Theory of Shape - Geometric Morphometrics for Biologists - page 100

After rotation to partial Procrustes superimposition, the square root of the sum of the
squared differences between the coordinates of corresponding landmarks can be further
reduced by rescaling the target to centroid size of cos(

ρ

). Configurations that satisfy this
condition are said to be in full Procrustes superimposition on the reference; and the resulting
distance between shapes (square root of the sum of the squared differences between the
coordinates of corresponding landmarks) is the full Procrustes distance . The set of shapes in
full Procrustes superimposition comprises a hypersphere of radius one-half, inside the
hypersphere of shapes in partial Procrustes superimposition, and tangent to the larger
hypersphere at the reference. This smaller, inner hypersphere is Kendall's shape space .

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