The Spherical General Regression Network for reconstruction in medical robotics

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 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 a Spherical General Regression 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 such a network. This article presents the design principles and a comparison with 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 reconstruct automatically the shape of a human organ. We show reconstruction results of an organ using our new geometric network.