Many contemporary studies utilize grid-based models for neural field
representation, but a systematic analysis of grid-based models is still
missing, hindering the improvement of those models. Therefore, this paper
introduces a theoretical framework for grid-based models. This framework points
out that these models' approximation and generalization behaviors are
determined by grid tangent kernels (GTK), which are intrinsic properties of
grid-based models. The proposed framework facilitates a consistent and
systematic analysis of diverse grid-based models. Furthermore, the introduced
framework motivates the development of a novel grid-based model named the
Multiplicative Fourier Adaptive Grid (MulFAGrid). The numerical analysis
demonstrates that MulFAGrid exhibits a lower generalization bound than its
predecessors, indicating its robust generalization performance. Empirical
studies reveal that MulFAGrid achieves state-of-the-art performance in various
tasks, including 2D image fitting, 3D signed distance field (SDF)
reconstruction, and novel view synthesis, demonstrating superior representation
ability. The project website is available at
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该论文介绍了一种基于网格的模型的理论框架，并提出了一种名为 MulFAGrid 的新型基于网格的模型，该模型在各种任务中展示了卓越的表征能力和较低的泛化性能。