On the learning machine for three dimensional mapping

In this paper, we investigate the neural network with three-dimensional parameters for applications like 3D image processing, interpretation of 3D transformations, and 3D object motion. A 3D vector represents a point in the 3D space, and an object might be represented with a set of these points. Thus, it is desirable to have a 3D vector-valued neural network, which deals with three signals as one cluster. In such a neural network, 3D signals are flowing through a network and are the unit of learning. This article also deals with a related 3D back-propagation (3D-BP) learning algorithm, which is an extension of conventional back-propagation algorithm in the single dimension. 3D-BP has an inherent ability to learn and generalize the 3D motion. The computational experiments presented in this paper evaluate the performance of considered learning machine in generalization of 3D transformations and 3D pattern recognition. © 2010 Springer-Verlag London Limited.