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Generalized multidimensional scaling

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Generalized multidimensional scaling (GMDS) is an extension of metric multidimensional scaling, in which the target space in non-Euclidean. In case 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, A. M, Bronstein, M.M, and Kimmel, R. (2006), Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching, Proc. National Academy of Sciences (PNAS), Vol. 103/5, pp. 1168-1172.
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