Image colour edge detection using hypercomplex convolution

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.