Mathematical Image Processing: University of Orléans, France, March 29th - April 1st, 2010

209 Pages·2011·0.63 MB·English

by  Stéphane Jaffard

Springer Proceedings in Mathematics
Volume 5
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Ma¨ıtine Bergounioux
Editor
Mathematical Image
Processing
University of Orle´ans, France,
March 29th - April 1st, 2010
123
Editor
Ma¨ıtineBergounioux
UMR6628-MAPMO
Fe´de´rationDenisPoisson
Universite´d’Orle´ansBP6759
45067Orle´ansCedex2
France
[email protected]
ISSN2190-5614
ISBN978-3-642-19603-4 e-ISBN978-3-642-19604-1
DOI10.1007/978-3-642-19604-1
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2011927924
(cid:2)c Springer-VerlagBerlinHeidelberg2011
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Preface
This volume collects a number of the contributionspresented at the Second Con-
ference“Mathematicsand Image Processing”held at the Universityof Orle´ansin
2010.
Duringthe periodMarch 29th–April1st, 2010,roughly80 peopleattendedthe
conference and 20 invited talks were delivered covering various areas of Mathe-
maticalImageProcessing.Themaintopicsdiscussedduringthismeetingwerethe
following:
– H.Ammari:GeneralizedPolarizationTensors:RecoveryofFineShapeDetails
– H.Bierme´:Mode´lisationetanalysefractaledetexturesanisotropes.Applications
limagerieme´dicale
– X. Bonnefond:The back and forth nudging method applied to thermoacoustic
tomography
– A. Cohen: Theory and algorithms for anisotropic triangulations with applica-
tionstoimagerepresentations
– P.L.Combettes:Me´thodesd’e´clatementproximalesentraitementdel’image
– F.Dibos:Invariantsprojectifs:uneapprocheparlegroupedesrecalages
– L.Duval:StatisticalestimatorsbasedonStein’sprincipleforM-bandwavelets
andfilterbanks
– O. Faugeras: Hyperbolic planforms in relation to visual edges and textures
perception
– A. Glaunes: Mesures et courantscomme mode`les des sous-varie´te´s en analyse
dimage.Applications
– Y.Gousseau:Mode`les“germe-grain”etprincipesdeformationdesimages
– S.Jaffard:Me´thodesd’analysemultifractalepourlaclassificationd’images
– P.Kornprobst:Fromalgorithmictobio-inspiredvision:isitsodifferent?
– J.Lefe`vre:Analyseetmode´lisationdude´veloppementce´re´bral
– S.Mallat:SparseMixtureModelsforInverseProblems
– V. Perrier: Divergence-free and Curl-free Wavelets on the cube and related
applications
– L.Piffet: BV2modelsforimagedenoisingandtextureidentification
v
vi Preface
– F.Rossi:ImageReconstructionviahypoellipticdiffusiononthebundleofdirec-
tionsoftheplane
– O.Scherzer:DerivativeFreeFunctionalsforImaging
– D.Tschumperle´: PDEs on the space of patches for image denoising and
registration
– P.Weiss:OnthedesignofgradientcoilsforMRIwithminimaxcurrentdensity
The conference was organizedby the “Image Group” of the Research Federation
“Denis-Poisson” of Orle´ans and Tours Universities (France). As the chair of the
OrganizingCommittee,Iwouldliketoextendmythanksthefollowinginstitutions
fortheirfinancialandmaterialsupport:
– Re´gionCentre
– ConseilGe´ne´ralduLoiret
– Mairied’Orle´ans
– Universite´d’Orle´ans
– Fe´de´rationDenis-Poisson(CNRS)etLaboratoireMAPMOd’Orle´ans
– Commissariata` l’EnergieAtomique(CEA)
The contributions appearing in this volume are a snapshot of the different
topics that were discussed during the conference. They mainly concern, image
reconstruction, texture extraction and image classification and involve a variety
of disparate methods and applications. Therefore it was impossible to split the
papers into generic groups, which is why they are presented in alphabetic order.
Allcontributionsarepeer-reviewed.
I would like to thank all the contributors for their effort and the anonymous
referees for their comments and suggestions. The help provided by the staff of
Springer-Verlagisalsogreatlyappreciated.
Orle´ans Ma¨ıtineBergounioux
December2010
Contents
FunctionSpacesVs.ScalingFunctions:ToolsforImageClassification ... 1
Ste´phaneJaffard,PatriceAbry,andSte´phaneRoux
ASecondOrderModelfor3D-TextureExtraction.................... 41
Ma¨ıtineBergouniouxandMinhPhuongTran
Analysis of Texture Anisotropy Based on Some Gaussian Fields
withSpectralDensity ............................................ 59
HermineBierme´ andFre´de´ricJ.P.Richard
Image Reconstruction Via Hypoelliptic Diffusion on the Bundle
ofDirectionsofthePlane ......................................... 75
UgoBoscain,JeanDuplaix,Jean-PaulGauthier,andFrancescoRossi
ProjectiveInvariantFeaturesDetectionandtheRegistrationGroup..... 91
Franc¸oiseDibos
MorphologicalComponentAnalysisforDecomposing
DynamicTextures ............................................... 107
SlovenDubois,RenaudPe´teri,andMichelMe´nard
TextureEnhancingBasedonVariationalImageDecomposition......... 127
FlorianFru¨hauf,CarstenPontow,andOtmarScherzer
ALocallyAnisotropicModelforImageTextureExtraction ............ 141
Lo¨ıcPiffet
ANeuralFieldModelforMotionEstimation ........................ 159
E´milien Tlapale, Pierre Kornprobst, Guillaume S. Masson,
andOlivierFaugeras
Non-LocalRegularizationandRegistrationofMulti-ValuedImages
ByPDE’sandVariationalMethodsonHigherDimensionalSpaces...... 181
DavidTschumperle´andLucBrun
vii

List of Contributors
PatriceAbry CNRSUMR5672LaboratoiredePhysique,ENSdeLyon,46,alle´e
d’Italie,F-69364Lyoncedex,France,[email protected]
Ma¨ıtine Bergounioux Laboratoire MAPMO - UMR 6628, Fe´de´ration
Denis-Poisson,Universite´d’Orle´ans,France,[email protected]
HermineBierme´ Universite´ ParisDescartes,LaboratoireMAP5(CNRSUMR
8145),45ruedesSaints-Pe`res,75270ParisCedex06,France,
[email protected]
UgoBoscain CMAP,E´colePolytechniqueCNRS,Palaiseau,France,
[email protected]
LucBrun ImageTeam,LaboratoireGREYC,6BdMare´chalJuin,14050Caen
Cedex/France,[email protected]
Franc¸oise Dibos LAGA, Institut Galile´e, Universite´ Paris 13, 99 avenueJ-B
Ce´ment,93430Villetaneuse,France,[email protected]
Sloven Dubois LaboratoireMathe´matiques, Image et Applications(MIA) et
LaboratoireInformatique,ImageetInteraction(L3i),AvenueMichelCre´peau,
17042LaRochelle,France,[email protected]
JeanDuplaix LaboratoireLSIS,Universite´deToulon,France,
[email protected]
Olivier Faugeras NeuroMathCompProject Team, INRIA Sophia-Antipolis
Me´diterrane´e,2004RoutedesLucioles,06902SophiaAntipolis,France,
[email protected]
FlorianFru¨hauf Hauptstrasse1c/1,6074,Rimm,Austria,
fl[email protected]
Jean-PaulGauthier LaboratoireLSIS,Universite´deToulon,France,
[email protected]
ix