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Biologically Inspired Hexagonal Deep Learning for Hexagonal Image Generation

Tobias Schlosser, Frederik Beuth, Danny Kowerko

TL;DR

This work motivates and develops hexagonal image processing for deep learning as a biologically inspired alternative to traditional square lattices. It introduces Hexnet and a hexagonal addressing scheme to build hexagonal deep neural networks (H-DNNs) for hexagonal image generation, including H-SWWAE and H-ACGAN models. The authors implement hexagonal layers and demonstrate, on datasets like MNIST, CIFAR-10, and COIL-100, that hexagonal models can achieve higher transformation efficiency and PSNR while reducing trainable parameters compared to square counterparts. Overall, the results suggest hexagonal architectures can outperform conventional DNNs in image generation tasks and motivate broader adoption of hexagonal representations and datasets in future research.

Abstract

Whereas conventional state-of-the-art image processing systems of recording and output devices almost exclusively utilize square arranged methods, biological models, however, suggest an alternative, evolutionarily-based structure. Inspired by the human visual perception system, hexagonal image processing in the context of machine learning offers a number of key advantages that can benefit both researchers and users alike. The hexagonal deep learning framework Hexnet leveraged in this contribution serves therefore the generation of hexagonal images by utilizing hexagonal deep neural networks (H-DNN). As the results of our created test environment show, the proposed models can surpass current approaches of conventional image generation. While resulting in a reduction of the models' complexity in the form of trainable parameters, they furthermore allow an increase of test rates in comparison to their square counterparts.

Biologically Inspired Hexagonal Deep Learning for Hexagonal Image Generation

TL;DR

This work motivates and develops hexagonal image processing for deep learning as a biologically inspired alternative to traditional square lattices. It introduces Hexnet and a hexagonal addressing scheme to build hexagonal deep neural networks (H-DNNs) for hexagonal image generation, including H-SWWAE and H-ACGAN models. The authors implement hexagonal layers and demonstrate, on datasets like MNIST, CIFAR-10, and COIL-100, that hexagonal models can achieve higher transformation efficiency and PSNR while reducing trainable parameters compared to square counterparts. Overall, the results suggest hexagonal architectures can outperform conventional DNNs in image generation tasks and motivate broader adoption of hexagonal representations and datasets in future research.

Abstract

Whereas conventional state-of-the-art image processing systems of recording and output devices almost exclusively utilize square arranged methods, biological models, however, suggest an alternative, evolutionarily-based structure. Inspired by the human visual perception system, hexagonal image processing in the context of machine learning offers a number of key advantages that can benefit both researchers and users alike. The hexagonal deep learning framework Hexnet leveraged in this contribution serves therefore the generation of hexagonal images by utilizing hexagonal deep neural networks (H-DNN). As the results of our created test environment show, the proposed models can surpass current approaches of conventional image generation. While resulting in a reduction of the models' complexity in the form of trainable parameters, they furthermore allow an increase of test rates in comparison to their square counterparts.

Paper Structure

This paper contains 15 sections, 1 equation, 4 figures, 3 tables.

Table of Contents

  1. Introduction and motivation
  2. Application areas and related work
  3. Contribution of hexagonal image generation
  4. Fundamentals and methods
  5. The hexagonal addressing scheme
  6. Conventional and hexagonal deep neural networks
  7. Assessing the quality of hexagonal representations
  8. Implementation of the hexagonal deep learning Framework
  9. Hexagonal layers
  10. Models for hexagonal image generation
  11. Results, evaluation, and discussion
  12. Square and hexagonal deep neural networks
  13. Quality assessment
  14. Conclusion and outlook
  15. Acknowledgment

Figures (4)

  • Figure 1: Lattice format comparison. Schlosser2019_ICMLA
  • Figure 2: Hexagonal addressing scheme construction. Schlosser2019_ICMLA
  • Figure 3: Exemplary models for hexagonal image generation. a) Hexagonal Deeply Stacked Residual What-Where Autoencoder (H-SWWAE). b) Hexagonal Auxiliary Classifier Generative Adversarial Network (H-ACGAN).
  • Figure 4: Exemplary test results for S- and H-SWWAE (left column) as well as S- and H-ACGAN (right column) with the MNIST (top), CIFAR-10 (middle), and COIL-100 (bottom) data sets after 100 epochs of training.