Hexagonal Image Processing in the Context of Machine Learning: Conception of a Biologically Inspired Hexagonal Deep Learning Framework

TL;DR

This paper addresses the gap in hexagonal image processing for machine learning by proposing Hexnet, a TensorFlow/Keras-based framework that integrates hexagonal addressing, hexagonal convolutional and pooling layers, and hexagonal image transformation. It introduces a hybrid hex addressing scheme and Hexarray/Hexint constructs, enabling efficient hexagonal representations and compatible transformations from square data. The work demonstrates hexagonal neural networks (H-DNNs) that can achieve competitive or improved performance with fewer trainable parameters compared to traditional square CNNs, and shows substantial runtime advantages over existing hexagonal frameworks. The results suggest hexagonal architectures can offer rotational invariance and reduced data augmentation needs, with practical implications for faster training and potential gains in accuracy on augmented or hexagonally-represented data. Hexnet lays a foundation for broader adoption of hexagonal DL in real-world applications, with open-source tools to facilitate further research and deployment.

Abstract

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.

Figures (7)

• Figure 1: Square and hexagonal lattice format in comparison.
• Figure 2: Construction of hexagonal addressing schemes.
• Figure 3: Exemplary structure of a hexagonal convolutional neural network with convolutional (CL) and pooling layers (PL) of order $1$, fully connected layers (FCL), and feature maps (FM).
• Figure 4: Visualized feature maps for exemplary S-CNN (t.) and H-CNN (b.) test results with one convolutional layer. Shown are ten different classes for the COIL-100 data set Nene1996b.
• Figure 5: Hexagonal convolutional and pooling layer kernels for even and odd row indices as based on their underlying addressing scheme.