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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Discrimina)ve‘VirtualViews’forCross-
ViewAc)onRecogni)on
RuonanLiandToddZickler
HarvardSchoolofEngineeringandAppliedSciences
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Cross-ViewRecogni)on
“kick”
View1
2
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Cross-ViewRecogni)on
“kick”
View2View1
3
?
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Cross-ViewRecogni)on
“kick”
View2View1
4
?
x x�
�=
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Cross-ViewRecogni)on
5
x x�
?
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Cross-ViewRecogni)on
6
x x�W
Ourapproach:1. Dimensionexpansionfordiscrimina)vecross-viewfeatures;
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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OurApproach:
Cross-ViewDimensionExpansion
7
x x�
=x̂ x̂� W=
Ourapproach:1. Dimensionexpansionfordiscrimina)vecross-viewfeatures;
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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OurApproach:
Cross-ViewDimensionExpansion
8
x x�
=x̂ x̂� W=
Ourapproach:1. Dimensionexpansionfordiscrimina)vecross-viewfeatures;2. Exploitvariouscross-viewannota)ontypesthatwere
consideredseparatelybefore.
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Case1:WeaklyLabeledTargetView
View2(TargetViewView1(SourceView
?
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Case1:WeaklyLabeledTargetView
Domain2(TargetDomainDomain1(SourceDomain
• DomainAdapta)on/Cross-DomainRecogni)on
• Ben-David2007;Blitzer2006,2007;DaumeIII2007;Duan2009,2010,2011;
Jhuo2012;Kulis2011;Pan2010,2011;Saenko2010;andmanyothers.
?
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Case2:UnlabeledCorrespondence
View1(SourceView View2(TargetView
• Farhadi2008,2009;Liu2011
Thesameunknownac)on
executedbythesamesubject
andsimultaneouslyobservedinbothviews
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Case3:NoSupervisionintheTargetView
View1(SourceView View2(TargetView
• Gong2012;Gopalan2011;
?
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Intra-ClassSimilarity
“kick” “kick”
View2(TargetViewView1(SourceView
x x�
=x̂ x̂
�
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Inter-ClassSeparability
“kick” “wavehand”
View2(TargetViewView1(SourceView
x x�
=x̂ x̂
�
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Intra-ClassSimilarityandInter-ClassSeparability
maxW
I (Wx; c)
W W
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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UnlabeledCorrespondence
View2(TargetViewView1(SourceView
Thesameunknownac)on
executedbythesamesubject
andsimultaneouslyobservedinbothviews
x x�
=x̂ x̂
�
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UnlabeledCorrespondence
maxW
I (Wx; c)− γ H (Wx−Wx�)
W W
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Cross-ViewTransformObjec)ve
W W
maxW
I (Wx; c)− γ H (Wx−Wx�)
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Cross-ViewTransformObjec)ve
maxW
lndetΣall−1
2lndetΣClass1−
1
2lndetΣClass2−γ ln detΣ∆
Assump)ons:
• Uniformdistribu)onforclassprior;
• Gaussiandistribu)onforcross-viewfeatures.
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Cross-ViewTransformObjec)ve
maxW
lndetΣall−1
2lndetΣClass1−
1
2lndetΣClass2−γ lndetΣ∆
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Cross-ViewTransformObjec)ve
maxW
lndetΣall−1
2lndetΣClass1−
1
2lndetΣClass2−γ lndetΣ∆
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Cross-ViewTransformObjec)ve
maxW
lndetΣall−1
2lndetΣClass1−
1
2lndetΣClass2−γ lndetΣ∆
∆ =Wx−Wx�
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Cross-ViewTransform
SourceView TargetView
AS
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Cross-ViewTransform
SourceView TargetView
AS
AT
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Cross-ViewTransform
SourceView TargetView
AS
AT
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Cross-ViewTransform
SourceView TargetView
x
=
AS
AT
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Cross-ViewTransform
SourceView TargetView
x
=
AS
AS
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Cross-ViewTransform
SourceView TargetView
x
=
AS
AT
AS
AT
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Cross-ViewTransform
SourceView TargetView
x
=
AS
AT
A1
AS
AT
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Cross-ViewTransform
SourceView TargetView
x
=
AS
AT
A1
A2
AS
AT
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Cross-ViewTransform
SourceView TargetView
x
=
AS
AT
A1
A2
A3
AS
AT
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Discrimina)veVirtualViews
x
=
AS
AT
A1
A2
A3
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Discrimina)veVirtualViews
x
=
AS
AT
A1
A2
A3
Allrealandvirtualviews
Sourceview
Targetview
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Discrimina)veVirtualViews
x
=
AS
AT
A1
A2
A3
Allrealandvirtualviews
Sourceview
Targetview
`Virtualviews’
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Discrimina)veVirtualViews
x
=
AS
AT
A1
A2
A3
Allrealandvirtualviews
Sourceview
Targetview
`Virtualviews’
Cross-ViewDiscrimina)ve
‘DimensionExpansion’W
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TheOverallObjec)ve
x
=
AS
AT
A1
A2A3
W
maxAT ,AS
I (Wx; c)− γ H (Wx−Wx�)
• Close-forminterpola)onofvirtualviewtransformsfromand;
AS
AT
subject to AS AT S = I and AT A
T T = I
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Solu)on
x
=
AS
AT
A1
A2A3
W
maxAT ,AS
I (Wx; c)− γ H (Wx−Wx�)
• Close-forminterpola)onofvirtualviewtransformsfromand;
AS
AT
subject to AS AT S = I and AT A
T T = I
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Solu)on
x
=
AS
AT
A1
A2
A3
W
maxAT ,AS
I (Wx; c)− γ H (Wx−Wx�)
• Close-forminterpola)onofvirtualviewtransformsfromand;
• andini)alizedwithLDA(orPCAwheneverLDAisunavailable;
AS AT
AS
AT
subject to AS AT S = I and AT A
T T = I
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Solu)on
x
=
AS
AT
A1
A2
A3
W
maxAT ,AS
I (Wx; c)− γ H (Wx−Wx�)
• Close-forminterpola)onofvirtualviewtransformsfromand;
• andini)alizedwithLDA(orPCAwheneverLDAisunavailable;
• Approximategradientascenton.
SO(D)
AS AT
AS
AT
A(i)�
A(i+1)�
=
R(i)opt
subject to AS AT S = I and AT A
T T = I
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Recap
W W
x
=
AS
AT
A1
A2
A3
W
• Discrimina)vecross-view`dimensionexpansion’;• Uniformlyaccountforvariouscross-viewsemi-supervisions.
![Page 41: CVPR2012: discriminative virtual views for cross-view action recognition](https://reader036.vdocuments.mx/reader036/viewer/2022062906/577ce68a1a28abf103930db6/html5/thumbnails/41.jpg)
7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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IXMASDataset• 11ac)oncategoriesperformedby10actors,takenfrom5views.
View0
View1
View2
View3
View4
Check-watch Scratch-head Sit-down Wave-hand Kicking Pick-up
![Page 42: CVPR2012: discriminative virtual views for cross-view action recognition](https://reader036.vdocuments.mx/reader036/viewer/2022062906/577ce68a1a28abf103930db6/html5/thumbnails/42.jpg)
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Case1Result:WeaklyLabeledTargetView
• ViewMixing:ASVMtrainedontheunionofsourceandtargetviews
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Case1Result:WeaklyLabeledTargetView
• ViewConcatena)on:DaumeIII2007
x̂ = [xT ,0
T ,x
T ]T , x̂
� = [0T ,x
�T ,x
�T ]T
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Case1Result:WeaklyLabeledTargetView
• CombiningClassifier:Schweikert2008
f (x) = β f S (x) + (1− β )f T (x)
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7/31/2019 CVPR2012: discriminative virtual views for cross-view action recognition
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Case1Result:WeaklyLabeledTargetView
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Case2Result:UnlabeledCorrespondence
• Farhadi2008,2009
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Case2Result:UnlabeledCorrespondence
• Liu2011
V i e w
1
V i e w
2
+
e x a m p l e s
Training data vectorsM
Source view Target view
Unlabelled AcƟon Videos A1
Unlabelled AcƟon Videos A2
Vocabulary V1
Vocabulary V2
BoVWmodels M1
BoVWmodels M2
Bilingual Words
BoBWmodels
Visual Words
BiparƟteGraph
BiparƟte
Graph
ParƟƟoning
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Case2Result:UnlabeledCorrespondence
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Case3Result:NoSupervisionintheTargetView
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Case3Result:NoSupervisionintheTargetView
• Gopalan2011
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Case3Result:NoSupervisionintheTargetView
• Non-discrimina)vevirtualviews
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Case3Result:NoSupervisionintheTargetView
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FourSourceViews+SingleTargetView
Case1
Case2
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Summary
• A‘dimensionexpansion’transformtoproducecross-viewfeatureswhich(1arediscrimina)ve;(2encodethe
transi)onfromthesourcetothetarget;
--SeealsoGonget.al.,CVPR2012
• Accommodatevarioustypesofsemi-supervisions,including(1weaklylabeledtargetview;(2Unlabeled
correspondencebetweentwoviews;(3completely
unsupervisedtargetview.
• Applicabletogeneraldomaintransfer/adapta)onproblems.
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Discrimina)ve‘VirtualViews’forCross-View
Ac)onRecogni)on
W W
x
=
AS
AT
A1
A2
A3
W
i b f i l i d
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VaryingNumberofVirtualViewsand
VaryingDimensionsofVirtualViews