Modeling an isosurface with a neural network

Abstract

In this paper, we present a novel method for modeling an isosurface that is defined by an unstructured set of control points. The principle is to model the scalar field underlying the isosurface with a neural network: the inputs of the neural network are the three coordinates of a point in space and its output is the value of the scalar field at this point. The isosurface is requested to satisfy some constraints related to the control points: it must pass through these points and its normal and curvature may be imposed over these points. Consequently, the neural network is trained to comply with these constraints. The type of network considered so far is a multilayer feedforward neural network with two internal layers. The learning techniques (for finding relevant values of the connection weights) on which we are currently working are an expanded version of the backpropagation algorithm and a genetic algorithm. The aim of this paper is to lay the bases of the neural network modeling approach. Some directions for further development are also indicated.