International Journal of Signal Processing, Image Processing and Pattern Recognition Vol.9, No.2 (2016), pp.313-322 http://dx.doi.org/10.14257/ijsip.2016.9.2.27 ISSN: 2005-4254 IJSIP Copyright ⓒ 2016 SERSC Image Segmentation by Student's-t Mixture Models Based on Markov Random Field and Weighted Mean Template Xu Pan, Hongqing Zhu * and Qunyi Xie School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China hqzhu@ecust.edu.cn Abstract Finite mixture model (FMM) with Gaussian distribution has been widely used in many image processing and pattern recognition tasks. This paper presents a new Student's-t mixture model (SMM) based on Markov random field (MRF) and weighted mean template. In this model, the Student's-t distribution is considered as an alternative to the Gaussian distribution due to the former is heavily tailed than Gaussian distribution, thus providing robustness to outliers. With the help of the weighted mean template, the spatial information between neighboring pixels of an image is considered during the learning step. In addition, the proposed method is able to impose the smoothness constraint on the pixel label by using MRF. Furthermore, an efficient energy function and a novel factor are applied in current model to decrease the computational complexity. Numerical experiments are presented on simulated and real world images, and the results are compared with other FMM-based models. Keywords: Student's-t mixture model, Markov random field, image segmentation, spatial information, mean template 1. Introduction Segmentation is one of the most difficult problems in image processing [1] and pattern recognition [2]. The purpose of image segmentation is to cluster all image pixels into non-overlapped groups with respect to some real world objects. One of the most commonly used clustering methods is finite mixture model (FMM). Due to the ease of implementation, the standard Gaussian mixture model (GMM) has been selected most widely as a particular case of FMM. Applying GMM had good segmentation results on images without noise. However, its accuracy in noisy images is not enough mainly because the prior probability π j is not related to pixel i so that the spatial relationship between neighboring pixels is not taken into account. For this reason, the segmentation result of GMM is extremely sensitive to noise. To reduce the sensitivity of the noise in segmented image, the finite Student's-t mixture model (SMM) has been recently introduced in [3] as an alternative to GMM. It is because that the Student's-t distribution has heavily tailed than Gaussian distribution. Compared to the GMM, each component of the SMM has one more parameter called the degrees of freedom v. However, both GMM and SMM don't consider the fact that spatially adjacent pixel points most likely should belong to the same cluster. Recently, Markov Random Field (MRF) has been applied to impose spatial smoothness constraints on the image segmentation. But one main difficulty concerning the use of MRF as smoothness constraints is their high computational complexity. In this paper, we present a new finite Student's-t mixture model, based on MRF and weighted mean template. In this model, the M-step of the EM algorithm [4] can be * Corresponding Author