CoSegmentation of 3 D Shapes via Subspace Clustering

Co-Segmentation of 3 D Shapes via Subspace Clustering Ruizhen Hu Lubin Fan Ligang Liu

Co-segmentation Input Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 2

Co-segmentation Output Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 3

Related works Shuffler [Kraevoy et al. 2007] [Golovinskiy and Funkhouser 2009] Joint segmentation [Huang et al. 2011] Hu et al. Supervised segmentation Consistent segmentation Style separation [Xu et al. 2010] [Kalogerakis et al. 2010] Supervised correspondence Co-Segmentation of 3 D Shapes via Subspace Clustering [van Kaick et al. 2011] 4

Related works • Unsupervised co-segmentation [Sidi et al. 2011] – via Descriptor-Space Spectral Clustering Pre-segmentation Hu et al. Clustering Co-Segmentation of 3 D Shapes via Subspace Clustering Result 5

Motivation Unsupervised clustering Over-segmentation [Huang et al. 2011] Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 6

Key observation • Corresponding patches lie in a common subspace Co-segmentation Key id ea 1 Subspace clustering AGD Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 7

Subspace clustering [Vidal 2010] • Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 8

Sparse subspace clustering(SSC) [Elhamifar and Vidal 2009] • 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. 0 56 0 39 0 88 56 0 45 0 87 0 135 0 Co-Segmentation of 3 D Shapes via Subspace Clustering 9

Sparse subspace clustering(SSC) [Elhamifar and Vidal 2009] • 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 3 D Shapes via Subspace Clustering 10

Sparse subspace clustering(SSC) [Elhamifar and Vidal 2009] • 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 3 D Shapes via Subspace Clustering 11

Sparse subspace clustering(SSC) [Elhamifar and Vidal 2009] • 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 3 D Shapes via Subspace Clustering 12

SSQP [Wang et al. 2011] Hu et al. Des i for red pr affi o nity perty ma trix ! Co-Segmentation of 3 D Shapes via Subspace Clustering 13

Co-segmentation • Single feature: Hu et al. 0 56 0 39 0 88 56 0 45 0 87 0 135 0 AGD Co-Segmentation of 3 D Shapes via Subspace Clustering 14

Co-segmentation • Single feature: [Shi and Malik 2000] Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 15

Choices of features • Different sets favor different features – Single feature is not enough CF [Kalogerakis et al. 2010] Hu et al. [Ben-Chen and Gostman 2008] Co-Segmentation of 3 D Shapes via Subspace Clustering 16

Multiple features Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 17

How to combine different features? • Traditional way: 1. concatenate all features into one descriptor 2. use single-feature subspace clustering algorithm • Problem: – Corresponding patches may not be similar in all features – Concatenated feature vectors may not lie in a common subspace any more Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 18

How to combine different features? • Key id Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering ea 2 19

Consistent multi-feature penalty • Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 20

Consistent multi-feature penalty • Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 21

Consistent multi-feature penalty • Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 22

Co-segmentation • Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 23

Results • 20 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 3 D Shapes via Subspace Clustering 24

Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 25

Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 26

Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 27

Evaluation & Comparisons 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 – CFV: the subspace clustering technique on the concatenated feature vector Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 28

Comparisons • Supervised method: [Kalogerakis et al. 2010] Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 29

Comparisons • Unsupervised method: [Sidi et al. 2011] Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 30

Comparisons • Unsupervised method: [Sidi et al. 2011] Our algorithm Hu et al. [Sidi et al. 2011] Co-Segmentation of 3 D Shapes via Subspace Clustering 31

Limitations Cannot always: 1. distinguish two different parts with high geometric similarity 2. recognize corresponding parts with low geometric similarity Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 32

Conclusion • Key ideas: – Formulate co-segmentation as subspace clustering – Consistent multi-feature penalty • Advantages: – More flexible and efficient – Capable of handling more kinds of models – Results are better compared to previous unsupervised methods Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 33

Future work • Look for more semantic feature descriptors • Add control on the contribution of different features Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 34

Thank you! Hu et al. Co-Segmentation of 3 D Shapes via Subspace Clustering 35