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A 3-stage algorithm is proposed for automatic detection of the four primary landmarks in 3D face imagery: eyes, nose, and mouth. Pose and facial expression variations which raise major difficulties in landmark processing are the primary focus of this work. In the first stage, Gaussian and Mean curvatures are used to extract ridge and valley points. The second stage utilizes a recursive grouping algorithm to generate candidate landmarks. In the last stage, a geometric model imposing a set of distance and angle constraints to the arrangement of candidate landmarks is utilized to select the final four landmarks. The algorithm is robust against variations in pose and expression with an overall success rate of 98.3%, using the Bosphorus Database as the test input.