital subtraction radiography; Automatic registration for dental radiographs; Local correlation
1. Introduction Digital subtraction radiography (DSR) is a useful technique for diagnosing subtle changes in radiographic density by longitudinal evaluation of serial radiographs of the same anatomical region. Most of DSR methods currently used are based on manual registration techniques [1,2]. In these methods, the landmarks or reference points are marked manually in both images to be registered or in only one of them. Exquisite attention to detail is required during selecting reference points. Therefore, the quality of adjustment is affected by degree of precision in positioning landmarks. As a result, the registration depends on observer experience placing the landmarks. In this study, we have developed an automatic registration method without using the manual selection of reference points.
* Corresponding author. Department of Oral and Maxillofacial Radiology, BK21, College of Dentistry, Seoul National University, Seoul, South Korea. Tel.: +82-2-760-3049; fax: +82-2-744-3919. E-mail address: [email protected] (W.-J. Yi). 0531-5131/ D 2004 CARS and Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2004.03.060
1158
W.-J. Yi et al. / International Congress Series 1268 (2004) 1157–1161
2. Materials and methods In DSR, reference point-based algorithms have been used affine or perspective (projective) transforms to achieve alignment between two intra-oral radiographs. All the components of tube, object, and sensor in intra-oral radiography may be moved and rotated between the acquisitions of two radiographs. Because the transforms are based on approximations of 18 displacements of the system [3], the transform parameters may be different in local areas of interest. To overcome these problems, we restricted a geometrical matching of images to a local region before alignment. A region of interest (ROI) was selected as a rectangle window in a baseline image or in a follow-up image. This allowed one to compare only the similarity measure between the ROIs of two radiographs. The measure used for comparing similarity between two local regions was cross-correlation coefficient (Eq. (1)). The transform parameters satisfying maximum of cross-correlation between local regions was selected finally. X
ðI2 ðx; yÞ I2 ÞðI1 ðx; yÞ I1 Þ
ðx;yÞaR
ffi ffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CðI1 ; I2 Þ ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X X ðI2 ðx; yÞ I2 Þ2 ðI1 ðx; yÞ I1 Þ2 ðx;yÞaR
ð1Þ
ðx;yÞaR
where I1: a reference image; I2: an unregistered image; R: a selected ROI; I1 ; I2: means of I1 and I2 in a ROI (R). The parameters were searched iteratively by a fast searching algorithm of ‘down hill simplex method’ [4]. When calculating the similarity measure between local regions, we reformatted only a local region from a follow-up image that corresponded to a ROI selected in a baseline image by reverse mapping. In this approach, every pixel in the follow-up image was not necessarily processed. Only pixels that appeared in the local output image were actually transformed. It could minimize the time required to transform the image in iterative searching of transform parameters considerably. In addition to this, the searching of transform parameters proceeded in two stages. First, transform parameters were searched on the 1/4 scale image coarsely and then, the fine registration was performed on the original scale image. The result of coarse registration was used as initial parameters for the following searching. This strategy also reduced the parameter searching time. The density histogram of a transformed image was matched to that of the other image using the method developed by Ruttimann et al. [5]. Then, the one image was subtracted from the other and 128 gray levels were added to the resultant image. The accuracy of image registration was measured as a standard deviation of the subtraction image (SDS). The accuracy measure should be zero for perfect registration of an image pair with only geometric variations. It was calculated over a sample region that included the pre-selected ROI for each image pair. The performance of the developed method was compared with the manual method.
W.-J. Yi et al. / International Congress Series 1268 (2004) 1157–1161
1159
3. Results Fig. 1 shows overall procedure for registration of dental implant radiographs using the developed method. A ROI as a rectangle window is selected in a follow-up image (Fig. 1(A)). The initial ROI in a baseline image is created automatically at the same position (Fig. 1(B)). The only area corresponding to the ROI is reformatted from the baseline image using the updated parameters at each iteration. The whole matched image is reformatted from the baseline image using the final parameters by a bilinear interpolation method (Fig. 1(C)). The follow-up image is subtracted from the reformatted image with contrast correction and 128 gray levels are added to all pixels (Fig. 1(D)). We can observe quantitative and qualitative changes of the bone at the alveolar ridge around the implant fixture from the subtraction image. The performance of the developed method was also analyzed using simulation images created from the in vivo implant images. The images were produced by transforming the original intra-oral image by a rotation-scale-translation (RST) transform in the presence of noise. The performance accuracy was evaluated using images with increasing noise levels. The noise level is quantified as a square root of noise variance. The accuracy between
Fig. 1. Overall procedure for registration of dental implant radiographs. (A) A ROI selected as a rectangle window in a follow-up image. (B) The initial ROI created automatically at the same position in a baseline image. (C) Whole matched image reformatted from the baseline image using the final parameters. (D) Subtraction image of the follow-up image from the reformatted image after contrast correction.
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Fig. 2. Mean SDS values over different simulations for 5 implant images with increasing noise variance.
original and registered images is measured over the ROI used for matching two images. The data in Fig. 2 represents the mean SDS values over different simulations for five implant images at each noise level. The horizontal axis indicates the SDS values from images without any transform simulation. It represents the amount of the noise added to the original image. The vertical axis indicates the mean SDS values over 100 simulation images at each noise level. There is no significant difference between two means of SDS with increasing the noise levels ( P>0.05, paired t-test). Generally, the developed method can register the images corrupted by Gaussian noise of large variances with success. Table 1 SDS values for 11 pairs of implant images by affine, perspective transform and manual methods Implant no.
Affine
Perspective
Manual 1
Manual 2
1 2 3 4 5 6 7 8 9 10 11 Mean
11.0 25.3 18.8 11.9 17.9 16.9 26.0 24.0 21.5 11.7 22.8 18.9
10.7 24.9 18.8 11.8 18.1 16.4 25.0 23.7 21.1 11.5 22.5 18.6
11.3 31.5 20.3 12.2 19.6 18.3 27.6 24.9 23.8 13.4 24.9 20.7
15.9 27.0 22.8 12.2 21.0 20.5 39.9 26.3 22.6 14.1 30.0 22.9
W.-J. Yi et al. / International Congress Series 1268 (2004) 1157–1161
1161
Two dentists with clinical experiences in a department of oral and maxillofacilal radiology registered implant images manually. Table 1 lists the SDS values for 11 pairs of implant images by affine, perspective transform and manual methods. The results by affine and perspective methods show significant differences to those by manual methods ( P < 0.01, paired t-test). The perspective method provided higher accuracy than any other methods. Overall, the registration accuracy of the perspective method measured by SDS showed a 17% improvement over the manual method. 4. Discussion The registration based on a local ROI has several advantages. First, it can provide more accurate matching for the selected ROI than for any other areas in the radiographs. Because the transforms that have been used in DSR for intra-oral radiographs are based on geometrical approximations of the imaging system, the parameters representing transforms may be different according to the local areas of interest. Second, the ROI based method significantly decreases the processing time in iterative searching of transform parameters. It can considerably minimize the time required not only to calculate the similarity measure of cross-correlation, but also to reformat a region corresponding area by considering only the selected ROI. The parameter searching time can be further reduced by using the 1/4 scale images at the beginning of the searching. Third, the two ROIs selected in both images can provide initial parameters for approximate translation in searching. The difference of centers of mass for the ROI areas can be used as an initial translation of the two images. When one of the images is transformed with large translation value, this strategy can help to prevent the search from getting stuck in a local maximum and to find a global maximum faster. The developed method could register the images corrupted by Gaussian noise of large variances with the same accuracy for the images without any transform. The method was also independent of the observer because it did not use the manually selected landmarks. The developed method can be used in clinical applications for DSR without any special experiences or education with high accuracy. Therefore, the method for DSR can provide a useful diagnostic tool to be employed in such areas as dental implants for non-radiologists. References [1] J. Samarabandu, et al., Algorithm for the automated alignment of radiographs for image subtraction, Oral Surg. Oral Med. Oral Pathol. 77 (1994) 75 – 79. [2] V. Byrd, et al., Semiautomated image registration for digital subtraction radiography, Oral Surg. Oral Med. Oral Pathol. Oral Radiol. Endo. 85 (1998) 473 – 478. [3] T.M. Lehmann, H.G. Gro¨ndahl, D.K. Benn, Computer-based registration for digital subtraction in dental radiology, Dentomaxillofacacial Radiol. 29 (2000) 323 – 346. [4] W.H. Press, et al., Numerical Recipes in C, Cambridge Univ. Press, Cambridge, 1992, pp. 394 – 455. [5] U.E. Ruttiman, R.L. Webber, E. Schmidt, A robust digital method for film contrast correction in subtraction radiography, J. Periodontal Res. 21 (1986) 486 – 495.