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Applied Bionics and Biomechanics
Volume 4 (2007), Issue 3, Pages 125-136
http://dx.doi.org/10.1080/11762320701797745

Surface Approximation using Growing Self-Organizing Nets and Gradient Information

Jorge Rivera-Rovelo and Eduardo Bayro-Corrochano

Department of Electrical Engineering and Computer Sciences, CINVESTA V del IPN, Unidad Guadalajara, Av. Científica 1145, El Bajío, Zapopan, Jalisco, 45010, Mexico

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we show how to improve the performance of two self-organizing neural networks used to approximate the shape of a 2D or 3D object by incorporating gradient information in the adaptation stage. The methods are based on the growing versions of the Kohonen's map and the neural gas network. Also, we show that in the adaptation stage the network utilizes efficient transformations, expressed as versors in the conformal geometric algebra framework, which build the shape of the object independent of its position in space (coordinate free). Our algorithms were tested with several images, including medical images (CT and MR images). We include also some examples for the case of 3D surface estimation.