DeformationDriven TopologyVarying 3 D Shape Correspondence Ibraheem Alhashim
Deformation-Driven Topology-Varying 3 D Shape Correspondence Ibraheem Alhashim Kai Xu Junjie Cao Patricio Simari Yixin Zhuang Hao Zhang Presenter: Ibraheem Alhashim Simon Fraser University Sponsored by
Shape Correspondence Fundamental task in: Object recognition Classification Statistical shape modeling Shape morphing 2 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Shape Correspondence Corresponding man-made 3 D shapes is challenging Large variability in geometry & structure Real-world data is inconsistent & unlabeled 3 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Shape Correspondence [Averkiou 14] [Zheng 13] [Xu 12] [Jain 12] [Kalogerakis 12] Part-level correspondences 4 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Shape Correspondence Continuous fine-grained correspondence is critical for continuous shape blending [Alhashim et al. 14] 5 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Previous Works Rigid alignment not sufficient for diverse shapes [Golovinskiy & Funkhouser 08] 6 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Previous Works Co-analysis methods Coarse results Forced correspondence Set of shapes [Laga et al. 14] [Huang et al. 14] [Kim et al. 13] [Zheng et al. 14] 7 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
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] 8 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D 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 9 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Our Proposal The Geo. Topo transform ü ü ü Piece-wise continuous part correspondence Supports topological changes No prior or fixed number of segments Efficient to compute Works on pairs 10 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Our Proposal The Geo. Topo transform Distortion Energy Deformation model 11 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Deformation Model Deformation suitable for man-made shapes Supports disconnected components Structure-aware (preserving part relations) Allows for topological changes 12 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D 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 13 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Shape Representation • A structure graph of part skeletons [Alhashim et al. 2014] • Skeletons are fitted by parametric curves / sheets Parametric curves Parametric sheet 14 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Structural Rods 3 D shape Curve-sheet abstractions Structural rods 15 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Energy • Distortion term Ed Overall change of part arrangements – Change in angle – 16 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Energy • Distortion term Ed Before deformation After deformation Best correspondence 17 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Energy • Connectivity term Ec – Relative length of shortest rods before and after deformation Source shape Deformed shape Target 18 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
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 – High Low High 19 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Energy • Solidity term Es ? ? 20 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Deformation Process Deform-to-fit matched parts, then propagate 1. Align centers 2. Match extremities 3. Deform towards target 4. Propagate edit to others Curves Sheets 21 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Search • Search tree path: set of matched parts on the source • Beam search + pruning seat-seat back-back leg front leg back 3 D shapes Curve-sheet abstractions back bar 22 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Results 23 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Results 24 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Applications Shape blending fully automatically! 25 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Applications Shape Classification Topological medoid 26 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Evaluation Ground truth • 75 shapes, 5 categories (chair, airplane, table, bed, velocipede) • Fine and coarse labels 27 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D 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. 28 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Evaluation Fine-grained correspondence benchmark 29 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Evaluation Coarse correspondence benchmark (co-analysis) 30 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Summary Geo. Topo: topology-varying deformation model for a fine-grained correspondence search Key contribution: a deformation model and a selfdistortion 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 31 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Limitations Initial segmentation Large geo. and topo. differences 32 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Future Work Segmentation Online shape repositories are not well segmented Incorporate a segmentation search along with the correspondence search High energy Low energy segmentation 33 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Future Work Co-analysis Fine-grained correspondence on a set Looking for consistent assignments 34 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
gruvi. cs. sfu. ca/project/geotopo THANK YOU! ACKNOWLEDGMENTS Anonymous reviewers, authors who provided code, funding from: NSFC SA 2015. SIGGRAPH. ORG Sponsored by
Partial Matching 36 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Energy Terms 37 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Automatic Segmentation Convex. Analysis SDF Con. Aware Approximate Convexity Analysis 38 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Cost & Quality Trade-off 39 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Timing & Shapes Complexity 40 SA 2015. SIGGRAPH. ORG Deformation-Driven Topology-Varying 3 D Shape Correspondence
Structure Preservation • Edit propagation – Reinforce symmetry and contact relations Topology-Varying Shape Matching and Modeling 41
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