Full Quaternion Representation of Color images: A Case Study on QSVD-based Color Image Compression

TL;DR

This paper introduces a full quaternion representation for color images that enables holistic processing without extra costs, and demonstrates its effectiveness in a QSVD-based compression method with improved performance over pure quaternion approaches.

Contribution

It proposes a novel full quaternion image representation using neural networks, enabling efficient holistic processing and improved compression performance compared to existing methods.

Findings

Full quaternion representation improves compression quality.

The proposed method reduces processing time and file size.

Model performs acceptably on the UCID dataset.

Abstract

For many years, channels of a color image have been processed individually, or the image has been converted to grayscale one with respect to color image processing. Pure quaternion representation of color images solves this issue as it allows images to be processed in a holistic space. Nevertheless, it brings additional costs due to the extra fourth dimension. In this paper, we propose an approach for representing color images with full quaternion numbers that enables us to process color images holistically without additional cost in time, space and computation. With taking auto- and cross-correlation of color channels into account, an autoencoder neural network is used to generate a global model for transforming a color image into a full quaternion matrix. To evaluate the model, we use UCID dataset, and the results indicate that the model has an acceptable performance on color images. Moreover, we propose a compression method based on the generated model and QSVD as a case study. The method is compared with the same compression method using pure quaternion representation and is assessed with UCID dataset. The results demonstrate that the compression method using the proposed full quaternion representation fares better than the other in terms of time, quality, and size of compressed files.