Morphometrics

"Morphometrics", in the broader sense, is also used to precisely locate certain areas of organs such as the brain,[6][7] and in describing the shapes of other things.

Traditional morphometric data are nonetheless useful when either absolute or relative sizes are of particular interest, such as in studies of growth.

These data are also useful when size measurements are of theoretical importance such as body mass and limb cross-sectional area and length in studies of functional morphology.

However, these measurements have one important limitation: they contain little information about the spatial distribution of shape changes across the organism.

Landmark-based studies have traditionally analyzed 2D data, but with the increasing availability of 3D imaging techniques, 3D analyses are becoming more feasible even for small structures such as teeth.

[9] Finding enough landmarks to provide a comprehensive description of shape can be difficult when working with fossils or easily damaged specimens.

Type 2 landmarks are intermediate; this category includes points such as the tip structure, or local minima and maxima of curvature.

In addition to landmarks, there are semilandmarks, points whose position along a curve is arbitrary but which provide information about curvature in two[11] or three dimensions.

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.

[14][15] Additionally, any information that cannot be captured by landmarks and semilandmarks cannot be analyzed, including classical measurements like "greatest skull breadth".

Diffeomorphometry[16] 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.

[17] Diffeomorphic registration,[18] introduced in the 90s, is now an important player with existing code bases organized around ANTS,[19] DARTEL,[20] DEMONS,[21] LDDMM,[22] StationaryLDDMM[23] are examples of actively used computational codes for constructing correspondences between coordinate systems based on sparse features and dense images.

[33] Likewise, neither compares homologous points, and global change is always given more weight than local variation (which may have large biological consequences).

Eigenshape analysis requires an equivalent starting point to be set for each specimen, which can be a source of error EFA also suffers from redundancy in that not all variables are independent.

[33] On the other hand, it is possible to apply them to complex curves without having to define a centroid; this makes removing the effect of location, size and rotation much simpler.

The pattern of clustering of samples in this morphospace represents similarities and differences in shapes, which can reflect phylogenetic relationships.

[48][49][50][51][52] Many other applications of shape analysis in ecology and evolutionary biology can be found in the introductory text: Zelditch, ML; Swiderski, DL; Sheets, HD (2012).

In neuroimaging, the shape and structure of the brains of living creatures can be measured using magnetic resonance imaging.