Homographic

Homographic is an adjective used in linguistics and in mathematics and computer vision to describe phenomena involving identical form across domains. In linguistics, a homographic relation refers to two or more words that share the same spelling. These words may have different meanings, and possibly different pronunciations.

A common example is lead, which can be pronounced differently as in lead (to guide) and lead (the metal). If the pronunciation differs, such words are called heteronyms, a subset of homographs. The term homographic thus characterizes the orthographic identity rather than phonetic identity.

In mathematics and related fields, homographic relates to a homography, a projective transformation that maps points in one plane to another while preserving straight lines. Objects related by a homography are described as being homologous with respect to the transformation. In computer vision and image processing, homographic transformations are used to rectify images, stitch panoramas, or model planar scenes. The transformation is typically represented by a 3x3 matrix in homogeneous coordinates.

Etymology: the word derives from Greek homo- meaning same and graph- meaning writing or drawing. The term is used to distinguish the idea of identical written form in language from the geometric concept of a projective mapping in geometry and vision. See also homograph, heteronym, and homography.