Recognizing Recognizing Deformable Deformable

ShapesShapesSalvador Ruiz CorreaSalvador Ruiz Correa

Ph.D. Thesis, Electrical Ph.D. Thesis, Electrical EngineeringEngineering

Basic IdeaBasic Idea

Generalize existing Generalize existing numeric surface numeric surface

representationsrepresentations for matching 3-D objects for matching 3-D objects to the problem of to the problem of identifying shape classes identifying shape classes allowing for shape deformationsallowing for shape deformations..

What Kind Of Deformations?What Kind Of Deformations?

Toy animals

3-D Faces

Normal

Mandibles

Neurocranium

Normal

Abnormal

Abnormal

Shape classes: significantamount of intra-class variability

DeformedDeformed Infants’ Skulls Infants’ Skulls

Sagittal

Coronal

NormalSagittal

Synostosis

BicoronalSynostosis

FusedSutures

Metopic

Occurs when sutures of the cranium fuse prematurely (synostosis).

Alignment-VerificationAlignment-Verification LimitationsLimitations

The approach does not extend well to the problemThe approach does not extend well to the problem

of identifying classes of similar shapes. In general:of identifying classes of similar shapes. In general:

Numeric shape representations are Numeric shape representations are not robust to not robust to deformations.deformations.

There are There are not exact correspondencesnot exact correspondences between between model and scene.model and scene.

Objects in a shape class Objects in a shape class do not aligndo not align..

AssumptionsAssumptions All shapes are represented as oriented surface All shapes are represented as oriented surface

meshes of fixed resolution.meshes of fixed resolution.

The The verticesvertices of the meshes in the of the meshes in the training settraining set are are in full correspondence.in full correspondence.

Finding full correspondences : hard problem yes … Finding full correspondences : hard problem yes … but it is approachable ( use but it is approachable ( use morphable models morphable models techniquetechnique:: Blantz and Vetter, SIGGRAPH 99; C. R. Blantz and Vetter, SIGGRAPH 99; C. R. Shelton, IJCV, 2000; Allen et al., SIGGRAPH 2003).Shelton, IJCV, 2000; Allen et al., SIGGRAPH 2003).

Four Key Elements To Our Four Key Elements To Our ApproachApproach

Architectureof

Classifiers

NumericSignatures

Components

SymbolicSignatures

4

+

1

2

3

Recognition And Recognition And Classification OfClassification Of

Deformable Deformable Shapes Shapes

The Spin Image SignatureThe Spin Image Signature

P

Xn

P is the selected vertex.

X is a contributing point of the mesh.

is the perpendicular distance from X to P’s surface normal.

is the signed perpendicular distance from X to P’s tangent plane.

tangent plane at P

Numeric Signatures: Spin Numeric Signatures: Spin ImagesImages

Rich set of surface shape descriptors.Rich set of surface shape descriptors.

Their spatial scale can be modified to include local and Their spatial scale can be modified to include local and non-local surface features. non-local surface features.

Representation is robust to scene clutter and occlusions.Representation is robust to scene clutter and occlusions.

P

Spin images for point P

3-D faces

Shape Class Components: Clusters Shape Class Components: Clusters of 3D Points with Similar Spin of 3D Points with Similar Spin

ImagesImages

……

……

ComponentComponentDetectorDetector

ComputeComputeNumericNumeric

SignaturesSignatures

Training SetTraining SetSelectSelectSeedSeedPointsPoints

RegionRegionGrowingGrowing

AlgorithmAlgorithm

Grown componentsGrown componentsaround seedsaround seeds

Labeled Labeled Surface MeshSurface Mesh

Selected 8 seedSelected 8 seedpoints by handpoints by hand

Component Extraction Component Extraction ExampleExample

Region Region GrowingGrowing

Grow one region at the time Grow one region at the time (get one detector(get one detectorper component)per component)

DetectedDetectedcomponents on acomponents on atraining sampletraining sample

How To Combine Component How To Combine Component Information?Information?

…Extracted components on test samples

12

3

76

4

8

5

1112 2 222 2

Note: Numeric signatures are invariant to mirror symmetry;our approach preserves such an invariance.

Symbolic SignatureSymbolic Signature

Symbolic Symbolic Signature at PSignature at P

3344556688 77

Labeled Labeled Surface MeshSurface Mesh

Matrix storing Matrix storing componentcomponent

labelslabels

EncodeEncodeGeometricGeometric

ConfigurationConfiguration

Critical Point P

Symbolic Signatures Are Symbolic Signatures Are Robust Robust

To DeformationsTo Deformations

PP3344

55

66 7788

3333 33 3344 44 44 44

88 88 88 8855 55 55 55

666666 77 77 77 7766

Relative position of Relative position of components is stable across components is stable across deformations: experimental deformations: experimental

evidenceevidence

Proposed ArchitectureProposed Architecture(Classification Example)(Classification Example)

InputInput

LabeledLabeledMeshMesh

ClasClasss

LabeLabell

-1-1(Abnormal(Abnormal

))

Verify spatial configuration

of the components IdentifyIdentify

SymbolicSymbolicSignaturesSignatures

IdentifyIdentifyComponentsComponents

Two classification Two classification stagesstages

Surface Surface MeshMesh

Architecture Architecture ImplementationImplementation

ALL our classifiers are (off-the-shelf) ALL our classifiers are (off-the-shelf) νν--Support Vector Machines (Support Vector Machines (νν--SVMsSVMs) ) (Sch(Schöölkopf et al., 2000 and 2001).lkopf et al., 2000 and 2001).

Component (and symbolic signature) Component (and symbolic signature) detectors are detectors are one-class classifiers.one-class classifiers.

Component label assignment: Component label assignment: performed with a performed with a multi-way classifiermulti-way classifier that uses that uses pairwise classification pairwise classification scheme.scheme.

Gaussian kernel. Gaussian kernel.

Experimental ValidationExperimental Validation

Recognition Tasks: 4 (T1 - T4)Recognition Tasks: 4 (T1 - T4)

Classification Tasks: 3 (T5 – T7)Classification Tasks: 3 (T5 – T7)

No. Experiments: 5470 No. Experiments: 5470

SetupSetup

Recognition Recognition Classification Classification

LaserLaserRotary TableRotary Table

Shape ClassesShape Classes

Enlarging Training Sets Using Enlarging Training Sets Using Virtual SamplesVirtual Samples Displacement

Vectors

Originals Morphs

Twist (5deg)+ Taper- Push

+ Spherify (10%)

Push +Twist (10 deg)

+Scale (1.2)

Original

Global Morphing Operators

Morphs

Physical Modeling

(14)

University of WashingtonElectrical Engineering

Task 1: Recognizing Single Task 1: Recognizing Single Objects (1)Objects (1)

No. Shape classes: 9.No. Shape classes: 9. Training set size: 400 meshes.Training set size: 400 meshes. Testing set size: 200 meshes.Testing set size: 200 meshes. No. Experiments: 1960.No. Experiments: 1960. No. Component detectors:3.No. Component detectors:3. No. Symbolic signature detectors: 1.No. Symbolic signature detectors: 1. Numeric signature size: 40x40.Numeric signature size: 40x40. Symbolic signature size: 20x20.Symbolic signature size: 20x20. No clutter and occlusion.No clutter and occlusion.

Task 1: Recognizing Single Task 1: Recognizing Single Objects (2)Objects (2)

Snowman: 93%.Snowman: 93%. Rabbit: 92%.Rabbit: 92%. Dog: 89%.Dog: 89%. Cat: 85.5%.Cat: 85.5%. Cow: 92%.Cow: 92%. Bear: 94%.Bear: 94%. Horse: 92.7%.Horse: 92.7%.

Human head: Human head: 97.7%.97.7%.

Human face: 76%.Human face: 76%.

Recognition rates (true positives)Recognition rates (true positives)(No clutter, no occlusion, complete models)(No clutter, no occlusion, complete models)

Tasks 2-3: Recognition In Tasks 2-3: Recognition In Complex Scenes (1)Complex Scenes (1)

No. Shape classes: 3.No. Shape classes: 3. Training set size: 400 meshes.Training set size: 400 meshes. Testing set size: 200 meshes.Testing set size: 200 meshes. No. Experiments: 1200.No. Experiments: 1200. No. Component detectors:3.No. Component detectors:3. No. Symbolic signature detectors: 1.No. Symbolic signature detectors: 1. Numeric signature size: 40x40.Numeric signature size: 40x40. Symbolic signature size: 20x20.Symbolic signature size: 20x20. T2 – low clutter and occlusion.T2 – low clutter and occlusion.

Task 2-3: Recognition in Task 2-3: Recognition in Complex Scenes (2)Complex Scenes (2)

ShapeShape

ClassClassTrueTrue

PositivePositivess

FalseFalse

PositivePositivess

True True

PositivePositivess

FalseFalse

PositivePositivess

SnowmeSnowmenn

91%91% 31%31% 87.5%87.5% 28%28%

RabbitRabbit 90.2%90.2% 27.6%27.6% 84.3%84.3% 24%24%

DogDog 89.6%89.6% 34.6%34.6% 88.12%88.12% 22.1%22.1%

Task 2Task 2 Task 3Task 3

Task 2-3: Recognition in Task 2-3: Recognition in Complex Scenes (3)Complex Scenes (3)

Main Contributions (1)Main Contributions (1)

A novel A novel symbolic signature symbolic signature representationrepresentation of deformable shapes that of deformable shapes that is robust to intra-class variability and is robust to intra-class variability and missing information, as opposed to a missing information, as opposed to a numeric representationnumeric representation which is often which is often tied to a specific shape.tied to a specific shape.

A novel A novel kernel functionkernel function for quantifying for quantifying symbolic signature similarities. symbolic signature similarities.

Main Contributions (2)Main Contributions (2)

A A region growingregion growing algorithm for learning algorithm for learning shape class components. shape class components.

A novel A novel architecture of classifiersarchitecture of classifiers for for abstracting the geometry of a shape class.abstracting the geometry of a shape class.

A validation of our methodology in a set A validation of our methodology in a set of of large scalelarge scale recognition and recognition and classification experiments aimed at classification experiments aimed at applications in scene analysis and medical applications in scene analysis and medical diagnosis.diagnosis.