Removal of the Shadow of Cervical Vertebrae from Panoramic X-Ray Images with a Tomosynthesis Method ()
1. Introduction
In dental imaging, many imaging techniques and imaging receptors are used in intraand extra-oral dental radiology [1]. Among these imaging techniques, dental panoramic radiography [2,3] is a technique which images teeth and jaw bones aligned on a predefined curved plane. Two types of detector are used for this imaging: one is a scintillator with a charge coupled device (CCD) detector and the other is a semiconductor detector such as cadmium telluride (CdTe) [4]. The sensitivity of the former detector is basically low, requiring a time delay integration to improve the signal to noise ratio [5]. Moreover, the response speed of the CCD detector is too slow to acquire many images of the teeth and jaw bones with slightly different angles to the dental arch. This restricts the application of a tomosynthesis method [6] that is represented by the “shift-and-add” operations to many images acquired with slightly different angles. On the other hand, because the sensitivity and response speed of the latter detector are higher than those of the former one, we can obtain many strip images of an object acquired with slightly different angles. This enables us to reconstruct an image of the teeth and jaw bones focused at a given depth with a tomosynthesis method [7,8]. Once we acquire data of a patient, we can freely reconstruct a desired layer of a given depth, and so application of the tomosynthesis technique is gradually expanding in the field of panoramic imaging. In the tomosynthesis technique, a shift-amount at each angular position defined by the location of an x-ray source and detector is required in the process of the shift-and-add operation. This shiftamount controls the position of a focused plane in the dental arch, and so if we use a large shift-amount in the process of focusing, we can also reconstruct cervical vertebrae with the strip images originally acquired. Conventional panoramic radiography is intended to focus on the teeth and jaw bones, as a result of which a blurred shadow of the cervical vertebrae overlaps on the image, thereby reducing the image contrast at the front teeth.
Suppose an image model, in which objects to be reconstructed are located only on the dental arch and curved area located symmetrical to the dental arch. We named this curve that passes through the cervical vertebrae “a cervical curve.” The location of the cervical curve is symmetrical to that of the dental arch, and so we can define the shift-amount table that is required for reconstructing the image of the cervical vertebrae. Once we make these two shift-amount tables, we can reconstruct two panoramic images, one being the conventional image of the teeth and jaw bones on which a blurred shadow of the cervical vertebrae overlaps, and the other that of the cervical vertebrae on which a blurred shadow of the teeth and jaw bones overlaps. Using above two images, the shadow of the cervical vertebrae can be removed from the conventional panoramic image with the help of image processing techniques. This paper proposed a new method to remove the shadow of the cervical vertebrae from the conventional panoramic image focused on the teeth and jaw bones. The validity of the proposed method was evaluated with the clinically obtained data of two patients.
2. Materials and Method
2.1. Method
In our proposed method, the tomosynthesis method plays a very important role. To measure the shift-amount required for a “shift-and-add” operation in the tomosynthesis method, we used a calibration phantom [8]. In the phantom, several thin wires are located at specified angular positions on the standard imaging plane of the dental arch, and the shift-amount at each position is measured as the distance needed to match the positions of a thin wire between the adjacent frame images. Using this measurement, we can obtain a table of the shift-amount at each specified angular position. The details are described in the literature [8]. Figure 1 shows an example of the shift-amount table of an actual dental panoramic apparatus. During the rotation of the x-ray source and detector around an object, several thousands strip images of the object are acquired sequentially. And thus, the
Figure 1. Shift-amount table for reconstructing an image of the dental arch.
angular position of the detector corresponds to the frame number of a series of the strip images. If the distance between the x-ray source and dental arch is always the same for any angular position, the shift-amount becomes a constant value. However, the rotation center of the x-ray source and detector moves on a specified orbit in the conventional panoramic apparatus, as a result of which the distance between the x-ray source and dental arch changes, and the shift-amount table becomes a cosine-shaped curve as shown in Figure 1.
The cervical vertebrae are located on a curve that is almost symmetrical to the dental arch, and so we assumed an imaginary curve on which the cervical vertebrae are located. We named this curve “a cervical curve” as shown in Figure 2. To reconstruct the cervical vertebrae, a new shift-amount table is required. If the distance between rotation center C and point P on the dental arch is large (Figure 3(a)), the shift-amount, which corresponds to the moved distance (dSd) of point P on the dental arch for small angular movement (dq), becomes larger. If we exchange the positions of the x-ray source and detector as shown in Figure 3(c), the distance between rotation center C and point Q on the cervical curve becomes smaller, and the shift-amount, which corresponds to the moved distance (dSc) of point Q on the cervical curve for small angular movement (dq), becomes smaller. As a result, the shift amount table for the cervical curve will be nearly symmetrical (upside down) to that of the dental arch (Figures 3(b) and (d)). The theoretical background to calculate the shift-amount table is shown in the Appendix. An example of the shiftamount table for reconstructing the cervical vertebrae is shown in Figure 4.
Next, we will consider the relationship between the dental arch and cervical curve on a tomosynthesis image. For the illustration, we simplify the imaging objects, in which only two objects are located along the dental arch and cervical curve. Suppose the object distribution on the dental arch f1(α,β) and that of the cervical curve f2(α,β) as shown in Figure 5(a), where α indicates the position
Figure 2. Dental arch and an assumed cervical curve.
Figure 3. Geometry of the x-ray source and detector, and the shift-amount tables to make a tomosynthesis image. (a) A common geometry in the panoramic imaging, (b) A shift-amount table required to focus on the dental arch, (c) A geometry for making the tomosynthesis image of the cervical vertebrae, and (d) A shift-amount table required to focus on the cervical curve.
Figure 4. Shift-amount table for reconstructing an image of the cervical vertebrae.
along the dental arch or cervical curve, and β is the vertical position to the α-axis. The α- and β-axes correspond to the horizontal and vertical axes of a panoramic image, and α is the position on the curve of the dental arch for the case of the panoramic image of the tooth and jaw bones, and also α is the position on the cervical curve for the case of the panoramic image of the cervical vertebrae.
And we also assume the blurring functions h1(α;x) and h2(α;x). h1(α;x) is a blurring function at position α on the dental arch when the focal point is located on the cervical curve, and h2(α;x) is a blurring function at position α on the cervical curve when the focal point is located on the dental arch. x is a dummy variable in the α-axis. These functions are shift-variant for position α, that is, a blurring region depends on the shift-amount at position α. These functions are modeled with a Gaussian function whose full width at half maximum (FWHM) corresponds to the shift-amount at each angular position. The shape of the blurring function does not change markedly in the neighborhood of α, and so we assume that these functions are regionally shift-invariant in the small area for x = α.
A given tomosynthesis image can be represented by a
(a) (b) (c)
Figure 5. Geometry 1 (the rotation center of the x-ray source and detector located far from the dental arch). (a) Relationship between the two shift-amount tables and blurring functions, (b) The case when a panoramic image is focused on the dental arch, and (c) The case when a panoramic image is focused on the cervical curve.
summation of two images: one is an image focused on the teeth and jaw bones or on the cervical vertebrae, and the other is that defocused using one of the above-mentioned blurring functions. That is, tomosynthesis image g1(α,β) that is focused on the dental arch is represented as follows (see Figure 5(b)):
(1)
where 
means a one dimensional convolution operator for variable α. This equation means that the resultant image of the shift-and-add operation is a summation of the focused image of the teeth and jaw bones and the defocused image of the cervical vertebrae. In actual cases, a cross section of the maxillofacial region includes many organs, and we cannot represent the cross section with this simple model. However, the major attenuating objects are high density organs such as teeth and bones, and so the model can be acceptable as the first approximation.
In the same manner, tomosynthesis image g2(α,β) that is focused on the cervical curve is represented as follows (see Figure 5(c)):
(2)
Using the above two equations, we can remove the shadow of the cervical vertebrae that overlaps on the image of the dental arch, as follows:
(3)
Figure 6 show the case in which rotation center C is close to the dental arch, and in this case, the shift-amount required for reconstructing the cervical curve becomes larger as shown in Figure 6(a).
2.2. Materials
In this study, we used clinical data acquired with QRMasterP (Telesystems, Co. Ltd., Osaka, Japan). The number of strip images used for reconstructing a tomosynthesis image was 3600, and the size of a strip image was 50 × 1500 pixels. The size of a pixel was 0.2 × 0.2 mm2. The x-ray tube voltage was 90 kV and tube current was 10 mA. The data acquisition time was 12 sec. Using the above conditions, we acquired data of two patients (male, ages 45 and 52). This study received the approval of the ethics committee of Asahi University, School of Dentistry.
3. Results
Figure 1 shows the shift-amount table measured with the calibration phantom, which is required for reconstructing a panoramic x-ray image of the dental arch. Figure 4 shows the shift-amount table that is required for reconstructing the cervical vertebrae. This table was made by inverting the shape of the shift-amount curve shown in Figure 1. Figure 7(a) shows the original tomosynthesis image [g1(α,β)] focused on the dental arch, on which the shadows of the cervical vertebrae overlaps. Figure 7(b) shows the tomosynthesis image [g2(α,β)] of the cervical vertebrae, on which the shadows of the teeth and jaw bones overlap. Figure 7(c) shows the resultant image [f1(α,β)] of the teeth and jaw bones after removing the shadow of the cervical vertebrae from the original tomosynthesis image [g1(α,β)]. This image clearly visualized the shape of the front teeth and trabeculae in the jaw bones. Figure 8 shows the density profiles of Figures 7(a) and (c). Figure 9" target="_self"> Figure 9 shows the results of the other pa-