  Inspired by the human visual perception system, hexagonal image processing in
the context of machine learning deals with the development of image processing
systems that combine the advantages of evolutionary motivated structures based
on biological models. While conventional state-of-the-art image processing
systems of recording and output devices almost exclusively utilize square
arranged methods, their hexagonal counterparts offer a number of key advantages
that can benefit both researchers and users. This contribution serves as a
general application-oriented approach the synthesis of the therefore designed
hexagonal image processing framework, called Hexnet, the processing steps of
hexagonal image transformation, and dependent methods. The results of our
created test environment show that the realized framework surpasses current
approaches of hexagonal image processing systems, while hexagonal artificial
neural networks can benefit from the implemented hexagonal architecture. As
hexagonal lattice format based deep neural networks, also called H-DNN, can be
compared to their square counterparts by transforming classical square lattice
based data sets into their hexagonal representation, they can also result in a
reduction of trainable parameters as well as result in increased training and
test rates.
