Procrustes

Procrustes is a figure from Greek mythology and the name given to a family of statistical methods. In myth, Procrustes—also known as Damastes in some sources—was a robber who preyed on travellers along the road to Athens. He kept a bed of a fixed length and would force guests to fit it: those who were too long would be stretched, and those who were too short would be cut to match the bed. Theseus eventually confronted and killed him by applying the same method to him. The tale is often cited as an emblem of arbitrary conformity and brutal enforcement of standard forms. The adjective Procrustean and the phrase “Procrustean bed” are used metaphorically to describe forced or uniform standards.

In statistics and shape analysis, Procrustes analysis is a method for comparing shapes by removing differences in position, orientation, and size. The basic idea is to transform configurations of corresponding points to minimize the sum of squared distances between corresponding points. Ordinary Procrustes analysis handles a single configuration, while generalized Procrustes analysis extends the idea to multiple configurations to produce a common or consensus shape. Procrustes distance measures dissimilarity between shapes after alignment. The approach is widely used in morphometrics, computer vision, psychology, and biology for tasks such as landmark-based shape comparison, pattern recognition, and 3D model alignment, often employing techniques like singular value decomposition to compute optimal alignment.