Table Of ContentAssociation for Women in Mathematics Series
Kathryn Leonard
Sibel Tari Editors
Research in
Shape Modeling
Los Angeles, July 2013
Association for Women in Mathematics Series
Volume 1
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Kathryn Leonard (cid:129) Sibel Tari
Editors
Research in Shape Modeling
Los Angeles, July 2013
123
Editors
KathrynLeonard SibelTari
DepartmentofMathematics DepartmentofComputerEngineering
CaliforniaStateUniversityChannelIslands MiddleEastTechnicalUniversity
Camarillo,CA,USA Ankara,Turkey
ISSN2364-5733 ISSN2364-5741 (electronic)
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DOI10.1007/978-3-319-16348-2
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Preface
InJuly2013,agroupofaround30womenresearchersinshapemodelingattended
the Women in Shape Modeling (WiSh) workshop at the Institute for Pure and
AppliedMathematics(IPAM)intheUniversityofCaliforniaLosAngeles(UCLA)
campus to begin research collaborations on some of the major problems in shape
analysis and modeling. Participants from North America, Asia, Europe, and the
Middle East lived, ate, slept, and worked together for one week at IPAM, then
continued their collaborations from a distance. This proceedings volume contains
preliminary results from those collaborations and related work. We look forward
to future papers on these topics as participants continue their contributions to the
growingbodyofworkonmathematicalshapemodeling.
WiShparticipantsworkedononeofthefourresearchquestionsbelow.
1. Team Leaders: Luminita Vese, Sibel Tari. Simultaneous spectral and spatial
analysis of shape, investigating a new distance-like shape operator from the
spectral point of view, adopting signatures developed in the spectral literature,
andsolvingsimilarsymmetrydetectionproblems.Wealsodevelopaconnection
to image segmentation and registration using the yet unclear connection of the
newoperatortotheAmbrosio-Tortorellifunctional.
2. Team Leaders: Aasa Feragen, Megan Owen. Dimensionality reduction and
visualization of data in tree-spaces, studying dimensionality reduction in shape
spaceswheretheshapeshavethestructureofatree,suchasclassesofanatomical
treeslikeairwaysandbloodvessels,medialaxesof2Dshapes,orphylogenetic
trees.Wedeveloptechniquesforlow-distortionembeddingintoopenbooksand
hyperbolicspaceswhosegeometricstructureissimilartothatoftree-space.
3. Team Leaders: Kathryn Leonard, Erin Wolf Chambers. Geometric shape seg-
mentation, exploring shape segmentation from a Gestalt perspective, using
information from the Blum medial axis of edge fragments in an image. We
combine existing edge saliency measures together with medial data to increase
support for or against hypothesized edge interpolation and develop techniques
forconsideringrelatedappearancecues.
vii
viii Preface
4. Team Leaders: Marie-Paule Cani, Raphaelle Chaine. Representing and editing
self-similar details on 3D shapes, studying shape deformation and editing
techniques,suchaselongatingorcompressingpartsofashapewhilemaintaining
local style, copy-pasting details from one shape to another, or changing the
scale of details without changing lower resolution geometry. All are essential
forinteractiveshapedesign.Blendingpropertiesofimplicitsurfacesmakethem
good candidates for solving this problem. We explore the extension of multi-
resolution analysis to these surfaces and their deformations, enabling us to
characterizerepetitiveself-similarities,anddevelopmethodsforfilteringdetails
out and generating them again after low resolution shape editing. An extension
studiesmulti-resolutioneditingofanimatedshapes.
Ithasbeenanhonortoworkwiththisexceptionalgroupofwomenandwiththe
efficientstaffatIPAM.WearegratefultoIPAM,theNationalScienceFoundation,
MicrosoftResearch,andtheNationalGeospatialAgencyforprovidingfundingfor
theworkshop,andtotheUCLADepartmentofMathematicsforsharingspacewith
us.Inaddition,theAssociationforWomeninMathematics(AWM),andPresident-
ElectKristinLauterinparticular,playedakeyroleinencouragingmetoorganize
a research collaboration workshop in conjunction with AWM. These workshops
are now a regular part of AWM’s offerings, and AWM activities at the annual
JointMathematicsMeetingscenteronresearchtopicsemergingfromcollaboration
workshops.
Special thanks is due to my coeditor, Sibel Tari, who provided useful insights
duringtheworkshopandinvaluablehelpduringthepreparationofthismanuscript,
and to Stacey Beggs at IPAM who worked creatively to solve several unexpected
issuesduringthecourseoftheworkshop.
California,USA KathrynLeonard
May2014
Contents
1 AutomaticPriorShapeSelectionforImageSegmentation.............. 1
WeihongGuo,JingQin,andSibelTari
1.1 Introduction ............................................................. 1
1.2 ModelDescription ...................................................... 2
1.2.1 Ambrosio-Tortorelli Approximation
ofMumford-ShahSegmentationFunctional .................. 2
1.2.2 ShapeDescriptorLibrary....................................... 3
1.2.3 ProposedSegmentationModel................................. 5
1.3 Experiments............................................................. 6
1.4 Conclusion .............................................................. 7
References..................................................................... 8
2 AScalableFluctuatingDistanceField:AnApplication
toTumorShapeAnalysis.................................................... 9
R.AlpGuler,AndacHamamci,andGozdeUnal
2.1 Introduction ............................................................. 9
2.2 ScalableFluctuatingDistanceField.................................... 12
2.2.1 EnergyTerms ................................................... 12
2.2.2 ASignConstrainttoControlFluctuationScale............... 13
2.2.3 ASpaceofFluctuationScales ................................. 15
2.2.4 InteractiveTumorProtrusionSegmentation................... 18
2.3 TumorFollow-UpRegistrationUsing! Fields ....................... 19
2.3.1 RegistrationResultsandDiscussion........................... 20
2.4 Conclusion .............................................................. 23
References..................................................................... 23
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