Advances in virtual morphometrics: a new approach to generate 2D and 3D surface outlines on virtual specimens

Palaeoanthropology and Bioarchaeology make extensive use of outline-based morphometrics and this approach can be used to ex-tract information from several sources. 2D outlines are usually generated from teeth or lithic tools, as well as from skulls or longbones profiles, and this method is widespread in the study of human evolution [1, 2]. In many cases, the generation of outlines is avaluable alternative to traditional linear measurements or 2D landmark-based geometric morphometrics. 2D outlines are conven-tionally acquired through photography, a procedure prone to parallax errors . In recent years, the use of virtual collections increasedremarkably due to the availability of novel imaging techniques, such as CT-scanning, laser scanning and photogrammetry. anksto these new virtual environments, current methodological approaches can be improved and new techniques can be developed. Wepresent here a method to generate 2D and 3D outlines of complex specimens from a 3D surface model. e 3D contours recreatethe patterns of maximal breadth of the object outline. e procedure has been developed in the R statistical environment and usesα-shape approach and Bézier curves to generate the outlines. α-shape formalises the concept of “shape” for spatial point sets in com-putational geometry : a α-shape is built by connecting all the pairs of points lying on a circle which is not touching or overlappingany other point of the set. Bézier curves are used to approximate curves by generating a set of points through a polynomial fitting.Only three landmarks are needed to apply the method: these points define a reference plane to project all the vertices of the 3Dmodel onto. A α-shape is then obtained from the projected vertices and a Bézier approximation is used to generate evenly spacedlandmarks lying on the outline. e 3D outline is generated by bringing each point of the α-shape back on the surface model; aBézier curve is then calculated. is method allows high precision and reproducibility in outline generation and can be applied onboth skeletal and lithic material. 3D contours generated with this method consent to address new questions on functional trendsin skeletal morphology or in material culture, enhancing the morphometric approach on the study of human evolution.