# Novel computational workflows for natural and biomedical image processing based on hypercomplex algebras

arXiv: https://arxiv.org/abs/2502.07758 · HTML: https://mlsanity.com/paper/2502.07758/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 112 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Recovering Realistic Texture in Image Super-resolution by Deep Spatial Feature Transform](https://mlsanity.com/paper/1804.02815/) (2018)
- [Quaternion kinematics for the error-state Kalman filter](https://mlsanity.com/paper/1711.02508/) (2017)
- [A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks](https://mlsanity.com/paper/1902.05478/) (2019)
- [Applications of Clifford's Geometric Algebra](https://mlsanity.com/paper/1305.5663/) (2013)
- [Quaternion Fourier Transform on Quaternion Fields and Generalizations](https://mlsanity.com/paper/1306.1023/) (2013)

## Built on by (most cited first, 2 of 2)

- [V-EfficientNets: Vector-Valued Efficiently Scaled Convolutional Neural Network Models](https://mlsanity.com/paper/2505.05659/) (2025)
- [Ghost Features and Spooky Transfer Learning for Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2608.07735/) (2026)

## Abstract (arXiv)

Hypercomplex image processing extends conventional techniques in a unified paradigm encompassing algebraic and geometric principles. This work leverages quaternions and the two-dimensional orthogonal planes split framework (splitting of a quaternion - representing a pixel - into pairs of orthogonal 2D planes) for natural/biomedical image analysis through the following computational workflows and outcomes: natural/biomedical image re-colorization, natural image de-colorization, natural/biomedical image contrast enhancement, computational re-staining and stain separation in histological images, and performance gains in machine/deep learning pipelines for histological images. The workflows are analyzed separately for natural and biomedical images to showcase the effectiveness of the proposed approaches. The proposed workflows can regulate color appearance (e.g. with alternative renditions and grayscale conversion) and image contrast, be part of automated image processing pipelines (e.g. isolating stain components, boosting learning models), and assist in digital pathology applications (e.g. enhancing biomarker visibility, enabling colorblind-friendly renditions). Employing only basic arithmetic and matrix operations, this work offers a computationally accessible methodology - in the hypercomplex domain - that showcases versatility and consistency across image processing tasks and a range of computer vision and biomedical applications. The proposed non-data-driven methods achieve comparable or better results (particularly in cases involving well-known methods) to those reported in the literature, showcasing the potential of robust theoretical frameworks with practical effectiveness. Results, methods, and limitations are detailed alongside discussion of promising extensions, emphasizing the potential of feature-rich mathematical/computational frameworks for natural and biomedical images.