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In this paper, we propose an unsupervised variational two-phase image segmentation model based on Fuzzy Region Competition. This model uses probability density functions to design image regions and to set a homogeneity criterion for the competition between regions. The key idea of the proposed model is to optimize the probability distribution parameters while the segmentation procedure takes place. The experiments in natural and noisy images showed that the proposed model is robust in relation to noise and presents better segmentation results using texturized images than the unsupervised piecewise constant case of Fuzzy Region Competition method.