The application of three-dimensional (3D) facial analysis and landmarking algorithms in the field of maxillofacial surgery and other medical applications, such as diagnosis of diseases by facial anomalies and dysmorphism, has gained a lot of attention. In a previous work, we used a geometric approach to automatically extract some 3D facial key points, called landmarks, working in the differential geometry domain, through the coefficients of fundamental forms, principal curvatures, mean and Gaussian curvatures, derivatives, shape and curvedness indexes, and tangent map. In this article we describe the extension of our previous landmarking algorithm, which is now able to extract eyebrows and mouth landmarks using both old and new meshes. The algorithm has been tested on our face database and on the public Bosphorus 3D database. We chose to work on the mouth and eyebrows as a separate study because of the role that these parts play in facial expressions. In fact, since the mouth is the part of the face that moves the most and affects mainly facial expressions, extracting mouth landmarks from various facial poses means that the newly developed algorithm is pose-independent.
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