title: NeuRBF: A Neural Fields Representation with Adaptive Radial Basis
    Functions
summary: We present a novel type of neural fields that uses general radial bases for
  signal representation. State-of-the-art neural fields typically rely on
  grid-based representations for storing local neural features and N-dimensional
  linear kernels for interpolating features at continuous query points. The
  spatial positions of their neural features are fixed on grid nodes and cannot
  well adapt to target signals. Our method instead builds upon general radial
  bases with flexible kernel position and shape, which have higher spatial
  adaptivity and can more closely fit target signals. To further improve the
  channel-wise capacity of radial basis functions, we propose to compose them
  with multi-frequency sinusoid functions. This technique extends a radial basis
  to multiple Fourier radial bases of different frequency bands without requiring
  extra parameters, facilitating the representation of details. Moreover, by
  marrying adaptive radial bases with grid-based ones, our hybrid combination
  inherits both adaptivity and interpolation smoothness. We carefully designed
  weighting schemes to let radial bases adapt to different types of signals
  effectively. Our experiments on 2D image and 3D signed distance field
  representation demonstrate the higher accuracy and compactness of our method
  than prior arts. When applied to neural radiance field reconstruction, our
  method achieves state-of-the-art rendering quality, with small model size and
  comparable training speed.
paper_authors._id: 6515269791aa56a7b10910c3
paper_authors.name: Zhang Chen
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2023-09-28T19:03:15.096Z
paper_authors._id: 6515bec8c2aedaa7e6929991
paper_authors.avatarUrl: /avatars/29fa0acad5de98550cffd18bd118b4fb.svg
paper_authors.fullname: Zhang Chen
paper_authors.type: user
paper_authors.user: ZhangChenv
paper_authors._id: 6515269791aa56a7b10910c4
paper_authors.name: Zhong Li
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2023-09-28T19:03:18.766Z
paper_authors._id: 64fa3909dc465697354572d2
paper_authors.avatarUrl: /avatars/722fc3c3ce0229fc4243bcdcabb42ea5.svg
paper_authors.fullname: Zhong Li
paper_authors.type: user
paper_authors.user: lizhong323
paper_authors._id: 6515269791aa56a7b10910c5
paper_authors.name: Liangchen Song
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2023-10-02T07:00:12.873Z
paper_authors._id: 63d9ea2aaefaa7352587151c
paper_authors.avatarUrl: /avatars/2f02ee1b2a0018c74ef1d47883782bd5.svg
paper_authors.fullname: LSong
paper_authors.type: user
paper_authors.user: lsongx
paper_authors._id: 6515269791aa56a7b10910c6
paper_authors.name: Lele Chen
paper_authors._id: 6515269791aa56a7b10910c7
paper_authors.name: Jingyi Yu
paper_authors._id: 6515269791aa56a7b10910c8
paper_authors.name: Junsong Yuan
paper_authors._id: 6515269791aa56a7b10910c9
paper_authors.name: Yi Xu
paper_title: NeuRBF: A Neural Fields Representation with Adaptive Radial Basis
    Functions
paper_summary: We present a novel type of neural fields that uses general radial bases for
  signal representation. State-of-the-art neural fields typically rely on
  grid-based representations for storing local neural features and N-dimensional
  linear kernels for interpolating features at continuous query points. The
  spatial positions of their neural features are fixed on grid nodes and cannot
  well adapt to target signals. Our method instead builds upon general radial
  bases with flexible kernel position and shape, which have higher spatial
  adaptivity and can more closely fit target signals. To further improve the
  channel-wise capacity of radial basis functions, we propose to compose them
  with multi-frequency sinusoid functions. This technique extends a radial basis
  to multiple Fourier radial bases of different frequency bands without requiring
  extra parameters, facilitating the representation of details. Moreover, by
  marrying adaptive radial bases with grid-based ones, our hybrid combination
  inherits both adaptivity and interpolation smoothness. We carefully designed
  weighting schemes to let radial bases adapt to different types of signals
  effectively. Our experiments on 2D image and 3D signed distance field
  representation demonstrate the higher accuracy and compactness of our method
  than prior arts. When applied to neural radiance field reconstruction, our
  method achieves state-of-the-art rendering quality, with small model size and
  comparable training speed.
paper_ai_keywords: neural fields radial bases signal representation grid-based representations N-dimensional linear kernels feature interpolation grid nodes spatial adaptivity multi-frequency sinusoid functions Fourier radial bases frequency bands hybrid combination weighting schemes 2D image representation 3D signed distance field representation neural radiance field reconstruction rendering quality