  Surface reconstruction is very challenging when the input point clouds,
particularly real scans, are noisy and lack normals. Observing that the
Multilayer Perceptron (MLP) and the implicit moving least-square function
(IMLS) provide a dual representation of the underlying surface, we introduce
Neural-IMLS, a novel approach that directly learns the noise-resistant signed
distance function (SDF) from unoriented raw point clouds in a self-supervised
fashion. We use the IMLS to regularize the distance values reported by the MLP
while using the MLP to regularize the normals of the data points for running
the IMLS. We also prove that at the convergence, our neural network, benefiting
from the mutual learning mechanism between the MLP and the IMLS, produces a
faithful SDF whose zero-level set approximates the underlying surface. We
conducted extensive experiments on various benchmarks, including synthetic
scans and real scans. The experimental results show that {\em Neural-IMLS} can
reconstruct faithful shapes on various benchmarks with noise and missing parts.
The source code can be found at~\url{https://github.com/bearprin/Neural-IMLS}.
