P. Rodríguez, R. Dosil, X. M. Pardo, V. LeboránP. Rodríguez, R. Dosil, X. M. Pardo, V. Leborán

Grupo de Visión ArtificialGrupo de Visión ArtificialDepartamento de Electrónica e ComputaciónDepartamento de Electrónica e Computación

Universidade de Santiago de CompostelaUniversidade de Santiago de Compostela

Automatic Generation ofAutomatic Generation ofInitial Surfaces for Implicit SnakesInitial Surfaces for Implicit Snakes

IntroductionIntroduction Global Shape ModelGlobal Shape Model

CSG ModelCSG Model Superquadric primitivesSuperquadric primitives

MethodologyMethodology Prior Model ConstructionPrior Model Construction Image Feature Extraction Image Feature Extraction MatchingMatching

Results and ConclusionsResults and Conclusions

OutlineOutline

IntroductionIntroduction 33D surface reconstruction:D surface reconstruction:

Segmentation with deformable modelsSegmentation with deformable models

Good local approximationGood local approximation

Need of good initial estimationNeed of good initial estimation

IntroductionIntroduction Previous SolutionsPrevious Solutions

Manual initialization: Manual initialization: is not practical in 3Dis not practical in 3D

Landmark registration: Landmark registration: landmarks are not always identifiablelandmarks are not always identifiable

Part decomposition techniquesPart decomposition techniques need of joint detection or part recoveryneed of joint detection or part recovery lack of robustness when data is incomplete or noisylack of robustness when data is incomplete or noisy

IntroductionIntroduction ObjectivesObjectives

Automatic initialization of 3D medical imagesAutomatic initialization of 3D medical images(CT, MRI, …)(CT, MRI, …)

No use of landmarksNo use of landmarks

Application to multi-part objectsApplication to multi-part objects

Robustness to noise and presence of other Robustness to noise and presence of other objectsobjects

IntroductionIntroduction Proposal:Proposal:

matching with multi-part prior modelsmatching with multi-part prior models

Initialization by matching with prior modelsInitialization by matching with prior models RobustnessRobustness No need of part or joint detectionNo need of part or joint detection

Use of composite global shape modelsUse of composite global shape models Multi-part models: CSGMulti-part models: CSG Primitives: SuperquadricsPrimitives: Superquadrics

Image features are image surface pointsImage features are image surface points No use of landmarksNo use of landmarks

Average Surface

Prior Model

I. Modeling

I. Prior model construction from sample images

Volume Data

Surface Patches

II. Preprocessing

II. Object surface points extraction

III. Matching

Initial Model

III. Matching between surface model and object surface points

IntroductionIntroduction

Global Shape ModelGlobal Shape Model Constructive Solid Geometry (CSG)Constructive Solid Geometry (CSG)

Binary treeBinary tree Leaf nodes: solid primitivesLeaf nodes: solid primitives Internal nodes: Boolean operationsInternal nodes: Boolean operations Arcs: rigid transformationsArcs: rigid transformations

Primitives: Primitives: Superquadrics with global deformationsSuperquadrics with global deformations

Global Shape ModelGlobal Shape Model Superquadrics with global deformationsSuperquadrics with global deformations

Few parameters bring structural informationFew parameters bring structural information

Global Deformations: asymmetryGlobal Deformations: asymmetry

Implicit equationImplicit equation

1, qrf

MethodologyMethodologyI. Prior model construction from

sample images

Manual part decompositionManual part decomposition

Individual modeling of object partsIndividual modeling of object parts Shape parametersShape parameters Relative spatial distribution Relative spatial distribution

parametersparameters

Mqq ,...,1m

Average Surface

Prior Model

I. Modeling

siii

tisii

T qrqr

qqq

,

MethodologyMethodologyI. Prior model construction from

sample images

Optimization with Genetic Optimization with Genetic AlgorithmsAlgorithms

Minimization of error function:Minimization of error function:

where where

andand

N

iiDE

1

22 ,, qrq x

Average Surface

Prior Model

I. Modeling

qr

rqr,

11,

1εfD

Nrr ,...,1x

MethodologyMethodologyII. Image feature extraction

1.1. Smoothing by anisotropic Smoothing by anisotropic diffusiondiffusion

2.2. Non gradient maxima Non gradient maxima suppressionsuppression

3.3. Hysteresis thresholdingHysteresis thresholding

Volume Data

Surface Patches

II. Preprocessing

MethodologyMethodologyIII. Matching between model and object features

Find global rigid transformation Find global rigid transformation TT such that the such that the transformed model fits the object transformed model fits the object surfacesurface

GA to minimize error functionGA to minimize error function

N

iji

jD

NE

1

22 ',min1

, qrxm'

Surface Patches

III. Matching

Initial Model

Prior Model

',...,'1 Mqqm'

MethodologyMethodologyIII. Matching between model and object features

Radial distance to a Radial distance to a deformeddeformed implicit surface implicit surface

is difficult to calculateis difficult to calculate The following approximation is usedThe following approximation is used

sjijTTD qr ,11

', jiD qr

ResultsResults

ResultsResults

ConclusionsConclusions ContributionsContributions

Automatization of initializationAutomatization of initialization Easy handling of multipart shapes using a compound Easy handling of multipart shapes using a compound

modelmodel No part or joint detection No part or joint detection Easy optimization of the modelEasy optimization of the model

Future workFuture work Introduction of fine tuning of individual part Introduction of fine tuning of individual part

parametersparameters Incorporation of other Boolean operations to the CSG Incorporation of other Boolean operations to the CSG

model to handle concavitiesmodel to handle concavities