Procrustes

One of the types of objects in PRAAT.

An object of type Procrustes represents the special affine transform that consists of a combination of a translation, a shape preserving transformation and a scaling (this scaling is often called dilation). Because the transformation has to be shape preserving, only a combination of a rotation and a reflection is allowed. A configuration matrix X is transformed in the following way to a new configuration matrix Y:

Y = s X T+ 1t',

where s is the scaling factor, T is the shape preserving transformation matrix, t is the translation vector, and 1 is the vector with only ones as its elements.

For more information about the Procrustes transform and its algorithm see chapter 19 in Borg & Groenen (1997).

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© djmw, September 27, 2001