Thin-plate splines for 2D landmarks

This module shows a shape deformation from one landmark configuration to another. The expected data are specimens in rows, alternating x and y coordinates in columns. Procrustes standardization recommended.

Any shape selected in the From shape menu, is taken as a reference, with an associated square grid. The warps from this to all other specimens can be viewed. You can also choose the mean shape as the reference.

The 'Expansion factors' option will display the area expansion (or contraction) factor around each landmark in yellow numbers, indicating the degree of local growth. This is computed using the Jacobian of the warp. Also, the expansions are colour-coded for all grid elements, with green for expansion and purple for contraction.

At each landmark, the principal strains can also be shown, with the major strain in black and minor strain in brown. These vectors indicate directional stretching.

A description of thin-plate spline transformation grids is given by Dryden & Mardia (1998).


Dryden, I.L. & K.V. Mardia 1998. Statistical Shape Analysis. Wiley.

Published Nov. 5, 2020 11:27 AM - Last modified Nov. 5, 2020 11:27 AM