Color Image Segmentation in a Quaternion Framework

Abstract

In this paper, we present a feature/detail preserving color image segmentation framework using Hamiltonian quaternions. First, we introduce a novel Quaternionic Gabor Filter (QGF) which can combine the color channels and the orientations in the image plane. Using the QGFs, we extract the local orientation information in the color images. Second, in order to model this derived orientation information, we propose a continuous mixture of appropriate hypercomplex exponential basis functions. We derive a closed form solution for this continuous mixture model. This analytic solution is in the form of a spatially varying kernel which, when convolved with the signed distance function of an evolving contour (placed in the color image), yields a detail preserving segmentation.

Review of Quaternion-Based Color Image Processing Methods

“…Instead of the above models, there are other standard works in the quaternion domain. For example, the quaternion Gabor filter (QGF) [107,108] was introduced to extract the local orientation information. Later, Li et al [109] improved a multiscale QGF to describe texture attributes.…”