Recently, periodontitis has been studied also as related to cardiac diseases and diabetes mellitus. Thus the treatment of periodontitis is very important in the prophylaxis of several diseases. In the diagnosis of periodontitis, dental panoramic apparatus [1] with a tomosynthesis method [2] [3] is used gradually, because the tomosynthesis method can focus on a specified imaging layer in the dental arch and semi-quantitative analysis of the imaged layer is expected to be realized [4] [5] . This panoramic imaging apparatus would be useful, if we could detect the temporal changes around a tooth in the progression of periodontitis. In the dental diagnosis, the difference between an image photographed several weeks or months earlier and that photographed now yields important information about disease progression. Commonly, if we want to detect some changes between two radiographic images, we make a registration of these two images, and subtract one image from the other one. This is a simple approach that can be applied to most cases in digital subtraction angiography, because the photographic geometries of these images are almost the same between these two images. However, in the case of dental panoramic imaging, the deformation of images is markedly affected by the geometrical conditions between the patient’s head and imaging devices [1] . The reasons for the deformation are as follows: 1) a small tilting and/or rotation of the patient’s head makes a large deformation on panoramic images due to the relatively small distance between the x-ray tube and dental arch, and 2) the rotational speed of the detector and x-ray tube along with the movement of the rotational center makes a deformation of panoramic images in the horizontal axis. As a result, the registration of two images is very hard to accomplish. However, if we can succeed in this task, it can be expected to yield useful information for the dental diagnosis and treatment in terms of progression and prognosis.

For the registration methods in dental radiology, a review paper [6] described several transformations to yield an accurate registration. In these approaches on the registration of dental images, a few isolated teeth are targeted [7] -[12] , while there are very few papers that focused on panoramic images [13] . In the case of panoramic images, we also have to take care of the properties of a panoramic apparatus, such as the rotation speed of the detector and x-ray tube, and the geometrical positioning of the dental arch. So a dedicated algorithm is required for making an accurate registration of two temporal images acquired at different times. The purpose of this study is to develop an accurate registration method of two dental panoramic images acquired at different times and with a different geometry. In the proposed method, we normalized the two images using a non-rigid transformation, and conducted an accurate registration with a cross-correlation method using sub-images. Our method is very simple but reasonably effective without requiring annoying manipulations. This paper described the details of our proposed method and the validity of our proposed method.

Figure 6 shows the results of the experiments in terms of the head rotation. Image-A was an image photographed at the initial position and three images (image-B) were photographed at the second time. The three images were acquired without any rotation of the head and with a rotation of 2 or 4 degrees. The difference images are shown in this figure. We set four ROIs (shown in dotted rectangles) in the resultant image and calculated the mean squared error (MSE) and standard deviation (SD). Figure 7 shows the results of the experiments in terms of the face tilting. Image-A was the same as that used in the previous experiment. And three images (image-B) were photographed at the second time. The three images were acquired without any tilting of the face and with an upward tilting of 2 or 4 degrees. The difference images are shown in this figure. Figure 8 shows the shadow of the aluminum plates and the position of the ROI for quantitative analysis. The lower graph shows the relationship between the averaged intensity in the difference image and the thickness of the aluminum plate. In this graph, we added a theoretical curve.

The image registration of dental panoramic images is very important in the diagnosis of dental diseases, and this technique is also applicable to postmortem investigations. However, the registration of two images is very difficult in usual cases compared to the digital subtraction angiography commonly used in clinical practice, because the shapes of the photographed teeth and jaw bones significantly differ from each other. This is mainly caused by the geometrical photographic conditions in the process of data acquisition. The distance between the targeted regions such as teeth/jaw bones and the x-ray tube is short, and so a small difference in the positioning of a patient’s head makes a large deformation in a panoramic x-ray image. And so a dedicated approach is required for

the registration of panoramic x-ray images. Our proposed method consisted of two steps: one is a global registration and the other is local registration. In the process of the former, we used a manual operation to identify the targeted area. The number of teeth may change sometimes, if the interval between the two panoramic x-ray im-

ages is long, and so a full automatic selection of a targeted area may introduce a large registration error. However, the interactive operation in our method requires only the decision of seven positions around the upper or lower teeth, and so this operation is not burdensome to the dentist. In the selection of five anchor points along a teeth row, we need not worry about the accuracy of positioning between two acquisitions, because the curve of a teeth row is used for forming the targeted area approximately, and an accurate registration process is performed in the local registration. To make a well smoothed curve, we used the Lagrange polynomial. In our method, we pay attention to the length of a segmented curve such as. This length may change if the center of the head shifts slightly from the desired position for panoramic imaging. In addition, if the rotation speed of the x-ray tube and detector changes slightly, the length changes. However, the length changes gradually and it depends on the angular position, and so we used the Lagrange polynomial to calculate the position depending on the scaling ratio determined at each angular position. The above transformation improves the accuracy of the registration as a preprocessing step of panoramic x-ray images. In the local registration, we calculated the cross-correlation of sub-images. To increase the registration accuracy, we conducted this processing in three steps with sub-images with different sizes. The results of the experiments showed that if the two images were acquired under ideal conditions, the registration accuracy would be very high as shown in Figure 6. If the head rotated slightly, there were very small differences over all teeth. And the error increased when the rotation angle increased. In this experiment, we evaluated the rotation of the head by 4 degrees, which is an acceptable mis-positioning in a clinical study. For the tilting of the face, our proposed method yielded good results in registration between two images. In this experiment, we evaluated the tilting of the face by 4 degrees. The registration process was successful in this case, although a shadow of the cervical vertebrae appeared in the center of the processed image (Figure 7). We surmised that the path of the x-rays was more sensitive to the cervical vertebrae as compared to the case of rotation of the head. The experiment to quantify the change in different images showed that there was linearity between the intensity change and the thickness of the aluminum plate. However, the error between the measured value and the theoretical one increased as the thickness increased. This is caused by the beam hardening effect of x-rays.

In conclusion, we developed a new method to detect differences between two dental panoramic images acquired at different times. The method consisted of a non-rigid transformation of panoramic images and registration of transformed images in a hierarchical structure. The validity of our method was clarified with the results of experiments using a skull phantom. The results of registration showed that small changes can be detected with the help of difference image.

Let us assume the lengths of a bone and tooth to be l_b and l_t, and the linear attenuation coefficients of these materials m_b and m_t, respectively. The intensity of x-rays emitted as I₀ changes after passing through these materials is denoted as follows:

If there was some change in density of the alveolar bone or jaw bone due to periodontitis, the product of m_b and l_b would change as and. The measured intensity in the panoramic x-ray image at the different time can be denoted as follows:

If we divide these two equations and take a logarithm, the result becomes as follows:

This value corresponds to D(i, j) in Equation (5). If the intensity of x-rays changes between two images, this component remains as a bias component in the resultant image. So we can remove this component by subtracting the average value of image D(i, j), and we can detect the difference of two images with this image. The difference image may be expected to be useful as an index in diagnosing periodontitis or osteoporosis.