General morphometric protocol

Four simple steps to morphometric success

Four steps

• Data acquisition – images and landmarks• Remove shape variation and generate shape

variables – superimposition and TPS• Perform statistical analyses to test biological

hypotheses – standard multivariate analysis and resampling methods

• Produce graphical depiction of results – deformation grids, statistical plots, etc.

Data acquisition - images

• Transferring 3D to 2D depiction• Many ways to go wrong• Three things that don’t matter

– Location in plane– Scale– Rotation

Problems to avoid

• Paralax – pitch and roll• “bendiness” – look for straight lines and

include points on these lines• Articulated structures – can incorporate in

analysis or remove as noise, but easiest to avoid problem in beginning

Avoiding image problems

• Standardize image acquisition procedure• Independent quality check

Digitizing landmarks

• Homology• Type 1, 2, and 3 - sliding semilandmarks• Order is critical• Checking for errors and outliers• Symmetrical structures

Step two – remove nonshape variation and generate shape

variables

• 3 types of nonshape variation – relative position, scale, rotation

• Remove by a process called superimposition via generalized Procrustes analysis or GPA

Variation in images

Translation

Rotation

Scaling

Only shape variation left

Generate shape variables

Thin plate spline

Generates non-affine and affine components referred to as partial warps and uniform components

Affine and non-affine shape change

Shape coordinates

• Partial warps come in X and Y pairs, (2p-4)• Uniform components also a pair, X and Y• Combined referred to as the W (weight)

matrix• Scores are coordinates of a point along

partial warp axes• Nonsingular data matrix for multivariate

analysis of shape

Relative warps

• Can use PCA on W matrix to generate relative warp scores and use these as data matrix

• Useful for visualization of major axis of shape variation