Diffeomorphic Matching

Abstract

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

$$E_{I,I'} (\varphi ) = p(\varphi ) + D(\varphi.I,I').$$

(11.1)

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.