Fuzzy Distribution Fitting Energy-Based Active Contours for Image Segmentation

This paper presents an unsupervised fuzzy energy-based active contour model for image segmentation, based on techniques of curve evolution. The paper proposes a fuzzy energy functional which involves intensity distributions in regions of image to segment and value of fuzzy membership functions. The intensity distributions are derived using a Gaussian mixture model (GMM)-based intensity distribution estimator. Meanwhile, the fuzzy membership functions valued in [0,1] is used to measure the association degree of each image pixel to the region outside and inside the curve. The proposed energy functional is then incorporated into a pseudo-level set formulation. To minimize the energy functional, instead of solving Euler–Lagrange equation of underlying problem, we utilize a direct method to calculate the alterations of the fuzzy energy. In addition, since the parameters of intensity distributions are preestimated, the proposed model avoids the step of updating them at each iteration of curve evolution. The proposed model therefore overcomes the initialization problem of common gradient-descent-based active contour models and converges quickly. Besides, it can work with images with blurred object boundaries. In addition, the extension of the model for the more general case of local space-varying intensities enables dealing with images with intensity inhomogeneity. Experimental results for synthetic and real images validate the desired performances of the proposed model.