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Deep Structure, Singularities, and Computer Vision: First International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers PDF

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Lecture Notes in Computer Science 3753 CommencedPublicationin1973 FoundingandFormerSeriesEditors: GerhardGoos,JurisHartmanis,andJanvanLeeuwen EditorialBoard DavidHutchison LancasterUniversity,UK TakeoKanade CarnegieMellonUniversity,Pittsburgh,PA,USA JosefKittler UniversityofSurrey,Guildford,UK JonM.Kleinberg CornellUniversity,Ithaca,NY,USA FriedemannMattern ETHZurich,Switzerland JohnC.Mitchell StanfordUniversity,CA,USA MoniNaor WeizmannInstituteofScience,Rehovot,Israel OscarNierstrasz UniversityofBern,Switzerland C.PanduRangan IndianInstituteofTechnology,Madras,India BernhardSteffen UniversityofDortmund,Germany MadhuSudan MassachusettsInstituteofTechnology,MA,USA DemetriTerzopoulos NewYorkUniversity,NY,USA DougTygar UniversityofCalifornia,Berkeley,CA,USA MosheY.Vardi RiceUniversity,Houston,TX,USA GerhardWeikum Max-PlanckInstituteofComputerScience,Saarbruecken,Germany Ole Fogh Olsen Luc Florack Arjan Kuijper (Eds.) Deep Structure, Singularities, and Computer Vision First International Workshop, DSSCV 2005 Maastricht, The Netherlands, June 9-10, 2005 Revised Selected Papers 1 3 VolumeEditors OleFoghOlsen ITUniversityofCopenhagen,DepartmentofInnovation RuedLanggaardsVej7,2300CopenhagenS,Denmark E-mail:[email protected] LucFlorack TechnicalUniversityofEinhoven DepartmentofBiomedicalEngineering DenDolech2,Postbus513,5600MBEindhoven,TheNetherlands E-mail:[email protected] ArjanKuijper ITUniversityofCopenhagen,DepartmentofInnovation RuedLanggaardsVej7,2300Copenhagen,Denmark E-mail:[email protected] LibraryofCongressControlNumber:2005935534 CRSubjectClassification(1998):I.4,I.5,I.3.5,I.2.10,I.2.6,F.2.2 ISSN 0302-9743 ISBN-10 3-540-29836-3SpringerBerlinHeidelbergNewYork ISBN-13 978-3-540-29836-6SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable toprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springeronline.com ©Springer-VerlagBerlinHeidelberg2005 PrintedinGermany Typesetting:Camera-readybyauthor,dataconversionbyScientificPublishingServices,Chennai,India Printedonacid-freepaper SPIN:11577812 06/3142 543210 Preface Whatisactuallytheinformation directlyrepresentedinthescale-space? Istarted to wonder about this shortly after Peter Johansen, 15 years ago, showed me his intriguing paper on how uniquely to reconstruct a band-limited 1D signal fromitsscale-spacetoppoints.Still,Ihavenotfullyunderstooditsimplications. Merely recording where structure vanishes under blurring is sufficient to fully reconstruct the details. Of course, technicalities exist, for example, you must also know negative scale toppoints. Nevertheless, I find it surprising that we may trade the metric properties of a signal with the positions of its inherent structure.Theresulthasbeengeneralizedtoanalyticsignals,shownalsoforthe zero crossings of the Laplacean, but has not yet been generalized to 2D. This remains an open problem. In 2003, Peter Giblin, LiverpoolUniversity, Luc Florack,Eindhoven Univer- sity of Technology, Jon Sporring, University of Copenhagen, my colleague Ole Fogh Olsen, and severalothers started the project collaborationDeep Structure and Singularities in Computer Vision under the European Union, IST, Future and Emerging Technologies program, trying to obtain further knowledge about whatinformationisactuallycarriedbythesingularitiesofshapesandgray-scale images. In this project, we probed from several directions the question of how much of the metric information is actually encoded in the structure of shapes and images. We, and many others, have given hints in this direction. We have shownthat—to a verylarge degree—youmay reconstruct2D images fromtheir toppoints, and—to a very large degree—you may identify images in a database based solely on the toppoints. Likewise, we have shown that—to a very large degree—youmayindex shapes basedontheir singularities,aswasshownearlier byBenjaminKimiaandcolleagues.Hence,thestructuremaybeuseful.Butstill, we do not really know its limitations. This current volume of LNCS is the proceedings from the workshop held in Maastricht, June 10–11, 2005. This workshop was based on invited speakers and contributed papers subjected to peer review. From these, 22 papers were selected for this volume.They representthe year 2005state of the artin under- standingtherelationbetweenstructural,topologicalinformationrepresentedby singularities and metric information of signals, shapes, images, and colors. The concise results like “the toppoints encode all metric information” still remain, butprogressandinsighthavebeengainedoverthelast15years.Inthis volume, the reader will find papers by many of the people who have contributed to the discussion in the past: Does structure matter? Mads Nielsen The IT University of Copenhagen Organization Organizing Committee Luc Florack Ole Fogh Olsen Mads Nielsen Camilla Jørgensen Arjan Kuijper Technical Committee Bram Platel Mac Wendelboe Frans Kanters Program Chairs Ole Fogh Olsen Luc Florack Program Committee Mads Nielsen Frans Kanters Kim Steenstrup Pedersen Bram Platel Martin Lillholm Peter Giblin Arjan Kuijper Andre Diatta Anna Pagh Ali Shokoufandeh Philip Bille Benjamin B. Kimia Jon Sporring James Damon Kerawit Somchaipeng Referees Remco Duits Evguenia Balmachnova Marco Loog Invited Speakers James Damon (University of North Carolina) Ali Shokoufandeh (Drexel University) Benjamin B. Kimia (Brown University) VIII Organization Sponsoring Organizations NWO, the Netherlands Organisation for Scientific Research, and the IST Pro- gramme of the European Union are gratefully acknowledged for financial sup- port. Table of Contents Oral Presentations Blurred CorrelationVersus Correlation Blur Jan J. Koenderink, Andrea van Doorn............................ 1 A Scale Invariant Covariance Structure on Jet Space Bo Markussen, Kim Steenstrup Pedersen, Marco Loog .............. 12 Essential Loops and Their Relevance for Skeletons and Symmetry Sets Arjan Kuijper, Ole Fogh Olsen .................................. 24 Pre-symmetry Sets of 3D Shapes Andr´e Diatta, Peter Giblin ...................................... 36 Deep Structure of Images in Populations Via Geometric Models in Populations Stephen M. Pizer, Ja-Yeon Jeong, Robert E. Broadhurst, Sean Ho, Joshua Stough ................................................. 49 Estimating the Statistics of Multi-object Anatomic Geometry Using Inter-object Relationships Stephen M. Pizer, Ja-Yeon Jeong, Conglin Lu, Keith Muller, Sarang Joshi .................................................. 60 Histogram Statistics of Local Model-Relative Image Regions Robert E. Broadhurst, Joshua Stough, Stephen M. Pizer, Edward L. Chaney ............................................. 72 The Bessel Scale-Space Bernhard Burgeth, Stephan Didas, Joachim Weickert ............... 84 Linear Image Reconstruction from a Sparse Set of α-Scale Space Features by Means of Inner Products of Sobolev Type Remco Duits, Bart Janssen, Frans Kanters, Luc Florack ............ 96 A Riemannian Framework for the Processing of Tensor-Valued Images Pierre Fillard, Vincent Arsigny, Nicholas Ayache, Xavier Pennec .... 112 From Stochastic Completion Fields to Tensor Voting Markus van Almsick, Remco Duits, Erik Franken, Bart ter Haar Romeny ......................................... 124 X Table of Contents Deep Structure from a Geometric Point of View Luc Florack ................................................... 135 Maximum Likely Scale Estimation Marco Loog, Kim Steenstrup Pedersen, Bo Markussen .............. 146 Adaptive Trees and Pose Identification from External Contours of Polyhedra Yannick L. Kergosien .......................................... 157 Poster Presentations Exploiting Deep Structure Arjan Kuijper ................................................. 169 Scale-Space Hierarchy of Singularities Tomoya Sakai, Atsushi Imiya ................................... 181 Computing 3D Symmetry Sets; A Case Study Arjan Kuijper, Ole Fogh Olsen .................................. 193 Irradiation Orientation from Obliquely Viewed Texture Sylvia C. Pont, Jan J. Koenderink ............................... 205 Using Top-Points as Interest Points for Image Matching Bram Platel, Evguenia Balmachnova, Luc Florack, Frans Kanters, Bart M. ter Haar Romeny ........................ 211 Transitions of Multi-scale Singularity Trees Kerawit Somchaipeng, Jon Sporring, Sven Kreiborg, Peter Johansen ................................................ 223 A Comparison of the Deep Structure of α-Scale Spaces Remco Duits, Frans Kanters, Luc Florack, Bart ter Haar Romeny ... 234 A Note on Local Morse Theory in Scale Space and Gaussian Deformations Jan–Cees van der Meer ......................................... 249 Author Index................................................... 259 Blurred Correlation Versus Correlation Blur Jan J. Koenderink and Andrea van Doorn Universiteit Utrecht [email protected] Abstract. We discuss the topic of correlation in a scale space setting. Correlation involves two distinct scales. The “outer scale” is the scale of the region over which the correlation will be calculated. Classically this is the whole space of interest, but in many cases one desires the correlation over some region of interest. The “inner scale” is the scale at which the signals to be correlated are represented. Classically this meansinfiniteprecision.Forourpurposeswedefine“correlation” asthe point–wise product of two signals, “blurred correlation” as the integra- tionofthiscorrelation overtheregionofinterest,and“correlation blur” as this point–wise correlation applied to the signals represented at the inner scale. For generic purposes we are interested in “blurred correla- tion blur”. We discuss a well known (and practically important) exam- pleofblurredcorrelationforessentiallyzeroinnerscale.Suchasituation leadstoapparentlyparadoxicalresults.Wethendiscusscorrelationblur, which can beunderstood as a form of “regularized” correlation, leading tointuitivelyacceptableresultsevenforthecaseofpointsets(e.g.,tem- poraleventsorpointsetsinspace).Wedeveloptheformalstructureand present a numberof examples. 1 Blurred Correlation We will speak of a “correlation” r(s) of two signals f(r) and g(r) if r(s) is a blurred version of the product of blurred versions of f(r) and g(r). This is a slight generalization of the usual concept where the correlation is the fully blurredproductofthe unblurredfunctions.Notice thatthere existtwoessential scaleparametershere,namelythe“outerscale”,whichisthescaleoftheblurring of the product, and the “inner scale”, which is the scale of the blurring of the components. Firstwe willconsiderthe caseofverysmallinner scale,i.e., the components are fully resolved atthe point where they enter the multiplication process.Such cases are comparatively rare. A key instance of this “blurred correlation” occurs in human vision[10]. The causal chain in vision goes as follows: An illuminant causes an illumina- tion spectrum f(λ) on a surface with spectral reflectance g(λ), causing a beam to be scattered to the eye whose luminance—apart from an inessential con- stant factor—has a spectrum that equals the product f(λ)g(λ). The product is blurred in the retinal transduction process and gives rise to the blurred correla- tionk(λ;σ)◦(f(λ)g(λ)) ofwhichthreepointsamplesenterthe optic nerve.The O.F.Olsenetal.(Eds.):DSSCV2005,LNCS3753,pp.1–11,2005. (cid:1)c Springer-VerlagBerlinHeidelberg2005

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