A quaternion-based spectral clustering method for color image segmentation

Abstract

Spectral clustering method has been widely used in image segmentation. A key issue in spectral clustering is how to build the affinity matrix. When it is applied to color image segmentation, most of the existing methods either use Euclidean metric to define the affinity matrix, or first converting color-images into gray-level images and then use the gray-level images to construct the affinity matrix (component-wise method). However, it is known that Euclidean distances can not represent the color differences well and the component-wise method does not consider the correlation between color channels. In this paper, we propose a new method to produce the affinity matrix, in which the color images are first represented in quaternion form and then the similarities between color pixels are measured by quaternion rotation (QR) mechanism. The experimental results show the superiority of the new method.