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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Diffeomorphic Matching
verfasst von : Laurent Younes
Erschienen in: Shapes and Diffeomorphisms
Verlag: Springer Berlin Heidelberg
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A standard way to ensure the existence of a smooth solution of a matching problem is to add a penalty term in the matching functional. This term would complete (10.1) to form
11.1
$$E_{I,I'} (\varphi ) = p(\varphi ) + D(\varphi.I,I').$$
A large variety of methods have been designed, in approximation theory, statistics or signal processing for solving ill-posed problems. The simplest (and typical) form of penalty function is
$$p(\varphi ) = ||\varphi - id||_H^2 $$
for some Hilbert (or Banach) space of functions.