  This paper presents a robust filter called quaternion Hardy filter (QHF) for
color image edge detection. The QHF can be capable of color edge feature
enhancement and noise resistance. It is flexible to use QHF by selecting
suitable parameters to handle different levels of noise. In particular, the
quaternion analytic signal, which is an effective tool in color image
processing, can also be produced by quaternion Hardy filtering with specific
parameters. Based on the QHF and the improved Di Zenzo gradient operator, a
novel color edge detection algorithm is proposed. Importantly, it can be
efficiently implemented by using the fast discrete quaternion Fourier transform
technique. From the experimental results, we conclude that the minimum PSNR
improvement rate is 2.3% and minimum SSIM improvement rate is 30.2% on the
Dataset 3. The experiments demonstrate that the proposed algorithm outperforms
several widely used algorithms.
