Geometric Deep Learning has recently made striking progress with the advent
of continuous Deep Implicit Fields. They allow for detailed modeling of
watertight surfaces of arbitrary topology while not relying on a 3D Euclidean
grid, resulting in a learnable parameterization that is not limited in
resolution.
Unfortunately, these methods are often not suitable for applications that
require an explicit mesh-based surface representation because converting an
implicit field to such a representation relies on the Marching Cubes algorithm,
which cannot be differentiated with respect to the underlying implicit field.
In this work, we remove this limitation and introduce a differentiable way to
produce explicit surface mesh representations from Deep Signed Distance
Functions. Our key insight is that by reasoning on how implicit field
perturbations impact local surface geometry, one can ultimately differentiate
the 3D location of surface samples with respect to the underlying deep implicit
field. We exploit this to define MeshSDF, an end-to-end differentiable mesh
representation which can vary its topology.
We use two different applications to validate our theoretical insight:
Single-View Reconstruction via Differentiable Rendering and Physically-Driven
Shape Optimization. In both cases our differentiable parameterization gives us
an edge over state-of-the-art algorithms.

本文介绍一种基于 Deep Signed Distance Function 的不可微分网格表述方法 MeshSDF，通过推理隐式场的扰动如何影响局部表面几何，最终不限制分辨率和拓扑结构地将 Deep Implicit Field 显式地表示成一个可微分的网格形状，该方法在单视角重建和基于物理的形状优化方面优于现有技术。