Measuring facial traits by quantitative means is a prerequisite to investigate epidemiological, clinical, and forensic questions. This measurement process has received intense attention in recent years. We divided this process into the registration of the face, landmarking, morphometric quantification, and dimension reduction. Face registration is the process of standardizing pose and landmarking annotates positions in the face with anatomic description or mathematically defined properties (pseudolandmarks). Morphometric quantification computes pre-specified transformations such as distances. Landmarking: We review face registration methods which are required by some landmarking methods. Although similar, face registration and landmarking are distinct problems. The registration phase can be seen as a pre-processing step and can be combined independently with a landmarking solution. Existing approaches for landmarking differ in their data requirements, modeling approach, and training complexity. In this review, we focus on 3D surface data as captured by commercial surface scanners but also cover methods for 2D facial pictures, when methodology overlaps. We discuss the broad categories of active shape models, template based approaches, recent deep-learning algorithms, and variations thereof such as hybrid algorithms. The type of algorithm chosen depends on the availability of pre-trained models for the data at hand, availability of an appropriate landmark set, accuracy characteristics, and training complexity. Quantification: Landmarking of anatomical landmarks is usually augmented by pseudo-landmarks, i.e., indirectly defined landmarks that densely cover the scan surface. Such a rich data set is not amenable to direct analysis but is reduced in dimensionality for downstream analysis. We review classic dimension reduction techniques used for facial data and face specific measures, such as geometric measurements and manifold learning. Finally, we review symmetry registration and discuss reliability
