Multiscale approximation with hierarchical radial basis functions networks.


Journal Article

An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a self-organizing (by growing) multiscale version of a radial basis function (RBF) network. It is constituted of hierarchical layers, each containing a Gaussian grid at a decreasing scale. The grids are not completely filled, but units are inserted only where the local error is over threshold. This guarantees a uniform residual error and the allocation of more units with smaller scales where the data contain higher frequencies. Only local operations, which do not require any iteration on the data, are required; this allows to construct the network in quasi-real time. Through harmonic analysis, it is demonstrated that, although a HRBF cannot be reduced to a traditional wavelet-based multiresolution analysis (MRA), it does employ Riesz bases and enjoys asymptotic approximation properties for a very large class of functions. HRBF networks have been extensively applied to the reconstruction of three-dimensional (3-D) models from noisy range data. The results illustrate their power in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by MRA.

Full Text

Cited Authors

  • Ferrari, S; Maggioni, M; Borghese, NA

Published Date

  • January 2004

Published In

Volume / Issue

  • 15 / 1

Start / End Page

  • 178 - 188

PubMed ID

  • 15387258

Pubmed Central ID

  • 15387258

Electronic International Standard Serial Number (EISSN)

  • 1941-0093

International Standard Serial Number (ISSN)

  • 1045-9227

Digital Object Identifier (DOI)

  • 10.1109/tnn.2003.811355


  • eng