Result: Signal and image approximation with level-set constraints

Title:
Signal and image approximation with level-set constraints
Authors:
SCHNÖRR, C
Source:
Computing (Wien. Print). 81(2-3):137-160
Publisher Information:
Wien: Springer, 2007.
Publication Year:
2007
Physical Description:
print, 23 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Méthodes de calcul scientifique (y compris calcul symbolique, calcul algébrique), Methods of scientific computing (including symbolic computation, algebraic computation), Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Algorithme, Algorithm, Algoritmo, Analyse numérique, Numerical analysis, Análisis numérico, Approximation, Aproximación, Calcul scientifique, Scientific computation, Computación científica, Fonction convexe, Convex function, Función convexa, Méthode décomposition, Decomposition method, Método descomposición, Méthode optimisation, Optimization method, Método optimización, Méthode pénalité, Penalty method, Método penalidad, Méthode relaxation, Relaxation method, Método relajación, Méthode statistique, Statistical method, Método estadístico, Problème complémentarité, Complementarity problem, Problema complementariedad, Programmation mathématique, Mathematical programming, Programación matemática, 49XX, 65Kxx, Ensembe niveau, Level set, 68U10; 65K05; 65K10; 90C33, level-sets; image approximation; equilibrium constraints; complementarity constraints; DC-programming
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics and Computer Science, University of Heidelberg, Heidelberg, Germany
ISSN:
0010-485X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=20263230
Rights:
Copyright 2008 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems

Mathematics
Accession Number:
edscal.20263230
Database:
PASCAL Archive

Further Information

We present a novel variational approach to signal and image approximation using filter statistics (histograms) as constraints. Given a set of linear filters, we study the problem to determine the closest point to given data while constraining the level-sets of the filter outputs. This criterion and the constraints are formulated as a bilevel optimization problem. We develop an algorithm by representing the lower-level problem through complementarity constraints and by applying an interior-penalty relaxation method. Based on a decomposition of the penalty term into the difference of two convex functions, the resulting algorithm approximates the data by solving a sequence of convex programs. Our approach allows to model and to study the generation of image structure through the interaction of two convex processes for spatial approximation and for preserving filter statistics, respectively.