Reliability of measurements in geometric and traditional morphometrics of human skull

The aim of this study is to confront the methods of traditional (classical) morphometrics (TM) with geometric morphometrics (GM). TM applies direct measurements of an object using some anthropometric instruments. In GM, object is analyzed in a virtual space and except the metric characteristics it is allowed to measure also the object’s shape independently of its position, orientation, and/or size. Furthermore, the study is focused on the classification of measurement errors in TM and GM, as well as the possibilities of their minimization. An overview and classification of (semi)landmarks depending on their reliability are proposed. In 2D analysis, only three types of landmarks are differentiated but in 3D approach nine types of (semi)landmarks are described. Selected curves and surface patches on the skull are also defined. A comparison of 2D and 3D analyses shows that the 2D photos (projections) are suitable for measuring only if the skull itself is not available. Only a slight rotation of the skull from the standardized planes (anthropometric norms) leads to artificial optical deformations, which increases distortion of the real variability. Contrary to 2D approach, the 3D one is offering not only richer information on the object using three coordinates additionally to only two, but more accurate measurements using mathematical definition of Frankfort horizontal and sagittal plane as well. The complexity of human skull measured by landmark coordinates is augmented by geometrically homologous (semi)landmarks on curves and surfaces, which are very important also backwards to calculate linear measurements from (semi)landmark coordinates. The major advantage of GM methods is the preservation of the full geometry of the object under study and the possibility to generate clear graphical outputs of the associated shape changes.