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Benefiting from the continuous representation ability, deep implicitfunctions can represent a shape at infinite resolution. However, extractinghigh-resolution iso-surface from an implicit function requiresforward-propagating a network with a large number of parameters for numerousquery points, thus preventing the generation speed. Inspired by the Taylorseries, we propose Taylo3DNet to accelerate the inference of implicit shaperepresentations. Taylor3DNet exploits a set of discrete landmark points andtheir corresponding Taylor series coefficients to represent the implicit fieldof a 3D shape, and the number of landmark points is independent of theresolution of the iso-surface extraction. Once the coefficients correspondingto the landmark points are predicted, the network evaluation for each querypoint can be simplified as a low-order Taylor series calculation with severalnearest landmark points. Based on this efficient representation, ourTaylor3DNet achieves a significantly faster inference speed than classicalnetwork-based implicit functions. We evaluate our approach on reconstructiontasks with various input types, and the results demonstrate that our approachcan improve the inference speed by a large margin without sacrificing theperformance compared with state-of-the-art baselines.

Taylor3DNet: Fast 3D Shape Inference With Landmark Points Based Taylor Series