Here, we report a novel method of 3D image segmentation, using surface reconstruction from 3D point cloud data and 3D digital image information. For this task, we apply a mathematical model and numerical method based on the level set algorithm. This method solves surface reconstruction by the application of advection equation with a curvature term, which gives the evolution of an initial condition to the final state. This is done by defining the advective velocity in the level set equation as the weighted sum of distance function and edge detector function gradients. The distance function to the shape, represented by the point cloud, is computed using the fast sweeping method. The edge detector function is applied to the presmoothed 3D image. A crucial point for efficiency is the construction of an initial condition by a simple tagging algorithm, which allows us also to highly speed up the numerical scheme when solving PDEs. For the numerical discretization, we use a semi-implicit co-volume scheme in the curvature part and implicit upwind scheme in the advective part. The method was tested on representative examples and applied to real data representing 3D biological microscopic images of developing mammalian embryo.

中文翻译：

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点云支持的3D图像分割

在这里，我们报告了一种使用3D点云数据和3D数字图像信息进行表面重建的3D图像分割新方法。为此，我们基于水平集算法应用数学模型和数值方法。该方法通过应用带有曲率项的对流方程来解决表面重建问题，该方程将初始条件演化为最终状态。这是通过将水平集方程中的对流速度定义为距离函数和边缘检测器函数梯度的加权和而实现的。使用快速扫掠方法计算到由点云表示的形状的距离函数。边缘检测器功能应用于预平滑的3D图像。效率的关键是通过简单的标记算法构建初始条件，这也使我们在求解PDE时也可以大大加快数值方案的速度。对于数值离散，我们在曲率部分使用半隐式共体积格式，在对流部分使用隐式迎风格式。该方法在代表性实例上进行了测试，并应用于代表发育中的哺乳动物胚胎的3D生物显微图像的真实数据。