Abstract In oral surgery, accurate segmentation of the teeth has critical significance for the orthodontic treatment and research. However, in the cone beam computed tomography (CBCT) images, the boundaries of the teeth are blurred and some tissues around the teeth have similar intensities to the teeth, which makes the tooth segmentation more difficult and challenging. In this paper, an accurate and automatic active contour model is proposed for the tooth segmentation. First, we apply deep convolutional neural networks to automatically detect the approximate position of each dental pulp. Then, we take the barycenter point of the pixels in the marked area as the center of the tooth. Based on this, we design the shape prior information by a series of mathematical methods to describe the shape, size and position of the tooth, which is achieved by further detecting the direction and length of the tooth. To make full use of the shape prior information, we define the prior constraint term to limit the segmentation curve to evolve around the shape prior information, while making the segmentation contour as close as possible to the shape prior information. Last, combining the image data term, the length term, the regularization term and the prior constraint term, we give the level set formulation of the energy functional and minimize it by the steepest descent method. To test the feasibility and effectiveness of the proposed model, we apply the proposed model to segment the tooth images in different slices. Experimental results show that the proposed model can accurately segment the tooth images. Qualitative comparison results demonstrate the proposed model is superior to the CV model, the RSF model, the LGIF model, the LIC model and the U-Net model in terms of the segmentation accuracy. In addition, the sensitivity test verifies that the proposed model is insensitive to the initial contours and deep network outputs.

中文翻译：

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基于深度卷积神经网络和水平集方法的精确自动牙齿图像分割模型

摘要 在口腔外科中，牙齿的精确分割对于正畸治疗和研究具有重要意义。然而，在锥形束计算机断层扫描（CBCT）图像中，牙齿的边界模糊，牙齿周围的一些组织具有与牙齿相似的强度，这使得牙齿分割更加困难和具有挑战性。在本文中，提出了一种用于牙齿分割的准确且自动的主动轮廓模型。首先，我们应用深度卷积神经网络来自动检测每个牙髓的大致位置。然后，我们将标记区域中像素的重心点作为牙齿的中心。在此基础上，我们通过一系列数学方法设计了形状先验信息来描述牙齿的形状、大小和位置，这是通过进一步检测牙齿的方向和长度来实现的。为了充分利用形状先验信息，我们定义了先验约束项来限制分割曲线围绕形状先验信息演化，同时使分割轮廓尽可能接近形状先验信息。最后，结合图像数据项、长度项、正则化项和先验约束项，我们给出了能量泛函的水平集公式，并通过最速下降法将其最小化。为了测试所提出模型的可行性和有效性，我们应用所提出的模型来分割不同切片中的牙齿图像。实验结果表明，该模型能够准确分割牙齿图像。定性比较结果表明，所提出的模型在分割精度方面优于 CV 模型、RSF 模型、LGIF 模型、LIC 模型和 U-Net 模型。此外，敏感性测试验证了所提出的模型对初始轮廓和深度网络输出不敏感。