  We introduce Explicit Neural Surfaces (ENS), an efficient smooth surface
representation that directly encodes topology with a deformation field from a
known base domain. We apply this representation to reconstruct explicit
surfaces from multiple views, where we use a series of neural deformation
fields to progressively transform the base domain into a target shape. By using
meshes as discrete surface proxies, we train the deformation fields through
efficient differentiable rasterization. Using a fixed base domain allows us to
have Laplace-Beltrami eigenfunctions as an intrinsic positional encoding
alongside standard extrinsic Fourier features, with which our approach can
capture fine surface details. Compared to implicit surfaces, ENS trains faster
and has several orders of magnitude faster inference times. The explicit nature
of our approach also allows higher-quality mesh extraction whilst maintaining
competitive surface reconstruction performance and real-time capabilities.
