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A discretization method for the numerical solution of Dieudonné–Rashevsky type problems with application to edge detection within noisy image data
Author(s) -
Franek Lucas,
Franek Marzena,
Maurer Helmut,
Wagner Marcus
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.996
Subject(s) - discretization , sequence (biology) , convergence (economics) , type (biology) , enhanced data rates for gsm evolution , mathematical optimization , image (mathematics) , mathematics , computer science , algorithm , artificial intelligence , mathematical analysis , ecology , genetics , economics , biology , economic growth
SUMMARY The present paper is concerned with the numerical solution of multidimensional control problems of Dieudonné–Rashevsky type by discretization methods and large‐scale optimization techniques. We prove first a convergence theorem wherein the difference of the minimal value and the objective values along a minimizing sequence is estimated by the mesh size of the underlying triangulations. Then we apply the proposed method to the problem of edge detection within raw image data. Instead of using an Ambrosio–Tortorelli type energy functional, we reformulate the problem as a multidimensional control problem. The edge detector can be built immediately from the control variables. The quality of our numerical results competes well with those obtained by applying variational techniques. Copyright © 2011 John Wiley & Sons, Ltd.