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Shape identification via metrics constructed from the oriented distance function

Delfour M. C., Zolesio J.-P.

Control and Cybernetics

2005

Vol. 34, no 1

137-164

This paper studies the generic identification problem: to find the best non-parametrized object [Omega] which minimizes some weighted sum of distances to I a priori given objects [Omega]_i for metric distances constructed from the W^1,p-norm on the oriented (resp. signed) distance function which occurs in many different fields of applications. It discusses existence of solution to the generic identification problem and investigates the Eulerian shape semiderivatives with special consideration to the non-differentiable terms occurring in their expressions. A simple example for the new cracked sets recently introduced in Delfour and Zolesio (2004b) is also presented. It can be viewed as an approximation of a cracked set by sets whose boundary is made up of pieces of lines or Bezier curves that are not necessarily connected.