2023/08/31 by Dizon, Neil D., Hogan, Jeffrey A.
#65T60 #68U10 #94A08 #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2308.16875
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.