Grounding and Enhancing Grid-based Models for Neural Fields

• URL: http://arxiv.org/abs/2403.20002v3
• Date: Fri, 7 Jun 2024 00:49:43 GMT
• Title: Grounding and Enhancing Grid-based Models for Neural Fields
• Authors: Zelin Zhao, Fenglei Fan, Wenlong Liao, Junchi Yan,
• Abstract summary: This paper introduces a theoretical framework for grid-based models. The framework points out that these models' approximation and generalization behaviors are determined by grid tangent kernels (GTK) The introduced framework motivates the development of a novel grid-based model named the Multiplicative Fourier Adaptive Grid (MulFAGrid)
• Score: 52.608051828300106
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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