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In order to extract the pixels of teeth from 3D Cone Beam Computed Tomography (CBCT) image, in this paper, a novel 3D segmentation approach based on deformable surface mode is developed for 3D tooth model reconstruction. Different forces are formulated to handle the segmentation problem by using different strategies. First, the proposed method estimates the deformation force of vertex model by simulating the deformation process of a bubble under the action of internal pressure and external force field. To handle the blurry boundary, a “braking force” is proposed deriving from the 3D gradient information calculated by transforming the Sobel operator into three-dimension representation. In addition, a “border reinforcement” strategy is developed for handling the cases with complicate structures. Moreover, the proposed method combines affine cell image decomposition (ACID) grid reparameterization technique to handle the unstable changes of topological structure and deformability during the deformation process. The proposed method was performed on 510 CBCT images. To validate the performance, the results were compared with those of two other well-studied methods. Experimental results show that the proposed approach had a good performance in handling the cases with complicate structures and blurry boundaries well, is effective to converge, and can successfully achieve the reconstruction task of various types of teeth in oral cavity.

Recently, more and more people pay attention to dental healthy [

3D scanning technology can obtain a more accurate description of exacted shape of tooth crown surface [

Deformable models, which include the popular deformable contours, or snakes, and deformable surfaces, are a powerful segmentation technique designed to meet the task of medical image segmentation and have proved to be successful in boundary integration and feature extraction [

In this paper, an effective segmentation approach based on deformable surface model is proposed which is able to conduct the segmentation and reconstruction process simultaneously while working on 3D CBCT volume data directly instead of individual slices. Based on deformable triangle mesh, the proposed method estimates the deformation force of vertex model by simulating the deformation process of a bubble under the action of internal pressure and external force field. To handle the blurry boundary, a “braking force” is proposed deriving from the 3D gradient information calculated by using 3D Sobel operator. In addition, a “border reinforcement” strategy is developed for handling the cases with complicate structures by weighting the points neighboring to each vertex according to its corresponding movement. Moreover, the proposed method combines ACID grid reparameterization technique to handle the unstable changes of topological structure and deformability during the deformation process. By combining CBCT and 3D scanning data, both entire topology structure information and occlusal surface details can be integrated conveniently. Experimental results with the implemented 3D reconstruction algorithm with CBCT image demonstrate that the proposed approach is efficient to segment the 3D images with complicate structure and blurry boundaries well and can successfully achieve the reconstruction task of various types of teeth in oral cavity.

Section

The purpose of the proposed method is to partition the image into object and background regions to finish the 3D model reconstruction. First, a triangular mesh model is initialized and placed into the volume data space. For each vertex, a deformation force is defined according to the image information and triangular mesh information that drives the initial triangular mesh model to slowly deform, one per a time, following forces that keep the surface well-spaced and smooth, while attempting to move toward the target’s edge. The deformation process is iterated until the deformation model fits to the target shape in volume data. Finally, a reparameterization is employed to keep the uniformity of deformed mesh model. The block diagram of the proposed method is shown in Figure

Block diagram of the proposed method.

The segmentation of the proposed method is started by specifying initial surface model. For producing the initial surface model, a tessellated sphere is generated by starting with an icosahedron and iteratively subdividing each triangle into several smaller triangles. The spherical tessellated surface is initially centered on a point selected from any slice of CBCT images produced by user’s interaction, with its radius set to half of the estimated target radius. An example of initial deformation model is shown in Figure

Example of initial deformation model: (a) icosahedron, (b) subdividing of icosahedron, and (c) sphere.

A deformable surface model is defined by a mesh within an image domain that allows an initialized model inside the target to deform by the forces coming from the surface itself and external forces derived from image data; this model is then “fitted” to the target surface in the image when it reaches an equilibrium in which the total force acting on each vertex is zero:

The proposed approach simulates the deformation process of a bubble under the action of internal pressure and external force in the gradient field of CBCT volume data. Assuming that

At the initial time, the bubble is in a balance state. Then we fill the bubble with predetermined pressure

The external pressure of vertex is

The driving force that drives the model to deform is provided by two aspects: internal pressure and intensity information of the image. The intensity-based thresholding is one of the most widely used image preprocessing methods because of its simplicity and ease to implement it. In this paper, we model a basic driving force based on local intensity thresholding to distinguish foreground and background firstly [

The basic driving force derived from local intensity thresholding method is based on an assumption of single target in the image. However, it may lead to incorrect segmentation due to the complex scene, and it is not suitable for separating individual tooth regions from the CBCT image where some teeth touch others and some are located inside of alveolar bone with similar intensity. To overcome the above, we propose to add an external force (braking force) to stop the deformation when the deforming model reached to the real tooth boundaries in complex scene and blurry boundaries. In this study, we use the gradient information of 3D space to model the braking force (Figure

Example of connection broken by using 3D Sobel operator.

Sobel operator is a gradient operator that is commonly used in edge detection in 2D image [

Similarly, the kernels of the rest of two directions can be acquired by rotating the kernel of

Example of gradient field: (a) original CT slice with neighboring teeth connected and (b) corresponding gradient field.

In CBCT images, the shape of some teeth is quite complicate and irregular (e.g., blind tube shape). To the initial deformation model with regular shape (Figure

Curvature variations in deformation process: (a) initial state, (b) deformation state 1, and (c) deformation state 2.

To the oversegmentation problem caused by the complicate target structures during the deformation process, we propose a “border reinforcement” strategy by adding a weight to each pixel that increases or decreases the weights of pixels neighboring to each vertex with vertices movement situation:

The proposed border reinforcement strategy is based on the following idea: if a vertex stops to deform in an iteration, the corresponding gradient filed will be increased. If a vertex does not move during several iterations, the corresponding gradient filed will be much stronger. Based on border reinforcement, the braking force is redefined as

The deformation force that drives the deformation is made up by three components:

Assume that the quality of each vertex model is

The proposed method utilizes triangular mesh model to initialize the deformable surface model. During deformation process, the position of each vertex is changed under the action of resultant force except topological structure. After several iterations, some vertices deviate far from the initial position but some others nearly stay in the original position, which may lead the deformed meshes to be nonuniform. Nonuniform meshes increase the errors of calculating discrete attribute information (e.g., curvature) and affect the deformation of surface model seriously. Therefore, it is necessary to reparameterize the deformed model.

To overcome the limitations of standard deformable models, in our study, affine cell image decomposition (ACID) is utilized to reparameterize the deformed triangle mesh model that significantly extends the abilities of standard parameters snakes. Instead of rectangular tessellation, we partition the space into tetrahedral cells by using the Coxeter-Freudenthal triangulation in 3D simplicial decomposition. Each grid is constructed by dividing the image volume using a uniform cubic grid and subdividing each cube into six tetrahedra (Figure

(a) Cube divided into six tetrahedra. (b) Object boundaries intersect with grid cells.

The reparameterization process is as follows:

Mesh model reparameterization.

Original mesh model

Reparameterized result

To produce a smooth and good quality mesh surface of deformed model, in this paper, a global Laplacian smoothing approach is utilized [

The initial parameters of the proposed method are set as follows. Assuming that the deformation is caused by the internal pressure

To avoid the oversegmentation caused by rapid deformation,

In addition, the minimum curve radius of target deformation is also computed according to the pixel pitch (

A database including 510 CBCT images is utilized as the test images for evaluating validation of the proposed method. The test images were obtained from Dental Hospital of Wu Han University and captured directly from CBCT image slices. The resolution of each image is

In the experiment, two other well-studied approaches, BET [

Figure

Reconstruction results by segmenting the images with BET, reparameterized BET, and the proposed method.

Another statistical evaluation of the efficiency of the proposed method is carried out with model volume variation via iteration during 500 iterations of BET method, reparameterized BET (R-BET) method, and the proposed method in four types of tooth derived from the center incisor of left mandibular, canine, the first premolar, and the first molar, respectively. It is seen from Figure

Model volume variation during 500 iterations of three methods.

Figure

Reconstruction results of different teeth: (a) molar, (b) lateral incisor, (c) central incisor, and (d) all teeth.

In this study, an effective 3D CBCT image segmentation approach is proposed based on deformation surface model for reconstructing the precious tooth model from the CBCT image slices. We propose a braking force that enables the segmentation process to stop the deformation when the contour of a tooth expands out to other teeth boundaries in deformation process. We also develop a “border reinforcement” strategy by weighting the points according to motion of vertices to overcome the problems that the deformed model exceeds the desired boundaries in the regions with complicate structures during the deformation process. Finally, we reparameterize the deformed model by employing ACID. In the experiment, a series CBCT image slices were employed to validate the reconstruction performance of the proposed method, and the reconstruction results of the proposed method were compared with the results of BET and reparameterized BET (R-BET) method. In addition, four types of tooth were utilized to evaluate the efficiency by evaluating model volume variation via iteration during 500 iterations. The process time of the proposed method is also more quickly than that of two other methods. Experimental results demonstrate that the proposed method can extract the 3D models from CBCT images with blurry boundaries and complicate structure well and reconstruct the 3D tooth model accurately and effectively.

The authors declare that there is no conflict of interests regarding the publication of this paper.

Financial support from the National Nature Science Foundation of China (NSFC) is greatly appreciated (Grant no. 61271093).