Geometric spherical networks for Visual Data processing

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 two new geometric network called Spherical Radial Basis Function Network and Spherical General Regression 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 these Networks 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 this network. This article presents the design principles and a comparison with a standard Radial Basis Function Network and a standard General regression Neural Network. In the area of medical robotics the use of haptics is quite common. This is an interesting domain to apply our network for capturing data with a haptic device and using spheres reconstruct automatically the shape of a human organ. As we shown in other works, the differential robot kinematics can be formulated using lines, planes and spheres using geometric algebra, having the organ tissue modelled also with spheres with the networks, this helps greatly to related the perceptual and the mechanical devices and ensure their control. We show reconstruction results of an organ using both Networks.