On non-uniform rational B-splines surface neural networks

A novel bi-variate non-uniform rational B-splines (NURBS) surface neural network consisting of four hidden layers is proposed in this paper. The blending functions are selected as the activation functions for the neurons in one of the hidden layers, instead of the commonly used sigmoid functions. With mathematical derivations, it is easy to find that the mathematical expression of the output of the proposed neural network is exactly the same as the NURBS surface. Since a set of 2-D gray scale image data can be considered as a 3-D surface, therefore the proposed NURBS surface neural network can be applied to deal with image processing problems. Two experiments, concerning image compression and corrupted image restoration, are conducted to demonstrate the feasibility of the proposed approach.