Computational workflows for natural and biomedical image processing based on hypercomplex algebras

Quaternions, a type of hypercomplex number, can be applied to handling three-dimensional data, i.e., color images. Here, we demonstrate, by leveraging quaternions and the two-dimensional orthogonal planes split framework, image processing workflows for natural and biomedical images, including natural and biomedical image recolorization, natural image decolorization, natural and biomedical image contrast enhancement, and computational restaining and stain separation in histological images. We also demonstrate performance gains in machine learning and deep learning pipelines for histological images. The proposed workflows can regulate color appearance and image contrast, be part of automated processing pipelines, and assist in digital pathology applications. Employing basic arithmetic and matrix operations, this work offers a computationally accessible methodology that showcases versatility and consistency across processing tasks and a range of computer vision and biomedical applications. The proposed non-data-driven methods achieve comparable or better results to those reported in the literature, showcasing the potential of robust theoretical frameworks with practical effectiveness.