Implicit Surface Modelling with a Globally Regularised Basis of Compact Support
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Date
2006
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Publisher
The Eurographics Association and Blackwell Publishing, Inc
Abstract
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
Description
@article{10.1111:j.1467-8659.2006.00983.x,
journal = {Computer Graphics Forum},
title = {{Implicit Surface Modelling with a Globally Regularised Basis of Compact Support}},
author = {Walder, C. and Schoelkopf, B. and Chapelle, O.},
year = {2006},
publisher = {The Eurographics Association and Blackwell Publishing, Inc},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2006.00983.x}
}