Deformation-Driven Topology-Varying 3D Shape Correspondence

1. Deformation-Driven Topology-Varying 3D Shape Correspondence Ibraheem Alhashim Kai Xu YixinZhuang Junjie Cao Patricio Simari HaoZhang Presenter: Ibraheem Alhashim Simon Fraser University

2. Shape Correspondence • Fundamental task in: Classification Shape morphing Statistical shape modeling Object recognition

3. Shape Correspondence • Corresponding man-made 3D shapes is challenging • Large variability in geometry & structure • Real-world data is inconsistent & unlabeled

4. Shape Correspondence • Part-level correspondences [Xu 12] [Zheng 13] [Kalogerakis 12] [Jain 12] [Averkiou 14]

5. Shape Correspondence Continuous fine-grained correspondence is critical for continuousshape blending [Alhashim et al. 14]

6. Previous Works • Rigid alignment not sufficient for diverse shapes [Golovinskiy & Funkhouser 08]

7. Previous Works • Co-analysis methods • Coarse results • Forced correspondence • Set of shapes [Zheng et al. 14] [Kim et al. 13] [Huang et al. 14] [Laga et al. 14]

8. Deformation-Driven Shape Matching • Best matching = minimal self-distortion as we deform one shape to match the other [Sederberg & Greenwood 92] [Zhang et al. 08]

9. 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. Our Proposal The GeoTopotransform • Piece-wise continuous part correspondence • Supports topological changes • No prior or fixed number of segments • Efficient to compute • Works on pairs

11. Our Proposal The GeoTopotransform Distortion Energy Deformation model

12. Deformation Model • Deformation suitable for man-made shapes • Supports disconnected components • Structure-aware (preserving part relations) • Allows for topological changes

13. Self-Distortion Energy • Structural distortion in three terms: • Distortion on all pairs of connected parts • Connectivity between parts • Solidity measure for parts changing topology

14. Shape Representation • A structure graph of part skeletons [Alhashim et al. 2014] • Skeletons are fitted by parametric curves / sheets Parametric curves Parametric sheet

15. Structural Rods 3D shape Curve-sheet abstractions Structural rods

16. Energy • Distortion term Ed • Overall change of part arrangements • Change in angle

17. Energy • Distortion term Ed Best correspondence Before deformation After deformation

18. Energy • Connectivity term Ec • Relative length of shortest rods before and after deformation Deformed shape Source shape Target

19. Energy • Solidity term Es • Ratio between the volume of a part to the volume of its convex hull • Measures the effect of a split / merge Low High High

20. Energy • Solidity term Es ? ?

21. Deformation Process • Deform-to-fit matched parts, then propagate 1. Align centers 3. Deform towards target 2. Match extremities 4. Propagate edit to others Curves Sheets

22. Search • Search tree path: set of matched parts on the source • Beam search + pruning leg front-leg front seat-seat back-back leg back-leg back back bar-back bar 3D shapes Curve-sheet abstractions

23. Results

24. Results

25. Applications fully automatically! • Shape blending

26. Applications Shape Classification Topological medoid

27. Evaluation • Ground truth • 75 shapes, 5 categories (chair, airplane, table, bed, velocipede) • Fine and coarse labels

28. 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. Evaluation • Fine-grained correspondence benchmark

30. Evaluation • Coarse correspondence benchmark (co-analysis)

31. 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. Limitations Initial segmentation Large geo. and topo. differences

33. Future Work • Segmentation • Online shape repositories are not well segmented • Incorporate a segmentation search along with the correspondence search High energy Low energy segmentation

34. Future Work • Co-analysis • Fine-grained correspondence on a set • Looking for consistent assignments

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

36. Partial Matching

37. Energy Terms

38. Automatic Segmentation Convex. Analysis SDF Con. Aware Approximate Convexity Analysis

39. Cost & Quality Trade-off

40. Timing & Shapes Complexity

41. Structure Preservation • Edit propagation • Reinforce symmetry and contact relations