Holdings: Variational methods

Variational methods: in imaging and geometric control

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Bibliographic Details
Other Authors:	Bergounioux, Maïtine (Editor), Peyré, Gabriel (Editor), Schnörr, Christoph (Editor), Caillau, Jean-Baptiste (Editor), Haberkorn, Thomas (Editor)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2017]
Series:	Radon series on computational and applied mathematics Volume 18
Subjects:	Kontrolltheorie Bildverarbeitung Variationsrechnung Monografische Reihe
Online Access:	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110439236&searchTitles=true Inhaltsverzeichnis
Physical Description:	XI, 523 Seiten Illustrationen, Diagramme
ISBN:	9783110430400 9783110439236

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MARC


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245	1	0	\|a Variational methods \|b in imaging and geometric control \|c edited by Maïtine Bergounioux, Gabriel Peyré, Christoph Schnörr, Jean-Baptiste Caillau, Thomas Haberkorn
264		1	\|a Berlin ; Boston \|b De Gruyter \|c [2017]
300			\|a XI, 523 Seiten \|b Illustrationen, Diagramme
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Record in the Search Index

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adam_text	CONTENTS PARTI MARTINE BERGOUNIOUX SECOND-ORDER DECOMPOSITION MODEL FOR IMAGE PROCESSING: NUMERICAL EXPERIMENTATION * 5 1.1 INTRODUCTION------5 1.2 PRESENTATION OF THE MODEL ----- 6 1.3 NUMERICAL ASPECTS ----- 8 1.3.1 DISCRETIZED PROBLEM AND ALGORITHM ----- 8 1.3.2 EXAMPLES------10 1.3.3 INITIALIZATION PROCESS ----- 12 1.3.4 CONVERGENCE ------ 20 1.3.5 SENSITIVITY WITH RESPECT TO SAMPLING AND QUANTIFICATION ----- 25 1.3.6 SENSITIVITY WITH RESPECT TO PARAMETERS ----- 27 1.4 CONCLUSION ------ 31 LAURENT HOELTGEN, MARKUS MAINBERGER, SEBASTIAN HOFFMANN, JOACHIM WEICKERT, CHING HOO TANG, SIMON SETZER, DANIEL JOHANNSEN, FRANK NEUMANN, AND BENJAMIN DOERR OPTIMIZING SPATIAL AND TONAL DATA FOR PDE-BASED INPAINTING * 35 2.1 INTRODUCTION------36 2.2 A REVIEW OF PDE-BASED IMAGE COMPRESSION ----- 38 2.2.1 DATA OPTIMIZATION ----- 38 2.2.2 FINDING GOOD INPAINTING OPERATORS ----- 39 2.2.3 STORING THE DATA ----- 40 2.2.4 FEATURE-BASED METHODS------40 2.2.5 FAST ALGORITHMS AND REAL-TIME ASPECTS ----- 41 2.2.6 HYBRID IMAGE COMPRESSION METHODS ----- 42 2.2.7 MODIFICATIONS, EXTENSIONS AND APPLICATIONS ----- 43 2.2.8 RELATIONS TO OTHER METHODS ----- 44 2.3 INPAINTING WITH HOMOGENEOUS DIFFUSION ----- 44 2.4 OPTIMIZATION STRATEGIES IN ID ----- 46 2.4.1 OPTIMAL KNOTS FOR INTERPOLATING CONVEX FUNCTIONS ----- 46 2.4.2 OPTIMAL KNOTS FOR APPROXIMATING CONVEX FUNCTIONS ----- 51 2.5 OPTIMIZATION STRATEGIES IN 2D ------- 55 2.5.1 OPTIMIZING SPATIAL DATA------55 2.5.2 OPTIMIZING TONAL DATA ----- 62 2.6 EXTENSIONS TO OTHER INPAINTING OPERATORS ----- 70 2.6.1 OPTIMIZING SPATIAL DATA ----- 71 2.6.2 OPTIMIZING TONAL DATA ----- 73 2.7 SUMMARY AND CONCLUSIONS ----- 74 QIAN XIE AND ANUJ SRIVASTAVA IMAGE REGISTRATION USING PHASE-AMPLITUDE SEPARATION ----- 84 3.1 INTRODUCTION ----- 84 3.1.1 CURRENT LITERATURE ----- 85 3.1.2 OUR APPROACH ----- 86 3.2 DEFINITION OF PHASE-AMPLITUDE COMPONENTS ----- 87 3.2.1 Q-MAP AND AMPLITUDE DISTANCE ----- 89 3.2.2 RELATIVE PHASE AND IMAGE REGISTRATION * 91 3.3 PROPERTIES OF REGISTRATION FRAMEWORK------92 3.4 GRADIENT METHOD FOR OPTIMIZATION OVER F ----- 95 3.4.1 BASIS ON 7XID ( 0 ----- 96 3.4.2 MEAN IMAGE AND GROUP-WISE REGISTRATION ----- 97 3.5 EXPERIMENTS ----- 97 3.5.1 PAIRWISE IMAGE REGISTRATION ----- 97 3.5.2 REGISTERING MULTIPLE IMAGES ----- 102 3.5.3 IMAGE CLASSIFICATION ----- 104 3.6 CONCLUSION ----- 105 MARTIN ELLER AND MASSIMO FORNASIER ROTATION INVARIANCE IN EXEMPLAR-BASED IMAGE INPAINTING * 108 4.1 INTRODUCTION TO INPAINTING ----- 108 4.1.1 THE INPAINTING PROBLEM------108 4.1.2 AIMS OF THIS W ORK ----- 112 4.1.3 NOTATION ----- 115 4.2 ROTATION INVARIANT IMAGE PATTERN RECOGNITION 115 4.2.1 PATCH ERROR FUNCTIONS------116 4.2.2 CIRCULAR HARMONICS BASIS ----- 118 4.2.3 MUTUAL ANGLE DETECTION ALGORITHMS------121 4.2.4 ROTATION INVARIANT Z.2-ERROR USING THE CIRCULAR HARMONICS BASIS ------ 126 4.2.5 ROTATION INVARIANT GRADIENT-BASED I 2-ERRORS AND THE CH-BASIS ----- 128 4.3 ROTATION INVARIANT EXEMPLAR-BASED INPAINTING 131 4.3.1 PATCH NON-LOCAL MEANS------132 4.3.2 PATCH NON-LOCAL POISSON------142 4.3.3 NUMERICAL EXPERIMENTS------147 4.4 DISCUSSION AND ANALYSIS ------- 154 4.4.1 PROOF OF CONVERGENCE ------ 155 4.4.2 ANALYSIS OF EV, R ----- 171 4.4.3 CONCLUSION AND FUTURE PERSPECTIVES ----- 178 JOSE A. IGLESIAS AND CLEMENS KIRISITS CONVECTIVE REGULARIZATION FOR OPTICAL FLOW * 184 5.1 INTRODUCTION ----- 184 5.2 MODEL ----- 187 5.2.1 CONVECTIVE ACCELERATION ----- 187 5.2.2 CONVECTIVE REGULARIZATION ----- 190 5.2.3 DATA TERM AND CONTRAST INVARIANCE ----- 193 5.3 NUMERICAL SOLUTION ----- 195 5.4 EXPERIMENTS ----- 196 5.5 CONCLUSION ----- 197 ELENA BERETTA, MONIKA MUSZKIETA, WOLF NAETAR, AND OTMAR SCHERZER A VARIATIONAL METHOD FOR QUANTITATIVE PHOTOACOUSTIC TOMOGRAPHY WITH PIECEWISE CONSTANT COEFFICIENTS * 202 6.1 QUANTITATIVE PHOTOACOUSTIC TOMOGRAPHY ------ 202 6.1.1 INTRODUCTION ----- 202 6.1.2 CONTRIBUTIONS OF THIS ARTICLE ----- 205 6.2 RECOVERY OF PIECEWISE CONSTANT COEFFICIENTS ----- 205 6.3 A MUMFORD-SHAH-LIKE FUNCTIONAL FOR QPAT ----- 207 6.3.1 EXISTENCE OF MINIMIZERS------209 6.3.2 APPROXIMATION ----- 211 6.3.3 MINIMIZATION ----- 212 6.4 IMPLEMENTATION AND NUMERICAL RESULTS ------ 215 A SPECIAL FUNCTIONS OF BOUNDED VARIATION AND THE SBV-COMPACTNESS THEOREM ----- 220 MARTIN BURGER, HENDRIK DIRKS, AND LENA FRERKING ON OPTICAL FLOW MODELS FOR VARIATIONAL MOTION ESTIMATION * 225 7.1 INTRODUCTION ----- 225 7.2 MODELS ------ 226 7.2.1 VARIATIONAL MODELS WITH GRADIENT REGULARIZATION ------ 227 7.2.2 EXTENSION OF THE REGULARIZE ----- 228 7.2.3 BREGMAN ITERATIONS------230 7.3 ANALYSIS ----- 231 7.3.1 EXISTENCE OF MINIMIZERS------231 7.3.2 QUANTITATIVE ESTIMATES ------ 234 7.4 NUMERICAL SOLUTION ------ 236 7.4.1 PRIMAL-DUAL ALGORITHM ------ 236 7.4.2 DISCRETIZATION AND PARAMETERS ----- 239 7.5 RESULTS------241 7.5.1 ERROR MEASURES FOR VELOCITY FIELDS------241 7.5.2 EVALUATION ----- 244 7.6 CONCLUSION AND OUTLOOK ------ 244 7.6.1 MASS PRESERVATION ------ 247 7.6.2 HIGHER DIMENSIONS ------ 247 7.6.3 JOINT MODELS ----- 248 7.6.4 LARGE DISPLACEMENTS ----- 248 LUCA CALATRONI, CHUNG CAO, JUAN CARLOS DE LOS REYES, CAROLA-BIBIANE SCHOENLIEB, AND TUOMO VALKONEN BILEVEL APPROACHES FOR LEARNING OF VARIATIONAL IMAGING MODELS * 252 8.1 OVERVIEW OF LEARNING IN VARIATIONAL IMAGING ----- 252 8.2 THE LEARNING MODEL AND ITS ANALYSIS IN FUNCTION SPACE ----- 257 8.2.1 THE ABSTRACT MODEL ------ 257 8.2.2 EXISTENCE AND STRUCTURE: L2-SQUARED COST AND FIDELITY ----- 258 8.2.3 OPTIMALITY CONDITIONS ----- 260 8.3 NUMERICAL OPTIMIZATION OF THE LEARNING PROBLEM ----- 262 8.3.1 ADJOINT-BASED METHODS ------ 262 8.3.2 DYNAMIC SAMPLING ----- 265 8.4 LEARNING THE IMAGE MODEL ----- 267 8.4.1 TOTAL VARIATION-TYPE REGULARIZATION ----- 267 8.4.2 OPTIMAL PARAMETER CHOICE FOR TV-TYPE REGULARIZATION ----- 269 8.5 LEARNING THE DATA MODEL ----- 274 8.5.1 VARIATIONAL NOISE MODELS ----- 275 8.5.2 SINGLE NOISE ESTIMATION------276 8.5.3 MULTIPLE NOISE ESTIMATION ----- 281 8.6 CONCLUSION AND OUTLOOK ------ 283 PART II PIERNICOLA BETTIOL AND NATHALIE KHALIL NON-DEGENERATE FORMS OF THE GENERALIZED EULER-LAGRANGE CONDITION FOR STATE-CONSTRAINED OPTIMAL CONTROL PROBLEMS * 295 9.1 INTRODUCTION -------- 295 9.2 MAIN RESULT -------- 299 9.3 PROOF OF THEOREM 2.1------301 9.4 PROOF OF LEMMA 3.2 ----- 309 9.5 EXAMPLE -------- 311 PIERNICOLA BETTIOL, BERNARD BONNARD, LAETITIA GIRALDI, PIERRE MARTINON, AND JEREMY ROUOT THE PURCELL THREE-LINK SWIMMER: SOME GEOMETRIC AND NUMERICAL ASPECTS RELATED TO PERIODIC OPTIMAL CONTROLS * 314 10.1 INTRODUCTION -------- 315 10.2 FIRST- AND SECOND-ORDER OPTIMALITY CONDITIONS * 316 10.3 THE PURCELL THREE-LINK SWIMMER ---- 318 10.3.1 MATHEMATICAL MODEL ----- 318 10.4 LOCAL ANALYSIS FOR THE THREE-LINK PURCELL SWIMMER * 320 10.4.1 COMPUTATIONS OF THE NILPOTENT APPROXIMATION * 321 10.4.2 INTEGRATION OF EXTREMAL TRAJECTORIES * 322 10.5 NUMERICAL RESULTS ----- 330 10.5.1 NILPOTENT APPROXIMATION ----- 331 10.5.2 TRUE MECHANICAL SYSTEM * 332 10.5.3 THE PURCELL SWIMMER IN A ROUND SWIMMING POOL * 339 10.6 CONCLUSIONS AND FUTURE WORK * 341 ZHENG CHEN AND YACINE CHITOUR CONTROLLABILITY OF KEPLERIAN MOTION WITH LOW-THRUST CONTROL SYSTEMS * 344 11.1 INTRODUCTION * 344 11.2 NOTATIONS AND DEFINITIONS * 345 11.2.1 DYNAMICS ----- 345 11.2.2 STUDY OF THE DRIFT VECTOR FIELD IN X ----- 347 11.2.3 ADMISSIBLE CONTROLLED TRAJECTORY OF ZSAT ----- 349 11.2.4 CONTROLLED PROBLEMS IN A ----- 350 11.3 CONTROLLABILITY ------ 351 11.3.1 CONTROLLABILITY FOR OTP ----- 353 11.3.2 CONTROLLABILITY FOR OIP * 355 11.3.3 CONTROLLABILITY FOR DOP------357 11.4 NUMERICAL EXAMPLES * 357 11.4.1 A NUMERICAL EXAMPLE FOR OIP * 357 11.4.2 A NUMERICAL EXAMPLE FOR DOP * 359 11.5 CONCLUSION ----- 362 11.6 APPENDIX ----- 362 THIERRY COMBOT HIGHER VARIATIONAL EQUATION TECHNIQUES FOR THE INTEGRABILITY OF HOMOGENEOUS POTENTIALS * 365 12.1 INTRODUCTION: INTEGRABLE SYSTEMS------365 12.2 AN ALGEBRAIC POINT OF VIEW * 366 12.2.1 ALGEBRAIC PRESENTATION OF A HAMILTONIAN SYSTEM * 366 12.2.2 FIRST-ORDER VARIATIONAL EQUATIONS------371 12.2.3 DIFFERENTIAL GALOIS THEORY * 374 12.3 INTRODUCTION TO MORALES-RAMIS THEOREM * 376 12.3.1 THE MORALES-RAMIS THEOREM * 376 12.3.2 HOMOGENEOUS POTENTIALS ----- 377 12.3.3 HIGHER VARIATIONAL EQUATIONS * 378 12.4 APPLICATION TO PARAMETRIZED POTENTIALS * 381 12.4.1 SPACE OF GERMS OF INTEGRABLE POTENTIALS * 381 12.4.2 EIGENVALUE BOUNDING OF SOME N-BODY PROBLEMS ----- 384 JACQUES FEJOZ INTRODUCTION TO KAM THEORY WITH A VIEW TO CELESTIAL MECHANICS * 387 13.1 TWISTED CONJUGACY NORMAL FORM * 388 13.2 ONE STEP OF THE NEWTON ALGORITHM ----- 391 13.3 INVERSE FUNCTION THEOREM * 396 13.4 LOCAL UNIQUENESS AND REGULARITY OF THE NORMAL FORM * 399 13.5 CONDITIONAL CONJUGACY * 403 13.6 INVARIANT TORUS WITH PRESCRIBED FREQUENCY* 404 13.7 INVARIANT TORI WITH UNPRESCRIBED FREQUENCIES * 408 13.8 SYMMETRIES ------ 411 13.9 LOWER DIMENSIONAL TO RI ----- 413 13.10 EXAMPLE IN THE SPATIAL THREE-BODY PROBLEM * 415 A ISOTROPY OF INVARIANT TO RI ------ 423 B TWO BASIC ESTIMATES * 424 C INTERPOLATION OF SPACES OF ANALYTIC FUNCTIONS * 426 MAREK GROCHOWSKI AND WOJCIECH KRYNSKI INVARIANTS OF CONTACT SUB-PSEUDO-RIEMANNIAN STRUCTURES AND EINSTEIN-WEYL GEOMETRY * 434 14.1 INTRODUCTION ------ 434 14.2 DIMENSION 3 ------435 14.3 EINSTEIN-WEYL GEOMETRY ----- 440 14.4 DIMENSION 2N + 1 ----- 444 14.5 CONTACT SUB-PSEUDO-RIEMANNIAN SYMMETRIES ----- 447 14.6 APPENDIX: ISOMETRIES IN DIMENSION 5 ----- 450 JEROME LOHEAC AND JEAN-FRAN^OIS SCHEID TIME-OPTIMAL CONTROL FOR A PERTURBED BROCKETT INTEGRATOR * 454 15.1 INTRODUCTION ----- 454 15.2 CONTROLLABILITY AND TIME-OPTIMAL CONTROLLABILITY ----- 456 15.3 AN APPROXIMATE LINEARIZED TIME-OPTIMAL CONTROL PROBLEM ----- 457 15.4 NUMERICAL COMPUTATION OF A TIME-OPTIMAL TRAJECTORY ----- 459 15.4.1 FINITE-DIMENSIONAL MINIMIZATION PROBLEM ------ 459 15.4.2 NUMERICAL EXAMPLE ----- 460 15.5 APPLICATION TO TIME-OPTIMAL MICRO-SWIMMERS ----- 463 15.5.1 MODELING AND PROBLEM FORMULATION ----- 463 15.5.2 NUMERICAL COMPUTATION OF A TIME-OPTIMAL TRAJECTORY ----- 468 15.6 CONCLUSION ----- 470 JEAN-PIERRE MARCO TWIST MAPS AND ARNOLD DIFFUSION FOR DIFFEOMORPHISMS * 473 16.1 FROM ARNOLD DIFFUSION TO TWIST MAPS ----- 473 16.2 SETTING AND MAIN RESULT ----- 479 16.3 PROOF OF THEOREM 1 ----- 483 16.3.1 CHOICE OF E 0 ------484 16.3.2 IMPLEMENTATION OF MOECKEL*S METHOD ----- 488 16.3.3 NORMALLY HYPERBOLIC SHADOWING ----- 491 16.3.4 CONCLUSION OF THE PROOF OF THEOREM 1 ----- 494 GIANNA STEFANI AND PIERLUIGI ZEZZA A HAMILTONIAN APPROACH TO SUFFICIENCY IN OPTIMAL CONTROL WITH MINIMAL REGULARITY CONDITIONS: PART I ----- 496 17.1 INTRODUCTION ------ 496 17.1.1 THE PROBLEM ----- 498 17.2 NOTATIONS AND PRELIMINARY RESULTS ----- 499 17.2.1 SYMPLECTIC NOTATIONS ----- 500 17.2.2 THE PONTRYAGIN MAXIMUM PRINCIPLE ----- 501 17.3 A HAMILTONIAN APPROACH TO OPTIM ALITY ----- 503 17.3.1 THE CARTAN FORM ----- 503 17.3.2 THE SUPER-HAMILTONIAN AND ITS PROPERTIES ------ 507 17.3.3 ABSTRACT SUFFICIENT OPTIMALITY CONDITIONS ----- 509 17.3.4 THE MINIMUM TIME PROBLEM ----- 512 17.4 FINAL COMMENTS ------ 513 INDEX ----- 517
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genre	(DE-588)4179998-7 Monografische Reihe gnd-content
genre_facet	Monografische Reihe
id	DE-604.BV043556411
illustrated	Illustrated
indexdate	2024-07-10T07:28:46Z
institution	BVB
isbn	9783110430400 9783110439236
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-028971563
oclc_num	969906562
open_access_boolean
owner	DE-703 DE-384 DE-29T
owner_facet	DE-703 DE-384 DE-29T
physical	XI, 523 Seiten Illustrationen, Diagramme
publishDate	2017
publishDateSearch	2017
publishDateSort	2017
publisher	De Gruyter
record_format	marc
series	Radon series on computational and applied mathematics
series2	Radon series on computational and applied mathematics
spelling	Variational methods in imaging and geometric control edited by Maïtine Bergounioux, Gabriel Peyré, Christoph Schnörr, Jean-Baptiste Caillau, Thomas Haberkorn Berlin ; Boston De Gruyter [2017] XI, 523 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Radon series on computational and applied mathematics Volume 18 Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf (DE-588)4179998-7 Monografische Reihe gnd-content Variationsrechnung (DE-588)4062355-5 s Bildverarbeitung (DE-588)4006684-8 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Bergounioux, Maïtine edt Peyré, Gabriel edt Schnörr, Christoph (DE-588)1023033348 edt Caillau, Jean-Baptiste edt Haberkorn, Thomas edt Erscheint auch als Online-Ausgabe, EPUB 978-3-11-043049-3 Erscheint auch als Online-Ausgabe, PDF 978-3-11-043039-4 Radon series on computational and applied mathematics Volume 18 (DE-604)BV023335470 18 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110439236&searchTitles=true Verlag DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028971563&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Variational methods in imaging and geometric control Radon series on computational and applied mathematics Kontrolltheorie (DE-588)4032317-1 gnd Bildverarbeitung (DE-588)4006684-8 gnd Variationsrechnung (DE-588)4062355-5 gnd
subject_GND	(DE-588)4032317-1 (DE-588)4006684-8 (DE-588)4062355-5 (DE-588)4179998-7
title	Variational methods in imaging and geometric control
title_auth	Variational methods in imaging and geometric control
title_exact_search	Variational methods in imaging and geometric control
title_full	Variational methods in imaging and geometric control edited by Maïtine Bergounioux, Gabriel Peyré, Christoph Schnörr, Jean-Baptiste Caillau, Thomas Haberkorn
title_fullStr	Variational methods in imaging and geometric control edited by Maïtine Bergounioux, Gabriel Peyré, Christoph Schnörr, Jean-Baptiste Caillau, Thomas Haberkorn
title_full_unstemmed	Variational methods in imaging and geometric control edited by Maïtine Bergounioux, Gabriel Peyré, Christoph Schnörr, Jean-Baptiste Caillau, Thomas Haberkorn
title_short	Variational methods
title_sort	variational methods in imaging and geometric control
title_sub	in imaging and geometric control
topic	Kontrolltheorie (DE-588)4032317-1 gnd Bildverarbeitung (DE-588)4006684-8 gnd Variationsrechnung (DE-588)4062355-5 gnd
topic_facet	Kontrolltheorie Bildverarbeitung Variationsrechnung Monografische Reihe
url	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110439236&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028971563&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV023335470
work_keys_str_mv	AT bergouniouxmaitine variationalmethodsinimagingandgeometriccontrol AT peyregabriel variationalmethodsinimagingandgeometriccontrol AT schnorrchristoph variationalmethodsinimagingandgeometriccontrol AT caillaujeanbaptiste variationalmethodsinimagingandgeometriccontrol AT haberkornthomas variationalmethodsinimagingandgeometriccontrol

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