Efficient Color Image Segmentation via Quaternion-based LRegularization

Tingting Wu, Zhihui Mao, Zeyu Li, Yonghua Zeng, Tieyong Zeng

Abstract: Color image segmentation is a key technology in image processing. In this paper, a two-stage image segmentation method is proposed that is based on the nonconvex \(L_1/L_2\) approximation of the Mumford-Shah (MS) model. Wherein, the nonconvex regularization term \(L_1/L_2\) on the gradient can approximate the Hausdorff measure and extract more boundary information. The first stage is to solve the nonconvex variant of the MS model and to obtain the smoothed image u. In our framework, we utilize the semi-proximal alternating direction method of multipliers (sPADMM) to sufficiently solve the proposed model. The second stage is segmenting the smoothed u into different phases with thresholds determined by the threshold clustering method. To better deal with the inherent color structures within different channels, we also apply the quaternion representation of the color image. Quantitative and qualitative results demonstrate clearly that our method is better than some state-of-the-art color image segmentation methods.