Quaternion and Split Quaternion Neural Networks for Low-Light Color Image Enhancement

Abstract

In this study, two models of multilayer quaternionic feedforward neural networks are presented. Whereas the first model is based on quaternion algebra, the second model uses split quaternion algebra. For both quaternionic neural networks, a learning algorithm was derived using an adaptation of the extended Kalman filter. In addition, to analyze the performance of these two neural network models, they were applied to address the problem of enhancing low-light color images, which for this work consists particularly in the recovery of illuminated color images by quaternionic neural network processing from underexposed images. The quaternion neural network enhances images in the RGB color space (Euclidean metric), whereas the split quaternion neural network enhances images in the HSV color space (Minkowski metric). From the results, we can observe that the split quaternion neural network using the HSV color model shows advantages that were not previously published and were not shown by the quaternion neural network using the RGB color model. Therefore, this article introduces a novel quaternionic neural network that uses the Minkowski metric for color image processing, which can be advantageously used by practitioners interested in working with the HSV color model.

Keywords

• Extended Kalman filter
• low-light image enhancement
• quaternion
• quaternion neural network
• RGB and HSV color space
• split quaternion