Grounding and Enhancing Grid-based Models for Neural Fields

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 https://sites.google.com/view/cvpr24-2034-submission/home.