  A windowed version of the Nearest Neighbour (WNN) classifier for images is
described. While its construction is inspired by the architecture of Artificial
Neural Networks, the underlying theoretical framework is based on approximation
theory. We illustrate WNN on the datasets MNIST and EMNIST of images of
handwritten digits. In order to calibrate the parameters of WNN, we first study
it on the classical MNIST dataset. We then apply WNN with these parameters to
the challenging EMNIST dataset. It is demonstrated that WNN misclassifies 0.42%
of the images of EMNIST and therefore significantly outperforms predictions by
humans and shallow ANNs that both have more than 1.3% of errors.
