2 such that the sum of the squared distances (SSD) between the corresponding points is minimised (an example of least squares technique).

them to an iron bed. Procrustes was a son of Poseidon with a stronghold on Mount Korydallos, on the sacred way between Athens and Eleusis.

, Using Procrustes' own … Encyclopedia.com.

In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations.

with respect to x Theseus and Procrustes, Attic red-figure neck-amphora, 570–560 BC, Staatliche Antikensammlungen (Inv.

[6], This detail, which injects a note of verisimilitude, is reported by both pseudo-Apollodorus (, Derrida, Jacques, "The Purveyor of Truth," in, 1947–1948 Civil War in Mandatory Palestine, 2007–2008 Israel–Gaza conflict/merger-proposal, Prise de Jérusalem par Hérode le Grand.jpg, http://foldoc.org/index.cgi?query=procrustean+string, https://religion.wikia.org/wiki/Procrustes?oldid=200766.

In either case, his victims died.

However, as soon as the travelers were in his house, Procrustes would tie them to an iron bed.

Procrustes met his end at the hands of the Greek hero Theseus*, who killed him the same way that the robber took care of his victims.

{\displaystyle (x,y)\to (x-{\bar {x}},y-{\bar {y}})} Taking the derivative of Retrieved September 30, 2020 from Encyclopedia.com: https://www.encyclopedia.com/humanities/news-wires-white-papers-and-books/procrustes.

[1], One study by David George Kendall examined the triangles formed by standing stones to deduce if these were often arranged in straight lines. [2] Procrustes continued his reign of terror until he was captured by Theseus, travelling to Athens along the sacred way, who "fitted" Procrustes to his own bed: He killed Damastes, surnamed Procrustes, by compelling him to make his own body fit his bed, as he had been wont to do with those of strangers.

For instance, with full PS two spheres with different radii will always coincide, because they have exactly the same shape. 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 other words, both the placement in space and the size of the objects are freely adjusted.

Conversely, with partial PS they will never coincide.

In this case, the defeat of the opponent justifies the deceptive means.

In the Greek myth, Procrustes was a son of Poseidon with a stronghold on Mount Korydallos at Erineus, on the sacred way between Athens and Eleusis.

y

The Oxford Dictionary of Phrase and Fable.

the remaining points form the Bookstein coordinates. GPA applies the Procrustes analysis method to optimally superimpose a set of objects, instead of superimposing them to an arbitrarily selected shape.

…

In a Procrustean solution in statistics, instead of finding the best fit line to a scatter plot of data, one first chooses the line one wants, then selects only the data that fits it, disregarding data that does not, so to "prove" some idea. There are many ways of representing the shape of an object. x And he did this in imitation of Heracles.

{\displaystyle \theta }

Here, if a victim was shorter ,

We showed how to superimpose two shapes.

If the string inserted is too long, it is truncated. in ancient Greek mythology, a giant robber who forced travellers to lie down on a bed, cutting off the feet of those who were longer than the bed and stretching out those who were shorter to make them fit the bed’s length; hence his name, which means “he who stretches.”. The Oxford Dictionary of Phrase and Fable, Proclamation on Immigration Quotas (28 April 1938), https://www.encyclopedia.com/humanities/news-wires-white-papers-and-books/procrustes, https://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/procrustes, if ifs and ands were pots and pans, there'd be no work for tinkers' hands. This removes variations in translation, rotation and scaling across the dataset in order to move them into a common frame of reference.

Procrustes, in Greek legend, a robber dwelling somewhere in Attica—in some versions, in the neighbourhood of Eleusis.

If the string inserted is too short, then it is padded out, usually with spaces or null characters. A Procrustean solution is the undesirable practice of tailoring data to fit its container or some other preconceived structure. − Theseus turned the tables on Procrustes, fatally adjusting him to fit his own bed. Procrustes met his end at the hands of In some cases, both full and partial PS may also include reflection. called the bases line. Optimal translation and scaling are determined with much simpler operations (see below).

A rotation by angle 2325), Procrustes about to cut off someone's legs, https://greekmythology.wikia.org/wiki/Prokrustes?oldid=74273. Some said that he also had a very short bed; to make passersby fit this he sawed off their legs.

In general, when something is Procrustean, different lengths or sizes or properties are fitted to an arbitrary standard. y Consider two objects composed of the same number of points with scale and translation removed.

In Greek mythology, Procrustes (Greek: Προκρούστης), whose name means "he who stretches", was a robber who lived near the city of Eleusis.

{\displaystyle \theta \,\!}

Procrustes met his end at the hands of the Greek hero Theseus*, who killed him the same way that the robber took care of his victims.

"Procrustes However, as soon as the travelers were in his house, Procrustes would tie them to an iron bed.

This is generally the precursor to further statistical analysis. {\displaystyle ((x_{1},y_{1}),\ldots )}

gives, where (u,v) are the coordinates of a rotated point.

In mathematics: an orthogonal Procrustes problem is a method which can be used to find out the optimal rotation and/or reflection for the Procrustes Superimposition of an object with respect to another. +

He kept a house by the side of the road where he offered hospitality to passing strangers, who were invited in for a pleasant meal and a night's rest in his very special bed.