  Benefiting from the continuous representation ability, deep implicit
functions can represent a shape at infinite resolution. However, extracting
high-resolution iso-surface from an implicit function requires
forward-propagating a network with a large number of parameters for numerous
query points, thus preventing the generation speed. Inspired by the Taylor
series, we propose Taylo3DNet to accelerate the inference of implicit shape
representations. Taylor3DNet exploits a set of discrete landmark points and
their corresponding Taylor series coefficients to represent the implicit field
of a 3D shape, and the number of landmark points is independent of the
resolution of the iso-surface extraction. Once the coefficients corresponding
to the landmark points are predicted, the network evaluation for each query
point can be simplified as a low-order Taylor series calculation with several
nearest landmark points. Based on this efficient representation, our
Taylor3DNet achieves a significantly faster inference speed than classical
network-based implicit functions. We evaluate our approach on reconstruction
tasks with various input types, and the results demonstrate that our approach
can improve the inference speed by a large margin without sacrificing the
performance compared with state-of-the-art baselines.
