论文标题
神经隐式表面进化
Neural Implicit Surface Evolution
论文作者
论文摘要
这项工作调查了使用平滑的神经网络在级别设置方程（LSE）下对隐式表面的动态变化进行建模。为此，它将神经隐式表面的表示形式扩展到时空$ \ mathbb {r}^3 \ times \ times \ mathbb {r} $，它为连续的几何变换打开了机制。例子包括将初始表面朝向通用矢量场，使用平均曲率方程式进行平滑和锐化，以及初始条件的插值。 网络培训考虑了两个约束。数据术语负责将初始条件拟合到相应的时间即时，通常$ \ Mathbb {r}^3 \ times \ {0 \} $。然后，LSE术语迫使网络在没有任何监督的情况下近似LSE给出的基本几何发展。该网络也可以根据先前训练的初始条件进行初始化，从而导致与标准方法相比，收敛速度更快。
This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time $\mathbb{R}^3\times \mathbb{R}$, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually $\mathbb{R}^3 \times \{0\}$. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.
