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Spelunking the deep: guaranteed queries on general neural implicit surfaces via range analysis

Authors:

Nicholas Sharp,

Alec JacobsonAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 41, Issue 4

Article No.: 107, Pages 1 - 16

https://doi.org/10.1145/3528223.3530155

Published: 22 July 2022 Publication History

Abstract

Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these representations are easy to fit, it is not clear how to best evaluate geometric queries on the shape, such as intersecting against a ray or finding a closest point. The predominant approach is to encourage the network to have a signed distance property. However, this property typically holds only approximately, leading to robustness issues, and holds only at the conclusion of training, inhibiting the use of queries in loss functions. Instead, this work presents a new approach to perform queries directly on general neural implicit functions for a wide range of existing architectures. Our key tool is the application of range analysis to neural networks, using automatic arithmetic rules to bound the output of a network over a region; we conduct a study of range analysis on neural networks, and identify variants of affine arithmetic which are highly effective. We use the resulting bounds to develop geometric queries including ray casting, intersection testing, constructing spatial hierarchies, fast mesh extraction, closest-point evaluation, evaluating bulk properties, and more. Our queries can be efficiently evaluated on GPUs, and offer concrete accuracy guarantees even on randomly-initialized networks, enabling their use in training objectives and beyond. We also show a preliminary application to inverse rendering.

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de Goes FDesbrun M(2024)Stochastic Computation of Barycentric CoordinatesACM Transactions on Graphics10.1145/365813143:4(1-13)Online publication date: 19-Jul-2024
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Index Terms

Spelunking the deep: guaranteed queries on general neural implicit surfaces via range analysis
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision representations
        Shape representations
  2. Computer graphics
    1. Shape modeling
      1. Shape analysis
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Interval arithmetic

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 41, Issue 4

July 2022

1978 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3528223

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Published: 22 July 2022

Published in TOG Volume 41, Issue 4

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King NSu HAanjaneya MRuuth SBatty C(2024)A Closest Point Method for PDEs on Manifolds with Interior Boundary Conditions for Geometry ProcessingACM Transactions on Graphics10.1145/367365243:5(1-26)Online publication date: 9-Aug-2024
https://dl.acm.org/doi/10.1145/3673652
Gillespie MYang DBotsch MCrane K(2024)Ray Tracing Harmonic FunctionsACM Transactions on Graphics10.1145/365820143:4(1-18)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658201
de Goes FDesbrun M(2024)Stochastic Computation of Barycentric CoordinatesACM Transactions on Graphics10.1145/365813143:4(1-13)Online publication date: 19-Jul-2024
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Liu SFischer MYoo PRitschel T(2024)Neural BoundingACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657442(1-10)Online publication date: 13-Jul-2024
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Bán RValasek G(2024)Generalized Lipschitz Tracing of Implicit SurfacesComputer Graphics Forum10.1111/cgf.15202Online publication date: 23-Sep-2024
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Coiffier GBéthune L(2024)1‐Lipschitz Neural Distance FieldsComputer Graphics Forum10.1111/cgf.15128Online publication date: 31-Jul-2024
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