Image segmentation is an essential processing step for many image analysis applications. In this paper, a novel image segmentation algorithm using fuzzy C-means clustering (FCM) with spatial constraints based on Markov random field (MRF) via Bayesian theory is proposed. Due to disregard of spatial constraint information, the FCM algorithm fails to segment images corrupted by noise. In order to improve the robustness of FCM to noise, a powerful model for the membership functions that incorporates local correlation is given by MRF defined through a Gibbs function. Then spatial information is incorporated into the FCM by Bayesian theory. Therefore, the proposed algorithm has both the advantages of the FCM and MRF, and is robust to noise. Experimental results on the synthetic and real-world images are given to demonstrate the robustness and validity of the proposed algorithm.

With a Gaussian kernel function, we find that the distance between two classes (DBTC) can be used as a class separability criterion in feature space since the between-class separation and the within-class data distribution are taken into account impliedly. To test the validity of DBTC, we develop a method of tuning the kernel parameters in support vector machine (SVM) algorithm by maximizing the DBTC in feature space. Experimental results on the real-world data show that the proposed method consistently outperforms corresponding hyperparameters tuning methods.