Landmarks can slide, brains can not: interpreting models of shape variation

Abstract

Since the earliest studies in morphometrics the geometric modelling of smooth surfaces and curves has represented a major challenge for anatomists and biostatisticians. Since the end of the 80’s geometric morphometrics supplied landmark-based methods able to support geo-metrical modelling using anatomical references, but scarcely effective when dealing with curves or outlines. Recent improvements have produced a toolkit using sliding semilandmarks which enables to combine outlines with landmarks in a non-arbitrary way. The introduction of the sliding techniques provided a basic tool to approach such diffcult task. However, the thorny algebra behind this issue, the theoretical constraints, the practical requirements, and the very user-friendly software interfaces, produced a heterogeneous framework of application which probably is hampering a full exploitation of these tools. Taking into account a case-study associated with human brain variation, here we present some comparative results between the common plain approach to outline by equidistant points (pseudolandmarks), and the two classic sliding semilandmark-techniques: minimisation of Procrustes distance and minimisa-tion of bending energy. It is clear that the structure of the morphospace is infuenced by the choice of methods. Two main points must be considered accordingly. First, the choice of a given sliding technique for each case-study should be carefully explained in terms of the relationship between the biological nature of the anatomical variation and the properties of the algebra involved. Second, possible differences represent bias only if the re-sulting morphospace is taken as “the reality”, and not as an interpretation (a model) of it.