Grounding and Enhancing Grid-based Models for Neural Fields
This work addresses a foundational gap in neural field representation for researchers, providing a framework to analyze and improve grid-based models, though it is incremental in advancing existing methods.
The paper tackles the lack of systematic analysis in grid-based models for neural fields by introducing a theoretical framework based on grid tangent kernels, leading to the development of MulFAGrid, which achieves state-of-the-art performance in tasks like 2D image fitting and 3D SDF reconstruction with a lower generalization bound.
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.