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Implicit Surface Modelling with a Globally Regularised Basis of Compact Support
Author(s) -
Walder C.,
Schölkopf B.,
Chapelle O.
Publication year - 2006
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2006.00983.x
Subject(s) - interpolation (computer graphics) , surface (topology) , kernel (algebra) , computer science , basis function , radial basis function , graphics , basis (linear algebra) , object (grammar) , computer graphics , series (stratigraphy) , set (abstract data type) , function (biology) , mathematics , algorithm , artificial intelligence , geometry , computer graphics (images) , image (mathematics) , mathematical analysis , discrete mathematics , artificial neural network , paleontology , evolutionary biology , biology , programming language
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. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations