Generalized multidimensional scaling (GMDS) is an extension of metric multidimensional scaling, in which the target space is non-Euclidean. When the dissimilarities are distances on a surface and the target space is another surface, GMDS allows finding the minimum-distortion embedding of one surface into another.
GMDS is an emerging research direction. Currently, main applications are recognition of deformable objects (e.g. for three-dimensional face recognition) and texture mapping.
References
Bronstein AM, Bronstein MM, Kimmel R (January 2006). "Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching". Proc. Natl. Acad. Sci. U.S.A. 103 (5): 1168–72. doi:10.1073/pnas.0508601103. PMC 1360551. PMID 16432211.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
