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Background: Analyzing MR scans of low-grade glioma, with highly accurate segmentation will have an enormous potential in neurosurgery for diagnosis and therapy planning. Low-grade gliomas are mainly distinguished by their infiltrating character and irregular contours, which make the analysis, and therefore the segmentation task, more difficult. Moreover, MRI images show some constraints such as intensity variation and the presence of noise. Methods: To tackle these issues, a novel segmentation method built from the local properties of image is presented in this paper. Phase-based edge detection is estimated locally by the monogenic signal using quadrature filters. This way of detecting edges is, from a theoretical point of view, intensity invariant and responds well to the MR images. To strengthen the tumor detection process, a region-based term is designated locally in order to achieve a local maximum likelihood segmentation of the region of interest. A Gaussian probability distribution is considered to model local images intensities. Results: The proposed model is evaluated using a set of real subjects and synthetic images derived from the Brain Tumor Segmentation challenge –BraTS 2015. In addition, the obtained results are compared to the manual segmentation performed by two experts. Quantitative evaluations are performed using the proposed approach with regard to four related existing methods. Conclusion: The comparison of the proposed method, shows more accurate results than the four existing methods.