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.

翻译：基于坐标的神经隐式表示或隐式场已被广泛应用于三维几何表示和新视角合成。近年来，一系列工作致力于加速基于坐标的隐式场学习的速度并提升其质量。为降低查询坐标的神经隐式值预测所需的繁重MLP计算负担，研究者提出结合神经体素或网格与浅层MLP，以实现高质量隐式场学习并减少优化时间。另一方面，诸如线性网格等轻量级场表示已被提出以进一步提升学习速度。本文旨在同时实现快速且高质量的隐式场学习，提出TaylorGrid——一种通过直接在二维或三维网格上进行泰勒展开优化即可高效计算的新型隐式场表示。作为一种通用表示方法，TaylorGrid可适配不同隐式场学习任务（如SDF学习或NeRF）。通过大量的定量与定性对比，TaylorGrid在线性网格与神经体素之间取得了良好平衡，展现了其在快速高质量隐式场学习中的优越性。