A Procrustes transformation is a geometric transformation that involves only
translation
Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...
,
rotation,
uniform scaling
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a ''scale factor'' that is the same in all directions. The result of uniform scaling is similar ...
, or a
combination
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are th ...
of these
transformations. Hence, it may change the size, position, and orientation of a geometric object, but not its
shape
A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type.
A plane shape or plane figure is constrained to lie ...
.
The Procrustes transformation is named after the mythical Greek robber
Procrustes
In Greek mythology, Procrustes (; Greek: Προκρούστης ''Prokroustes'', "the stretcher ho hammers out the metal), also known as Prokoptas, Damastes (Δαμαστής, "subduer") or Polypemon, was a rogue smith and bandit from Attica ...
who made his victims fit his bed either by stretching their limbs or cutting them off.
See also
*
Procrustes analysis
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name ''Procrustes'' ( el, Προκρούστης) refers to a bandit from Greek mythology who made his victims fi ...
*
Orthogonal Procrustes problem The orthogonal Procrustes problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices A and B and asked to find an orthogonal matrix \Omega which most closely maps A to B. Specifically,
:R = \arg\m ...
*
Singular value decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is re ...
*
Affine transformation, which also allows for
shear
Shear may refer to:
Textile production
*Animal shearing, the collection of wool from various species
**Sheep shearing
*The removal of nap during wool cloth production
Science and technology Engineering
*Shear strength (soil), the shear strength ...
External links
Procrustes transformation
Euclidean symmetries
{{Geometry-stub