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