A Comparison of Semilandmarking Approaches in the Visualisation of Shape Differences

This study extends previous work that examined the consequences of using different approaches to locating densely matched points (semilandmarks) over surfaces on subsequent estimates of their average shape and shape variation with size (allometric scaling). In that study, it was shown that different approaches yield different semilandmarks and, thus, different estimates of means, scaling, and distributions of surface shapes, although there is a high degree of consistency among some approaches. In this study, we compare the surfaces obtained by warping surfaces to the different estimates of landmark and semilandmark configurations that arose from the previous study. Such surfaces have utility in practical contexts, for example, in visualising analytic results as reference surfaces to use in the clinic to assess anomalies and the effects of treatment, or as the basis for building models for subsequent functional analyses. We show that these surfaces share many similarities but differ in detail. Thus, visualisations of shapes derived using semilandmarks from non-rigid semilandmarking approaches especially are likely to fairly represent surfaces and differences between them but are not identical. The extent to which these differences are important depends on the particular study context and aims. In landmark-based analyses of size and shape variation and covariation among biological structures, regions lacking clearly identifiable homologous landmarks are commonly described by semilandmarks. Different algorithms may be used to apply semilandmarks, but little is known about the consequences of analytical results. Here, we assess how different approaches and semilandmarking densities affect the estimates and visualisations of mean and allometrically scaled surfaces. The performance of three landmark-driven semilandmarking approaches is assessed using two different surface mesh datasets with different degrees of variation and complexity: adult human head and ape cranial surfaces. Surfaces fitted to estimates of the mean and allometrically scaled landmark and semilandmark configurations arising from geometric morphometric analyses of these datasets are compared between semilandmarking approaches and different densities, as well as with those from warping to landmarks alone. We find that estimates of surface mesh shape (i.e., after re-semilandmarking and then re-warping) made with varying numbers of semilandmarks are generally consistent, while the warping of surfaces using landmarks alone yields surfaces that can be quite different to those based on semilandmarks, depending on landmark coverage and choice of template surface for warping. The extent to which these differences are important depends on the particular study context and aims.