Oliver van Kaick 14 Kai Xu 2 Hao Zhang 1 Yanzhen Wang 2 Shuyang Sun 1 Ariel Shamir 3 Daniel CohenOr 4 4 Tel Aviv University 1 Simon Fraser University ID: 543896
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Co-Hierarchical Analysis of Shape Structures
Oliver van
Kaick1,4 Kai Xu2 Hao Zhang1 Yanzhen Wang2 Shuyang Sun1 Ariel Shamir3 Daniel Cohen-Or4
4
Tel Aviv University
1
Simon Fraser University
3The Interdisciplinary Center
2
HPCL, Nat. Univ. of Defense Tech.Slide2
Shape segmentation
2
Analysis of sets of shapesJoint segmentationHuang et al. 2011
Co-segmentation
Sidi et al. 2011
Active co-analysis
Wang et al. 2012Slide3
Shape segmentation
3
Segmentation: a flat representationSlide4
Part hierarchy
4
Hierarchy: a higher-level organization of shape partsSlide5
Applications of hierarchies
5
Use the hierarchy for various tasks
Structure-aware shape editing
[Wang et al. 2011]
Hierarchical segmentationSlide6
Part hierarchies
6
Extraction of hierarchies from individual or pairs of shapesSymmetry hierarchyWang et al. 2011
Geometry structuring
Martinet 2007
Part recombinationJain et al. 2012Slide7
Co-hierarchical analysis
7
Our goal: Extraction of a
unified (binary) hierarchy
Through an
unsupervised
co-analysis of the setSlide8
Co-hierarchical analysis
8
A
unified
explanation of the
structures
Top-down
to account for the
structural variabilitySlide9
Co-hierarchical analysis
9
The co-hierarchy of a set of velocipedesCapturing the functionality of the partsSlide10
Co-hierarchical analysis
10
The co-hierarchy of a set of velocipedesCapturing the functionality of the partsSlide11
Co-hierarchical analysis
11
The co-hierarchy of a set of velocipedesCapturing the functionality of the partsSlide12
Challenge of co-hierarchical analysis
12
Shapes can have
many possible
hierarchiesWe need to select
one hierarchy per shape
…Slide13
Challenge of co-hierarchical analysis
13
There can be
geometric variability
in the setWe need to compare the shape
structuresSlide14
Challenge of co-hierarchical analysis
14
There can also be much
structural variability
We need to account for thatSlide15
Challenge of co-hierarchical analysis
15
Cluster-and-select
scheme: clustering, representative selection, and resamplingSlide16
Overview
16Slide17
Overview
17Slide18
Sampling the space of hierarchiesWe sample the space by sampling the splits
Difficult to define a generic splitting criterionCriterion: balance of volume, compactness of parts, normalized cut?
We resort to random samplingWe sample splits in a top-down manner18Slide19
Tree-to-tree distance
19
Tree-to-tree distance: structural differencesSlide20
Node distance
20
Transformation between bounding boxesBounding boxes focus on the structural similaritySlide21
Shape distance
21
Shape distance: distance between hierarchiesSlide22
Cluster-and-select motivation
22
Representative selectionSlide23
Cluster-and-select
23
Minimal illustrative example with four shapesSlide24
Cluster-and-select
24
Multiple possible hierarchies per shapeSlide25
Cluster-and-select
25
Sampling of hierarchiesSlide26
Cluster-and-select
26
Multi-instance clusteringSlide27
Cluster-and-select
27
Representative selectionSlide28
Cluster-and-select
28
Traditional clustering: maximize similarity within clusters and dissimilarity between clustersSlide29
Cluster-and-select
29
Our problem: maximize similarity within clusters and similarity between clustersSlide30
Cluster-and-select
30
Samples maximize the similarity within clustersSlide31
Cluster-and-select
31
Also maximize the similarity between clustersSlide32
Cluster-and-select
32
Resampling of hierarchiesSlide33
Cluster-and-select
33
Resampling of hierarchiesSlide34
Cluster-and-select
34
Repeat the process: clustering, selectionSlide35
Cluster-and-select
35
Representative movementSlide36
Results of co-hierarchical analysis
36
The co-hierarchies are shown as a hierarchical segmentationSlide37
Results of co-hierarchical analysis
37
Hierarchical segmentation resultsSlide38
Results of co-hierarchical analysis
38
Hierarchical segmentation resultsSlide39
Results of co-hierarchical analysis
39
Hierarchical segmentation resultsSlide40
Results of co-hierarchical analysis
40
Consistency of the co-hierarchy[Wang et al. 2011]OursSlide41
Results of co-hierarchical analysis
41
Cluster-and-select on a mixed set of shapesSlide42
Summary of contributionsCo-hierarchical analysis of sets of
shapesStructure-driven shape analysisTo deal with geometric variability
Hierarchical analysisTo deal with structural variabilityA novel cluster-and-select schemeTo account for both variability and similarityThe structural co-hierarchy representationUnifies the learned structures42Slide43
Limitations and future workCo-hierarchical analysis:
only a first stepMore sophisticated node and tree distancesInitial random sampling
of treesIntegrate segmentation and hierarchical analysisMulti-class co-hierarchiesWhich hierarchy should be selected? 43Slide44
44
Co-Hierarchical Analysis of Shape Structures
Project page: http
://www.cs.sfu.ca/~
ovankaic/personal/conshier/
Thank you for your attention!Slide45
Appendix
45Slide46
Tree-to-tree distance46
Node distance
Recursive children distance
Ni
N
jSlide47
Tree-to-tree distance47
N
iNj
Node distance
Recursive children distanceSlide48
Results of co-hierarchical analysis48
Hierarchical segmentation resultsSlide49
Results of co-hierarchical analysis49
Hierarchical segmentation
results: deeper levelsSlide50
Results of co-hierarchical analysis50
Improvements shown by the cluster-and-select