  Over the past decade deep learning has revolutionized the field of computer
vision, with convolutional neural network models proving to be very effective
for image classification benchmarks. However, a fundamental theoretical
questions remain answered: why can they solve discrete image classification
tasks that involve feature extraction? We address this question in this paper
by introducing a novel mathematical model for image classification, based on
feature extraction, that can be used to generate images resembling real-world
datasets. We show that convolutional neural network classifiers can solve these
image classification tasks with zero error. In our proof, we construct
piecewise linear functions that detect the presence of features, and show that
they can be realized by a convolutional network.
