Learning can often be viewed as the problem of mapping from an input space to an output space. Examples of these mappings are used to construct a continuous function that approximates given data and generalizes for intermediate instances. Generalized Radial Basis Function (GRBF) networks are used to formulate this approximating function. A novel method is introduced to construct an optimal GRBF network for a given mapping and error bound using the integral wavelet transform. Simple one-dimensional examples are used to demonstrate how the optimal network is superior to one constructed using standard ad hoc optimization techniques. The paper concludes with an application of optimal GRBF networks to object recognition and pose estimation. The results of this application are favorable.