Recognizing Deformable Shapes Salvador Ruiz Correa UW Ph.D. Graduate Researcher at Children’s...
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![Page 1: Recognizing Deformable Shapes Salvador Ruiz Correa UW Ph.D. Graduate Researcher at Children’s Hospital.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649ef15503460f94c0208b/html5/thumbnails/1.jpg)
Recognizing Recognizing Deformable Deformable
ShapesShapesSalvador Ruiz CorreaSalvador Ruiz Correa
UW Ph.D. GraduateUW Ph.D. Graduate
Researcher at Children’s HospitalResearcher at Children’s Hospital
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GoalGoal We are interested in developing algorithms We are interested in developing algorithms
for recognizing and classifying deformable for recognizing and classifying deformable object shapes from range data.object shapes from range data.
3-D Output3-D OutputSurface MeshSurface Mesh3-D Laser Scanner3-D Laser Scanner
InputInput3-D3-D
ObjectObject
This is a difficult problem that is relevant in This is a difficult problem that is relevant in several application fields.several application fields.
RangeRangedatadata
(Cloud of (Cloud of 3-D points)3-D points)
Post-Post-processingprocessing
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Basic IdeaBasic Idea
Generalize existing Generalize existing numeric surface numeric surface
representationsrepresentations for matching 3-D for matching 3-D objects to the problem of identifying objects to the problem of identifying shape classes.shape classes.
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Main ContributionMain Contribution
An algorithmic framework based onAn algorithmic framework based on
symbolic shape descriptorssymbolic shape descriptors that are that are robust to deformations as opposed to robust to deformations as opposed to numeric descriptors that are often tied to numeric descriptors that are often tied to specific shapes.specific shapes.
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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
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DeformedDeformed Infants’ Skulls Infants’ Skulls
Sagittal
Coronal
NormalSagittal
Synostosis
BicoronalSynostosis
FusedSutures
Metopic
Occurs when sutures of the cranium fuse prematurely (synostosis).
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More Craniofacial More Craniofacial DeformationsDeformations
FacialAsymmetry
SagittalSynostosis
BicoronalSynostosis
UnicoronalSynostosis
MetopicSynostosis
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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..
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Recognition Problem (1)Recognition Problem (1)
We are given a set of surface meshes {We are given a set of surface meshes {CC11,C,C22,,…,C…,Cnn} which are random samples of two } which are random samples of two shape classes shape classes CC
C1 C2 Ck … Cn…
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Recognition Problem (2)Recognition Problem (2) The problem is to use the given meshes The problem is to use the given meshes
and labels to construct an algorithm that and labels to construct an algorithm that determines whether shape class members determines whether shape class members are present in a single view range scene.are present in a single view range scene.
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Classification Problem Classification Problem (1)(1)
We are given a set of surface meshes {We are given a set of surface meshes {CC11,C,C22,,…,C…,Cnn} which are random samples of two } which are random samples of two shape classes shape classes CC+1+1 and and CC-1-1,,
where each surface mesh is labeled either by where each surface mesh is labeled either by +1 or -1.+1 or -1.
+1+1 +1 +1 -1 -1 -1 -1
Normal Skulls C+1 Abnormal Skulls C-1
C1 C2 Ck Ck+1 Ck+2… Cn…
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Classification Problem Classification Problem (2)(2)
The problem is to use the given meshes and The problem is to use the given meshes and labels to construct an algorithm that predicts labels to construct an algorithm that predicts the label of a new surface mesh Cthe label of a new surface mesh Cnewnew..
Is this skull normal (+1) or abnormal (-1)?
Cnew
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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).
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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
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Numeric SignaturesNumeric Signatures
ArchitectureArchitectureof of
ClassifiersClassifiers
NumericNumericSignaturesSignatures
ComponentsComponents
SymbolicSymbolicSignaturesSignatures
44
++
11
22
33
Encode Local Encode Local Surface Geometry Surface Geometry
of an Objectof an Object
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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
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ComponentsComponents
NumericNumericSignaturesSignatures
ComponentsComponents
SymbolicSymbolicSignaturesSignatures
ArchitectureArchitectureof of
ClassifiersClassifiers
44
++
11
22
33
Equivalent Numeric Equivalent Numeric Signatures:Signatures:
Encode Local Encode Local GeometryGeometry
of a Shape Classof a Shape Class
definedefine
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How To Extract Shape Class How To Extract Shape Class Components?Components?
……
……
ComponentComponentDetectorDetector
ComputeComputeNumericNumeric
SignaturesSignatures
Training SetTraining Set
SelectSelectSeedSeedPointsPoints
RegionRegionGrowingGrowing
AlgorithmAlgorithm
Grown componentsGrown componentsaround seedsaround seeds
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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
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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.
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Symbolic SignaturesSymbolic Signatures
NumericNumericSignaturesSignatures
ComponentsComponents
SymbolicSymbolicSignaturesSignatures
Architectureof
Classifiers
4
+
11
22
33 Encode Geometrical Encode Geometrical Relationships Relationships
Among ComponentsAmong Components
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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
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Symbolic Signature Symbolic Signature ConstructionConstruction
Critical Point
P
aa
PP
bb
PP
aabb
Project labels Project labels to tangent planeto tangent plane
at Pat P
tangent planetangent plane
Coordinate systemCoordinate systemdefined up to a rotationdefined up to a rotation
NormalNormal
3344556688 77
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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
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Architecture of ClassifiersArchitecture of Classifiers
NumericSignatures
Components
SymbolicSignatures
Architectureof
Classifiers
4
+
1
2
3
Learns ComponentsLearns ComponentsAnd TheirAnd TheirGeometric Geometric
RelationshipsRelationships
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Proposed ArchitectureProposed Architecture(Classification Example)(Classification Example)
InputInput
LabeledLabeledMeshMesh
ClasClasss
LabeLabell
-1-1(Abnormal(Abnormal
))
Verify spatial configuration
of the components
IdentifyIdentifySymbolicSymbolic
SignaturesSignatures
IdentifyIdentifyComponentsComponents
Two classification Two classification stagesstages
Surface Surface MeshMesh
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At Classification Time (1)At Classification Time (1)
Bank ofBank ofComponentComponentDetectorsDetectors
Surface Surface MeshMesh
AssignsAssignsComponentComponent
LabelsLabels
Labeled Surface Mesh
Multi-wayMulti-wayclassifierclassifier
Identify ComponentsIdentify Components
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Labeled Labeled Surface MeshSurface Mesh
Bank ofBank ofSymbolicSymbolic
SignaturesSignaturesDetectorsDetectors
Symbolic pattern Symbolic pattern for componentsfor components
1,2,41,2,4
At Classification Time (2)At Classification Time (2)
Symbolic pattern Symbolic pattern for componentsfor components
5,6,85,6,8
AssignsAssignsSymbolicSymbolic
LabelsLabels
+1+1
-1-1
4
6 Two detectorsTwo detectors
5
8
1
2
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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.
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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
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Shape ClassesShape Classes
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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.
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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)
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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.
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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
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Task 2-3: Recognition in Task 2-3: Recognition in Complex Scenes (3)Complex Scenes (3)
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Task 4: Recognizing Human Task 4: Recognizing Human Heads (1)Heads (1)
No. Shape classes: 1.No. Shape classes: 1. Training set size: 400 meshes.Training set size: 400 meshes. Testing set size: 250 meshes.Testing set size: 250 meshes. No. Experiments: 710.No. Experiments: 710. No. Component detectors:8.No. Component detectors:8. No. Symbolic signature detectors: 2.No. Symbolic signature detectors: 2. Numeric signature size: 70x70.Numeric signature size: 70x70. Symbolic signature size: 12x12.Symbolic signature size: 12x12.
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Task 4: Recognizing Task 4: Recognizing Human Heads (2)Human Heads (2)
Reco
gnit
ion
Rate
% Clutter
% Clutter < 40 % Occlusion < 40
% Occlusion
FP rate: ~1%,
(44,0.9)(40,0.88)
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Task 4: Recognizing Human Task 4: Recognizing Human Heads (3)Heads (3)
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Task 5: Classifying Normal Task 5: Classifying Normal vs. Abnormal Human Heads vs. Abnormal Human Heads
(1)(1) No. Shape classes: 6.No. Shape classes: 6. 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: 50x50.Numeric signature size: 50x50. Symbolic signature size: 12x12.Symbolic signature size: 12x12.
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Task 5: Classifying Normal vs. Task 5: Classifying Normal vs. Abnormal Human Heads (1) Abnormal Human Heads (1)
ShapeShape
ClassesClassesClassification Classification Accuracy %Accuracy %
Normal vs. Normal vs. Abnormal 1Abnormal 1
9898
Normal vs. Normal vs. Abnormal 2Abnormal 2
100100
Abnormal 1 vs. Abnormal 1 vs. 33
9898
Abnormal 1 vs. Abnormal 1 vs. 44
9797
Abnormal 1 vs. Abnormal 1 vs. 55
9292
Full models
Normal
3
21
4 5
(convex combinationsof Normal and Abnormal 1)
65%-35% 50%-50% 25%-75%
Abnormal
Five C
ase
s
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Task 6: Classifying Normal vs. Task 6: Classifying Normal vs. Abnormal Human Heads In Complex Abnormal Human Heads In Complex
Scenes(1)Scenes(1)
No. Shape classes: 2.No. Shape classes: 2. 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: 100x100.Numeric signature size: 100x100. Symbolic signature size: 12x12.Symbolic signature size: 12x12.
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Task 6: Classifying Normal vs. Task 6: Classifying Normal vs. Abnormal Human Heads In Complex Abnormal Human Heads In Complex
Scenes(1)Scenes(1)
ShapeShape
ClassesClassesClassification Classification Accuracy %Accuracy %
Normal vs. Normal vs. Abnormal 1Abnormal 1
8888
Clutter < 15% and occlusion < 50%
Range scenes – single view
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Task 7: Classifying Normal vs. Task 7: Classifying Normal vs. Abnormal Neurocranium (1)Abnormal Neurocranium (1)
No. Shape classes: 2.No. Shape classes: 2. Training set size: 400 meshes.Training set size: 400 meshes. Testing set size: 200 meshes.Testing set size: 200 meshes. No. Experiments: 2200.No. Experiments: 2200. No. Component detectors:3.No. Component detectors:3. No. Symbolic signature detectors: 1.No. Symbolic signature detectors: 1. Numeric signature size: 50x50.Numeric signature size: 50x50. Symbolic signature size: 15x15.Symbolic signature size: 15x15.
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Task 7: Classifying Normal vs. Task 7: Classifying Normal vs. Abnormal Neurocranium (2)Abnormal Neurocranium (2)
ShapeShape
ClassesClassesClassificatiClassificati
on on Accuracy %Accuracy %
Normal vs. Normal vs. Abnormal Abnormal
8989
No clutter and occlusion
100 Experiments
Abnormal(sagittal synostosis )
Superimposedmodels
Normal
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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.
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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.
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Main Contributions (3)Main Contributions (3)
Our approach:Our approach:- Is general can be applied to a variety of Is general can be applied to a variety of
shape classes.shape classes.- Is robust to clutter and occlusion Is robust to clutter and occlusion - It Works in practiceIt Works in practice
- Is a step forward in 3-D object - Is a step forward in 3-D object recognition research.recognition research.