Procrustes superimposition. The figure shows the three transformation steps of an ordinary Procrustes fit for two configurations of landmarks. (a) Scaling of both configurations to the same size; (b) Transposition to the same position of the center of gravity; (c) Rotation to the orientation that provides the minimum sum of squared distances between corresponding landmarks.
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name Procrustes (Greek: Προκρούστης) refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off.
In mathematics:
an orthogonal Procrustes problem is a method which can be used to find out the optimal rotation and/or reflection (i.e., the optimal orthogonal linear transformation) for the Procrustes Superimposition (PS) of an object with respect to another.
a constrained orthogonal Procrustes problem, subject to det(R) = 1 (where R is an orthogonal matrix), is a method which can be used to determine the optimal rotation for the PS of an object with respect to another (reflection is not allowed). In some contexts, this method is called the Kabsch algorithm.
When a shape is compared to another, or a set of shapes is compared to an arbitrarily selected reference shape, Procrustes analysis is sometimes further qualified as classical or ordinary, as opposed to generalized Procrustes analysis (GPA), which compares three or more shapes to an optimally determined "mean shape".
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statistics, Procrustesanalysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name Procrustes (Greek: Προκρούστης)...
tellings, if the guest proved too tall, Procrustes would amputate the excess length; if the guest was too short Procrustes would stretch them until they died;...
Generalized Procrustesanalysis (GPA) is a method of statistical analysis that can be used to compare the shapes of objects, or the results of surveys...
sphere may be considered to have the same shape as a solid sphere. Procrustesanalysis is used in many sciences to determine whether or not two objects...
provided by the MFA is similar in its purpose to that provided by the Procrustesanalysis. In the example (figure 3), individual 1 is characterized by a small...
matrix and rotates the data to preserve procrustes distances. In other words, a principal components analysis preserves the shape variables that were...
they be related by a distance-preserving transformation — this is Procrustesanalysis. Some of the distances may also be missing or come unlabelled (as...
for geometric morphometrics in anthropology. Or an approach like Procrustesanalysis which finds an average shape. David George Kendall investigated the...
off. Procrustesanalysis Orthogonal Procrustes problem Singular value decomposition Affine transformation, which also allows for shear Procrustes transformation...
original shapes. These landmarks are aligned using the generalized procrustesanalysis, which minimizes the least squared error between the points. k {\displaystyle...
Wasserstein metric has a formal link with Procrustesanalysis, with application to chirality measures, and to shape analysis. In computational biology, Wasserstein...
statistical measure of its quality. Geographic coordinate conversion Procrustesanalysis Surveying "Equations Used for Datum Transformations". Toitū Te Whenua...
active contour model which would respect explicit shape constraints. Procrustesanalysis Point distribution model T.F. Cootes and C.J. Taylor and D.H. Cooper...
as multivariate analysis of variance and multivariate regression, can be used to test statistical hypotheses about shape. Procrustes-based analyses have...
the immigrationist and the continuity theories. According to a triple analysis – autosomal, mitochondrial and paternal — of available data from large-scale...
chimpanzees: neotenic hypothesis reconsidered with a tridimensional Procrustesanalysis". American Journal of Physical Anthropology. 118 (1): 50–62. doi:10...
position Pattern recognition Procrustesanalysis Ramsey theory, for a notion of "unavoidable coincidences" Statistical shape analysis Kendall, David G.; Kendall...
Wang, Chang; Sridhar Mahadevan (2008). Manifold Alignment using ProcrustesAnalysis (PDF). The 25th International Conference on Machine Learning.[permanent...
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