  Neural implicit surfaces are a promising tool for geometry processing that
represent a solid object as the zero level set of a neural network. Usually
trained to approximate a signed distance function of the considered object,
these methods exhibit great visual fidelity and quality near the surface, yet
their properties tend to degrade with distance, making geometrical queries hard
to perform without the help of complex range analysis techniques. Based on
recent advancements in Lipschitz neural networks, we introduce a new method for
approximating the signed distance function of a given object. As our neural
function is made 1- Lipschitz by construction, it cannot overestimate the
distance, which guarantees robustness even far from the surface. Moreover, the
1-Lipschitz constraint allows us to use a different loss function, called the
hinge-Kantorovitch-Rubinstein loss, which pushes the gradient as close to
unit-norm as possible, thus reducing computation costs in iterative queries. As
this loss function only needs a rough estimate of occupancy to be optimized,
this means that the true distance function need not to be known. We are
therefore able to compute neural implicit representations of even bad quality
geometry such as noisy point clouds or triangle soups. We demonstrate that our
methods is able to approximate the distance function of any closed or open
surfaces or curves in the plane or in space, while still allowing sphere
tracing or closest point projections to be performed robustly.
