The Spherical Radial Function Network for reconstruction in medical robotics

Abstract

The main goal of this work is to develop a geometric neural network which can be used as an interface between sensors and robot mechanisms. For this goal we have developed a new geometric network called Spherical Radial Basis Function Network using the conformal geometric algebra framework. The motivation to use circles or spheres as activation functions is due to the fact that the sphere is the computational unity of the conformal geometric algebra, as a result a Spherical Radial Basis Network can be advantageously used as interface between the sensor domain and the robotic mechanism so that all the computing can be done in the same mathematical framework. In fact, there will be no need to abandon the system for the interpolation or reconstruction using a network. This article presents the design principles and a comparison with a standard Radial Basis Function Network. Medical robotics is an interesting domain to apply our network for capturing data and reconstruct automatically the shape of a human organ.