  Neural implicit functions have emerged as a powerful representation for
surfaces in 3D. Such a function can encode a high quality surface with
intricate details into the parameters of a deep neural network. However,
optimizing for the parameters for accurate and robust reconstructions remains a
challenge, especially when the input data is noisy or incomplete. In this work,
we develop a hybrid neural surface representation that allows us to impose
geometry-aware sampling and regularization, which significantly improves the
fidelity of reconstructions. We propose to use \emph{iso-points} as an explicit
representation for a neural implicit function. These points are computed and
updated on-the-fly during training to capture important geometric features and
impose geometric constraints on the optimization. We demonstrate that our
method can be adopted to improve state-of-the-art techniques for reconstructing
neural implicit surfaces from multi-view images or point clouds. Quantitative
and qualitative evaluations show that, compared with existing sampling and
optimization methods, our approach allows faster convergence, better
generalization, and accurate recovery of details and topology.
