论文标题
明确流下神经隐式进化的水平集理论
A Level Set Theory for Neural Implicit Evolution under Explicit Flows
论文作者
论文摘要
基于坐标的神经网络参数化隐式表面已成为几何形状的有效表示。它们有效地充当参数水平集，其零级集合定义了感兴趣的表面。我们提出了一个框架，该框架允许将定义的三角形网格定义的变形操作应用于此类隐式表面。这些操作中的几个可以看作是能量最小化问题，这些问题会诱导显式表面上的瞬时流场。我们的方法使用流场通过扩展级别集的经典理论来变形参数隐式表面。我们还通过形式化与级别集理论的联系，来得出有关可区分表面提取和渲染的现有方法的合并视图。我们表明，这些方法从理论中偏离，我们的方法对诸如表面平滑，平均曲面流，反向渲染和用户定义的编辑等应用进行了改进。
Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a framework that allows applying deformation operations defined for triangle meshes onto such implicit surfaces. Several of these operations can be viewed as energy-minimization problems that induce an instantaneous flow field on the explicit surface. Our method uses the flow field to deform parametric implicit surfaces by extending the classical theory of level sets. We also derive a consolidated view for existing methods on differentiable surface extraction and rendering, by formalizing connections to the level-set theory. We show that these methods drift from the theory and that our approach exhibits improvements for applications like surface smoothing, mean-curvature flow, inverse rendering and user-defined editing on implicit geometry.
