  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 unlimited in
resolution.
  Unfortunately, these methods are often unsuitable 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 Implicit Fields. 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 DeepMesh - an end-to-end differentiable mesh representation that
can vary its topology.
  We validate our theoretical insight through several applications: Single view
3D Reconstruction via Differentiable Rendering, Physically-Driven Shape
Optimization, Full Scene 3D Reconstruction from Scans and End-to-End Training.
In all cases our end-to-end differentiable parameterization gives us an edge
over state-of-the-art algorithms.
