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Implicit Surface Modelling with a Globally Regularised Basis of Compact Support




We consider the problem of constructing a globally smooth analytic function that represents a surface implicitly by way of its zero set, given sample points with surface normal vectors. The contributions of the paper include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable interpolation properties previously only associated with fully supported bases. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem lying at the core of kernel-based machine learning methods. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data and four-dimensional interpolation between three-dimensional shapes.

Author(s): Walder, C. and Schölkopf, B. and Chapelle, O.
Journal: Computer Graphics Forum
Volume: 25
Number (issue): 3
Pages: 635-644
Year: 2006
Month: September
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1111/j.1467-8659.2006.00983.x
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Implicit Surface Modelling with a Globally Regularised Basis of Compact Support},
  author = {Walder, C. and Sch{\"o}lkopf, B. and Chapelle, O.},
  journal = {Computer Graphics Forum},
  volume = {25},
  number = {3},
  pages = {635-644},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = sep,
  year = {2006},
  month_numeric = {9}