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.

该论文提出了一种基于神经网络的隐式表面的参数化方法，利用能量最小化问题和水平集理论，实现对隐式表面的形变和后处理操作，这种方法优于已有方法在表面平滑、均值曲率流等方面的表现。