Title: Image colour edge detection using hypercomplex convolution

Authors: Rawan I. Zaghloul; Hazem Hiary

Addresses: Management Information Systems Department, Al-Balqa Applied University, Amman, 11934, Jordan ' Computer Science Department, The University of Jordan, Amman, 11942, Jordan

Abstract: Quaternions are considered for colour image edge detection. Most work on quaternions is based on a linear quaternion system (LQS) which applies multi-directional kernels (horizontal, vertical, and diagonal) using hypercomplex convolution, each kernel producing an edge map for a specific direction, and the final result is a combination of these maps. This paper introduces a new colour image edge detection filter based on LQS convolution. The process starts by applying quaternion convolution with the proposed filter, and then generating the final edge map by computing the magnitude of the result. The proposed filter is able to highlight both colour and greyscale edges in multiple directions using a single LQS convolution pass. The validity of the proposed filter is demonstrated, and its performance is supported experimentally through a set of comparisons with state-of-the-art methods.

Keywords: quaternions; colour image; edge detection; hypercomplex convolution; multi-directional kernels; LQS; linear quaternion system.

DOI: 10.1504/IJSISE.2020.113569

International Journal of Signal and Imaging Systems Engineering, 2020 Vol.12 No.1/2, pp.54 - 61

Received: 29 Nov 2019
Accepted: 14 Dec 2020
Published online: 11 Mar 2021 *

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