via Subspace Clustering Ruizhen Hu Lubin Fan Ligang Liu Cosegmentation Hu et al CoSegmentation of 3D Shapes via Subspace Clustering 2 Input Cosegmentation Hu et al ID: 812002
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Slide1
Co-Segmentation of 3D Shapes via Subspace Clustering
Ruizhen Hu Lubin Fan Ligang Liu
Slide2Co-segmentationHu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering2Input
Slide3Co-segmentationHu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering3
Output
Slide4Related worksHu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering4
[
Kraevoy et al. 2007]
Shuffler
[Huang et al. 2011]
Joint segmentation
[
Golovinskiy
and
Funkhouser
2009]
Consistent segmentation
[
Xu
et al. 2010]
Style separation
[
Kalogerakis
et al. 2010]
Supervised segmentation
[van
Kaick
et al. 2011]
Supervised correspondence
Slide5Related worksUnsupervised
co-segmentationvia Descriptor-Space Spectral ClusteringHu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
5
Pre-segmentation
Result
Clustering
[
Sidi
et al. 2011]
Slide6Motivation
Over-segmentation
[Huang et al. 2011]Unsupervised
Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering6
clustering
Slide7Key observationHu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering7
Corresponding patches lie in a common
subspace
AGD
Co-segmentation
Subspace clustering
Key idea 1
Slide8Subspace clustering
Input: high dimensional datasets having low intrinsic dimensions
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
8
[Vidal 2010]
Output:
multiple low-dimensional linear subspaces
Slide9Sparse subspace clustering(SSC)
Based on the observation:each point can always be represented as a linear combination of the points belonging to the same subspace
Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
9
[
Elhamifar
and Vidal 2009]
, where
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Slide10Sparse subspace clustering(SSC)
Based on the observation:each point can always be represented as a linear combination of the points belonging to the same subspace
Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
10
[
Elhamifar
and Vidal 2009]
, where
Slide11Sparse subspace clustering(SSC)
Based on the observation:
each point can always be represented as a linear combination of the points belonging to the same
subspace
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
11
[
Elhamifar
and Vidal 2009]
where
Slide12Sparse subspace clustering(SSC)
Based on the observation:
each point can always be represented as a linear combination of the points belonging to the same
subspace
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
12
[
Elhamifar
and Vidal 2009]
Slide13SSQPHu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering13
: provides better interpretations
: more efficient than SSC
Block diagonal property
:
where
is a permutation matrix, submatrix
Desired property for affinity matrix!
[Wang et al. 2011]
Slide14Co-segmentationSingle feature:
Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering14
0
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0
88
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45
0
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0
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39
0
88
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0
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0
#patch of all shapes in the set
dim of feature vector
AGD
Slide15Co-segmentationSingle feature:
Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering15
The
NCut
method is then applied to this affinity matrix
to segment patches into
clusters.
[Shi and Malik 2000]
Slide16Choices of features
Different sets favor different featuresSingle feature is not enoughHu et al.Co-Segmentation of 3D Shapes via Subspace Clustering16
[
Kalogerakis
et al. 2010]
[Ben-Chen and
Gostman
2008]
CF
Slide17Multiple featuresHu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering17
Slide18How to combine different features?
Traditional way: concatenate all features into one descriptoruse single-feature subspace clustering algorithmHu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering18
Problem:
Corresponding patches may not be similar in all features
Concatenated feature vectors may not lie in a common subspace any more
Slide19How to combine different features?
Our solution:apply subspace clustering in each feature spaceadd the consistent multi-feature penalty
where
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
19
Key idea 2
Slide20Consistent multi-feature penalty
To find the most similar patch pairs Corresponding patches don’t have to be similar in all features
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
20
Slide21Consistent multi-feature penalty
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
21
:
Induces column
sparsity
of
Identify the most similar patch pairs
Slide22Consistent multi-feature penalty
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
22
:
Induces the
sparsity
within each column of
Enables the prominent features to pop up
Slide23Co-segmentation
Multiple features:
Affinity matrix:
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
23
Slide24Results20 categories of shapes
16 from PSB [Chen et al. 2009, Kalogerakis et al. 2010]4 from [Sidi et al. 2011]Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
24
Slide25Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
25
Slide26Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
26
Slide27Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
27
Slide28Evaluation & Comparisons
Category
Ours
CFV
Category
Ours
CFV
Human
70.4
–
Plier
86.0
68.9
Cup
97.4
85.0
Fish
85.6
66.5
Glasses
98.3
97.9
Bird
71.5
71.4
Airplane
83.3
75.3
Armadillo
87.3
–
Ant
92.9
69.6
Vase
80.2
66.5
Chair
89.6
83.6
Fourleg
88.7
69.2
Octopus
97.5
95.3
Candelabra
93.9
44.2
Table
99.0
99.1
Goblet
99.2
59.8
Teddy
97.1
97.0
Guitar
98.0
90.0
Hand
91.9
88.2
Lamp
90.7
59.8
Average
90.4
–
Hu et al.
Co-Segmentation of 3D Shapes via Subspace Clustering
28
CFV
: the subspace clustering technique on the concatenated feature vector
Slide29ComparisonsSupervised method: [
Kalogerakis et al. 2010]Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
29
Slide30ComparisonsUnsupervised method: [
Sidi et al. 2011]Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering30
Slide31ComparisonsUnsupervised method: [
Sidi et al. 2011]Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering31
Our algorithm
[
Sidi
et al. 2011]
Slide32Limitations
Cannot always:distinguish two different parts with high geometric similarityrecognize corresponding parts with low geometric similarityHu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
32
Slide33ConclusionKey ideas:
Formulate co-segmentation as subspace clusteringConsistent multi-feature penaltyAdvantages:More flexible and efficient Capable of handling more kinds of modelsResults are better compared to previous unsupervised methods
Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering33
Slide34Future work
Look for more semantic feature descriptorsAdd control on the contribution of different featuresHu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
34
Slide35Hu et al.Co-Segmentation of 3D Shapes via Subspace Clustering
35Thank you!