of each landmark to the centroid. The configuration is rotated to minimize the deviation between it and a reference, typically the mean shape. In the case of semi-landmarks, variation in position along the curve is also removed. Because shape space is curved, analyses are done by projecting shapes onto a space tangent to shape space. Within the tangent space, conventional multivariate statistical methods such as multivariate analysis of variance and multivariate regression, can be used to test statistical hypotheses about shape. Procrustes-based analyses have some limitations. One is that the Procrustes superimposition uses a least-squares criterion to find the optimal rotation; consequently, variation that is localized to a single landmark will be smeared out across many. This is called the 'Pinocchio effect'. Another is that the superimposition may itself impose a pattern of covariation on the landmarks. Additionally, any information that cannot be captured by landmarks and semilandmarks cannot be analyzed, including classical measurements like "greatest skull breadth". Moreover, there are criticisms of Procrustes-based methods that motivate an alternative approach to analyzing landmark data. Euclidean distance matrix analysis Diffeomorphometry Diffeomorphometry is the focus on comparison of shapes and forms with a metric structure based on diffeomorphisms, and is central to the field of computational anatomy. Diffeomorphic registration, introduced in the 90s, is now an important player with existing code bases organized around ANTS, DARTEL, DEMONS, LDDMM, StationaryLDDMM are examples of actively used computational codes for constructing correspondences between coordinate systems based on sparse features and dense images. Voxel-based morphometry (VBM) is an important technology built on many of these principles. Methods based on diffeomorphic flows are used in For example, deformations could be diffeomorphisms of the ambient space, resulting in the LDDMM (Large Deformation Diffeomorphic Metric Mapping) framework for shape comparison. On such deformations is the right invariant metric of Computational Anatomy which generalizes the metric of non-compressible Eulerian flows but to include the Sobolev norm ensuring smoothness of the flows, metrics have now been defined associated to Hamiltonian controls of diffeomorphic flows. Outline analysis Outline analysis is another approach to analyzing shape. What distinguishes outline analysis is that coefficients of mathematical functions are fitted to points sampled along the outline. There are a number of ways of quantifying an outline. Older techniques such as the "fit to a polynomial curve" and Principal components quantitative analysis have been superseded by the two main modern approaches: eigenshape analysis,<ref name=Lohmann1983></ref> and elliptic