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We present a novel approach to accurately detect landmarks and segment regions on face meshes without the use of texture, pose or orientation information. The proposed approach is based on a 3D point distribution model (PDM) that is fitted to the region of interest using candidate vertices extracted from low-level feature maps. The robustness of the algorithm is evaluated in the presence of noise and at the variation of the number of scans and model points used in the learning phase. Experimental results demonstrate the accuracy of the proposed method in detecting landmarks, with an improvement of 55% over a state-of-the-art non-statistical approach.