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

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 with the synthesis of the therefor 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 counterpart 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.

Biologically inspired deep residual networks for computer vision applications

“…[19] has extended the theory of group equivariant convolutional neural networks to hexagonal lattice so as to exploit the six-fold symmetries in p6 and p6m groups. There are few other works [41,42] which utilise the square convolutional routines for hexagonal lattices. Unlike the previous techniques, the proposed approach is a hybrid technique which use the square equivalent of hexagonal filters along the skip connections of deep residual networks and show an improvised performance over the classical ResNet architectures.…”

Biologically Inspired Hexagonal Deep Learning For Hexagonal Image Generation

“…This contribution is meant as a general application-oriented approach to hexagonal image generation by synthesizing the advantages of the research fields of hexagonal image processing with deep learning. Following, the by Schlosser et al [18] introduced hexagonal deep learning framework Hexnet will therefore be utilized as a first approach to hexagonal image generation using hexagonal deep neural networks. As of the current state of art, true hexagonal images have to be captured using a hexagonal sensor.…”

“…2: Hexagonal addressing scheme construction. [18] This contribution leverages a hybrid approach that combines a 1-D linewise architecture with SAA (Fig. 2).…”

“…To quantify the information content and image quality of square and hexagonal lattice format based representations, the hereinafter so-called transformation efficiencies are obtained [18]. Given the original square lattice format based image S and its hexagonally sampled image H, the absolute error is derived by weighting the from projection of S onto H obtained subareas a ∈ A in subpixel resolution.…”

“…To solve the from two different sub-Hexarrays resulting offset mapping with or without strides corresponding to the current offsets, the mapping problem has to be approached in a more general manner. The mapping-based linear assignment problem is then solved by minimizing the resulting 2 norm based cost [18].…”