An Integrated Approach for Landmark-based Robust Shape Analysis in 3D

TORCIDA S; PEREZ S. I.; GONZALEZ P.

EVOLUTIONARY BIOLOGY

SPRINGER

Lugar: Berlin; Año: 2014 p. 351 - 366

0071-3260

The study of shape changes in morphology has seen a significant renovation in the last 20 years, particularly as a consequence of the development of geometric morphometric methods based on Cartesian coordinates of points. In order to extract information about shape differences when Cartesian coordinates are used, it is necessary to establish a common reference frame or coordinate system for all specimens being compared. A central issue in coordinate-based methods is therefore which criterion should be used to align these configurations of points, since shape differences highly depend on those alignments. This is usually accomplished by aligning the configurations in such a way that the sum of squared distances between coordinates of homologous landmarks are minimized (least-squares superimposition method). However, it is widely recognize that least-squares superimposition has some limitations when shape differences are not homogeneous across landmarks. Here, we present an integrated approach for the resistant shape comparison of 3D landmark sets. It includes a new ordinary resistant Procrustes superimposition (ORP) and its corresponding generalized resistant Procrustes version (GRP), and they are combined with existing resistant multivariate statistical techniques for depicting the results. We demonstrate, by using both simulated and real datasets, that the resistant Procrustes approach better detects and measures localized shape variation whenever presents in up to half but one of the landmarks. The resistant Procrustes results are highly concordant with a priori biological information and might dramatically improve the quality of inferences on patterns of shape variation.