  Coordinate-based neural implicit representation or implicit fields have been
widely studied for 3D geometry representation or novel view synthesis.
Recently, a series of efforts have been devoted to accelerating the speed and
improving the quality of the coordinate-based implicit field learning. Instead
of learning heavy MLPs to predict the neural implicit values for the query
coordinates, neural voxels or grids combined with shallow MLPs have been
proposed to achieve high-quality implicit field learning with reduced
optimization time. On the other hand, lightweight field representations such as
linear grid have been proposed to further improve the learning speed. In this
paper, we aim for both fast and high-quality implicit field learning, and
propose TaylorGrid, a novel implicit field representation which can be
efficiently computed via direct Taylor expansion optimization on 2D or 3D
grids. As a general representation, TaylorGrid can be adapted to different
implicit fields learning tasks such as SDF learning or NeRF. From extensive
quantitative and qualitative comparisons, TaylorGrid achieves a balance between
the linear grid and neural voxels, showing its superiority in fast and
high-quality implicit field learning.
