1. Sponsored by Deformation-Driven Topology-Varying 3D Shape Correspondence Ibraheem Alhashim Kai Xu Yixin Zhuang Junjie Cao Patricio Simari Hao Zhang Presenter: Ibraheem Alhashim Simon Fraser University

2. SA2015.SIGGRAPH.ORG 2 Deformation-Driven Topology-Varying 3D Shape Correspondence Shape Correspondence Fundamental task in: Shape morphing Statistical shape modeling Object recognition Classification

3. SA2015.SIGGRAPH.ORG 3 Deformation-Driven Topology-Varying 3D Shape Correspondence Shape Correspondence Corresponding man-made 3D shapes is challenging Large variability in geometry & structure Real-world data is inconsistent & unlabeled

4. SA2015.SIGGRAPH.ORG 4 Deformation-Driven Topology-Varying 3D Shape Correspondence Shape Correspondence Part-level correspondences [Jain 12] [Xu 12] [Zheng 13] [Averkiou 14] [Kalogerakis 12]

5. SA2015.SIGGRAPH.ORG 5 Deformation-Driven Topology-Varying 3D Shape Correspondence Shape Correspondence Continuous fine-grained correspondence is critical for continuous shape blending [Alhashim et al. 14]

6. SA2015.SIGGRAPH.ORG 6 Deformation-Driven Topology-Varying 3D Shape Correspondence Previous Works Rigid alignment not sufficient for diverse shapes [Golovinskiy & Funkhouser 08]

7. SA2015.SIGGRAPH.ORG 7 Deformation-Driven Topology-Varying 3D Shape Correspondence Previous Works [Zheng et al. 14] [Kim et al. 13] [Laga et al. 14] [Huang et al. 14] Co-analysis methods Coarse results Forced correspondence Set of shapes

8. SA2015.SIGGRAPH.ORG 8 Deformation-Driven Topology-Varying 3D Shape Correspondence Deformation-Driven Shape Matching Best matching = minimal self- distortion as we deform one shape to match the other [Zhang et al. 08] [Sederberg & Greenwood 92]

9. SA2015.SIGGRAPH.ORG 9 Deformation-Driven Topology-Varying 3D Shape Correspondence Challenge How to apply a deformation-driven search to complex man-made shapes? Many disconnected components Semantically similar yet very different Discrepancy in part count & structural relations Back Seat Legs

10. SA2015.SIGGRAPH.ORG 10 Deformation-Driven Topology-Varying 3D Shape Correspondence Our Proposal The GeoTopo transform Piece-wise continuous part correspondence Supports topological changes No prior or fixed number of segments Efficient to compute Works on pairs

11. SA2015.SIGGRAPH.ORG 11 Deformation-Driven Topology-Varying 3D Shape Correspondence Our Proposal The GeoTopo transform Deformation model Distortion Energy

12. SA2015.SIGGRAPH.ORG 12 Deformation-Driven Topology-Varying 3D Shape Correspondence Deformation Model Deformation suitable for man-made shapes Supports disconnected components Structure-aware (preserving part relations) Allows for topological changes

13. SA2015.SIGGRAPH.ORG 13 Deformation-Driven Topology-Varying 3D Shape Correspondence Self-Distortion Energy Structural distortion in three terms: 1.Distortion on all pairs of connected parts 2.Connectivity between parts 3.Solidity measure for parts changing topology

14. SA2015.SIGGRAPH.ORG 14 Deformation-Driven Topology-Varying 3D Shape Correspondence Shape Representation A structure graph of part skeletons [Alhashim et al. 2014] Skeletons are fitted by parametric curves / sheets Parametric curves Parametri c sheet

15. SA2015.SIGGRAPH.ORG 15 Deformation-Driven Topology-Varying 3D Shape Correspondence Structural Rods 3D shapeCurve-sheet abstractions Structural rods

16. SA2015.SIGGRAPH.ORG 16 Deformation-Driven Topology-Varying 3D Shape Correspondence Energy Distortion term E d – Overall change of part arrangements – Change in angle

17. SA2015.SIGGRAPH.ORG 17 Deformation-Driven Topology-Varying 3D Shape Correspondence Energy Distortion term E d Best correspondence Before deformation After deformation

18. SA2015.SIGGRAPH.ORG 18 Deformation-Driven Topology-Varying 3D Shape Correspondence Energy Connectivity term E c – Relative length of shortest rods before and after deformation Source shapeDeformed shapeTarget

19. SA2015.SIGGRAPH.ORG 19 Deformation-Driven Topology-Varying 3D Shape Correspondence Energy Solidity term E s – Ratio between the volume of a part to the volume of its convex hull – Measures the effect of a split / merge High Low High

20. SA2015.SIGGRAPH.ORG 20 Deformation-Driven Topology-Varying 3D Shape Correspondence Energy Solidity term E s ? ?

21. SA2015.SIGGRAPH.ORG 21 Deformation-Driven Topology-Varying 3D Shape Correspondence Deformation Process Deform-to-fit matched parts, then propagate Curves Sheets 1. Align centers 2. Match extremities 3. Deform towards target 4. Propagate edit to others

22. SA2015.SIGGRAPH.ORG 22 Deformation-Driven Topology-Varying 3D Shape Correspondence Search Search tree path: set of matched parts on the source Beam search + pruning 3D shapesCurve-sheet abstractions seat-seat back bar- back bar back-back leg back- leg back leg front- leg front

23. SA2015.SIGGRAPH.ORG 23 Deformation-Driven Topology-Varying 3D Shape Correspondence Results

24. SA2015.SIGGRAPH.ORG 24 Deformation-Driven Topology-Varying 3D Shape Correspondence Results

25. SA2015.SIGGRAPH.ORG 25 Deformation-Driven Topology-Varying 3D Shape Correspondence Applications Shape blending fully automatically!

26. SA2015.SIGGRAPH.ORG 26 Deformation-Driven Topology-Varying 3D Shape Correspondence Applications Topological medoidShape Classification

27. SA2015.SIGGRAPH.ORG 27 Deformation-Driven Topology-Varying 3D Shape Correspondence Evaluation Ground truth 75 shapes, 5 categories (chair, airplane, table, bed, velocipede) Fine and coarse labels

28. SA2015.SIGGRAPH.ORG 28 Deformation-Driven Topology-Varying 3D Shape Correspondence Evaluation [Xu 12] Fuzzy part correspondence (baseline) Works on pairs Match based on part OBB similarity [Zheng 14] Recurring part arrangements Find semantic consistency between part arrangements Performs better than co-segmentation in the presence of large shape variability [Kim 13] Deformable part-based templates Better suited for large shape sets Supports poorly segmented inputs + can be fully auto.

29. SA2015.SIGGRAPH.ORG 29 Deformation-Driven Topology-Varying 3D Shape Correspondence Evaluation Fine-grained correspondence benchmark

30. SA2015.SIGGRAPH.ORG 30 Deformation-Driven Topology-Varying 3D Shape Correspondence Evaluation Coarse correspondence benchmark (co- analysis)

31. SA2015.SIGGRAPH.ORG 31 Deformation-Driven Topology-Varying 3D Shape Correspondence Summary GeoTopo: topology-varying deformation model for a fine-grained correspondence search Key contribution: a deformation model and a self-distortion energy, defined on structural rods, assess shape matching quality based on preservation of structure Our framework shows promising results on challenging datasets with much room for improvement

32. SA2015.SIGGRAPH.ORG 32 Deformation-Driven Topology-Varying 3D Shape Correspondence Limitations Initial segmentation Large geo. and topo. differences

33. SA2015.SIGGRAPH.ORG 33 Deformation-Driven Topology-Varying 3D Shape Correspondence Future Work Segmentation Online shape repositories are not well segmented Incorporate a segmentation search along with the correspondence search High energyLow energy segmentation

34. SA2015.SIGGRAPH.ORG 34 Deformation-Driven Topology-Varying 3D Shape Correspondence Future Work Co-analysis Fine-grained correspondence on a set Looking for consistent assignments

35. SA2015.SIGGRAPH.ORG Sponsored by THANK YOU! gruvi.cs.sfu.ca/project/geotopo ACKNOWLEDGMENTS Anonymous reviewers, authors who provided code, funding from: NSFC

36. SA2015.SIGGRAPH.ORG 36 Deformation-Driven Topology-Varying 3D Shape Correspondence Partial Matching

37. SA2015.SIGGRAPH.ORG 37 Deformation-Driven Topology-Varying 3D Shape Correspondence Energy Terms

38. SA2015.SIGGRAPH.ORG 38 Deformation-Driven Topology-Varying 3D Shape Correspondence Automatic Segmentation SDFCon. AwareConvex. Analysis Approximate Convexity Analysis

39. SA2015.SIGGRAPH.ORG 39 Deformation-Driven Topology-Varying 3D Shape Correspondence Cost & Quality Trade-off

40. SA2015.SIGGRAPH.ORG 40 Deformation-Driven Topology-Varying 3D Shape Correspondence Timing & Shapes Complexity

41. Topology-Varying Shape Matching and Modeling Structure Preservation Edit propagation – Reinforce symmetry and contact relations 41