Holistic Processing of Colour Images Using Novel Quaternion-Valued Wavelets on the Plane
This work addresses color image processing for researchers and practitioners in computer vision, but it is incremental as it applies an existing theoretical wavelet construction to new applications without major breakthroughs.
The paper tackled the problem of processing color images by applying novel quaternion-valued wavelets, which are compactly supported and orthonormal, to tasks like compression, enhancement, segmentation, and denoising, demonstrating them as promising tools for end-to-end quaternion processing.
Recently, novel quaternion-valued wavelets on the plane were constructed using an optimisation approach. These wavelets are compactly supported, smooth, orthonormal, non-separable and truly quaternionic. However, they have not been tested in application. In this paper, we introduce a methodology for decomposing and reconstructing colour images using quaternionic wavelet filters associated to recently developed quaternion-valued wavelets on the plane. We investigate its applicability in compression, enhancement, segmentation, and denoising of colour images. Our results demonstrate these wavelets as promising tools for an end-to-end quaternion processing of colour images.