A Robust Color Edge Detection Algorithm Based on Quaternion Hardy Filter

TL;DR

This paper introduces a quaternion Hardy filter for robust color edge detection that enhances features and resists noise, utilizing quaternion analytic signals and fast Fourier transforms.

Contribution

It proposes a novel quaternion Hardy filter combined with an improved gradient operator for efficient, noise-resistant color edge detection.

Findings

Outperforms existing color edge detection algorithms

Effectively enhances edge features in noisy images

Efficient implementation via fast quaternion Fourier transform

Abstract

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. The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.