Neural Field Convolutions by Repeated Differentiation-Reference-Cited by-同舟云学术

Neural Field Convolutions by Repeated Differentiation

Published:2023-12-05 Issue:6 Volume:42 Page:1-11
ISSN:0730-0301
Container-title:ACM Transactions on Graphics
language:en
Short-container-title:ACM Trans. Graph.

Author:

Nsampi Ntumba Elie¹,Djeacoumar Adarsh¹,Seidel Hans-Peter¹,Ritschel Tobias²,Leimkühler Thomas¹

Affiliation:

1. MPI Informatik, Germany

2. University College London, United Kingdom

Abstract

Neural fields are evolving towards a general-purpose continuous representation for visual computing. Yet, despite their numerous appealing properties, they are hardly amenable to signal processing. As a remedy, we present a method to perform general continuous convolutions with general continuous signals such as neural fields. Observing that piecewise polynomial kernels reduce to a sparse set of Dirac deltas after repeated differentiation, we leverage convolution identities and train a repeated integral field to efficiently execute large-scale convolutions. We demonstrate our approach on a variety of data modalities and spatially-varying kernels.

Publisher

Association for Computing Machinery (ACM)

Subject

Computer Graphics and Computer-Aided Design

Link

https://dl.acm.org/doi/pdf/10.1145/3618340

Reference59 articles.

1. J Harold Ahlberg , Edwin Norman Nilson, and Joseph Leonard Walsh . 2016 . The Theory of Splines and Their Applications. Vol. 38 . Elsevier . J Harold Ahlberg, Edwin Norman Nilson, and Joseph Leonard Walsh. 2016. The Theory of Splines and Their Applications. Vol. 38. Elsevier.

2. Jonathan T. Barron , Ben Mildenhall , Matthew Tancik , Peter Hedman , Ricardo Martin-Brualla , and Pratul P . Srinivasan . 2021 . Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields. ICCV ( 2021). Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. 2021. Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields. ICCV (2021).

3. Jonathan T. Barron , Ben Mildenhall , Dor Verbin , Pratul P. Srinivasan , and Peter Hedman . 2022. Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields. CVPR ( 2022 ). Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. 2022. Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields. CVPR (2022).

4. E Oran Brigham . 1988. The fast Fourier transform and its applications . Prentice-Hall, Inc. E Oran Brigham. 1988. The fast Fourier transform and its applications. Prentice-Hall, Inc.

5. Real-time edge-aware image processing with the bilateral grid

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