WHAT IS AN AVERAGE SHAPE AND WHAT IS AN AVERAGE TEXTURE? THE CAVEATS OF USING MORPHING PROGRAMMES TO CREATE \u201cAVERAGE\u201d FACES

Morphing programmes have been used quite extensively in evolutionary psychology to create \u201caverage\u201d faces and warp the averaged faces along defined morphometric axis. Although the term average is used without much concern in the literature, a mathematical average can be performed only on scalar or vectorial variables and \u201cshape\u201d is neither a scalar nor a vectorial variable. The recent progress of geometric morphometry has allowed a landmark-based rigorous approach to shape statistics. Using this methodology, average shapes can be defined in a projection space (Kendall\u2019s shape space), however, the average shape critically depends on the choice of landmarks. Secondly, the outcome of a morphing procedure depends on the interpolant function. Many morphing programmes use elastic deformations. However, thin plate splines (TPS), is the interpolant function of minumum bending energy used in geometric morphometry. Here we will provide evidence that use of elastic deformation or TPS results in visibly different averages even when the same set of landmarks is used. Finally, up to now, an \u201caverage\u201d texture was created by superimposing images warped to conform a consensus shape. This approach results in a very smooth skin texture because it dilutes all the blemishes of the individual textures. However, especially when thinking in biological terms, blemishes and imperfections are the relevant signals that should be detected and blending images completely abolishes these signals. Rigorous methods to calculate an average textures are yet to be developed