Affiliations: Department of Electrical Engineering and Computer Sciences, CINVESTA V del IPN, Unidad Guadalajara, Av. Científica 1145, El Bajío, Zapopan, Jalisco, 45010, México
Note:  Corresponding Author Jorge Rivera-Rovelo, Department of Electrical Engineering and Computer Sciences, CINVESTAV del IPN, Unidad Guadalajara, Av. Científica 1145, El Bajío, Zapopan, Jalisco, 45010, México. Email: [email protected]
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.
Keywords: Segmentation, self-organizing neural networks, gradient vector flow, geometric algebra, 2D and 3D reconstruction