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Layered Analysis of Irregular Facades via Symmetry Maximization

Layered Analysis of Irregular Facades via Symmetry Maximization. Hao Zhang, Kai Xu , Wei Jiang, Jinjie Lin, Daniel Cohen-Or, Baoquan Chen. National University of Defense Technology. Shenzhen Institutes of Advanced Technology. Tel Aviv University. Simon Fraser University. Façade.

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Layered Analysis of Irregular Facades via Symmetry Maximization

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  1. Layered Analysis of Irregular Facades via Symmetry Maximization Hao Zhang, Kai Xu, Wei Jiang, Jinjie Lin, Daniel Cohen-Or, Baoquan Chen National University of Defense Technology Shenzhen Institutes of Advanced Technology Tel Aviv University Simon Fraser University

  2. Façade Rich interesting structure to analyze SFU, SIAT, NUDT, TAU

  3. Our goal Split Decomposition Layering 2. Instantiation • A high-level understanding of the structure of irregular facades • A generative model • An explanation of how the input facade was seemingly generated SFU, SIAT, NUDT, TAU

  4. Generative model A hierarchyof decompositions SFU, SIAT, NUDT, TAU

  5. Generative model + Input Split Two substructures Two decomposition operations: split + layering SFU, SIAT, NUDT, TAU

  6. Generative model + Layering Input Two substructures (layers) Structure completion Two decomposition operations: split + layering SFU, SIAT, NUDT, TAU

  7. More compact generative model input split only 8 ops. split + layering 4 ops. Two decomposition operations: split + layering SFU, SIAT, NUDT, TAU

  8. A good generative model min. # ops. • Two objectives • Structural: Occam’s Razor (Simplest explanation) SFU, SIAT, NUDT, TAU

  9. A good generative model Two substructures are most symmetric! Symmetry maximization  decomposition terminates the fastest • The two objectives can be optimized simultaneously. • Two objectives • Structural: Occam’s Razor (Simplest explanation) • Perceptual:Law of Gestalt (Symmetry maximization) SFU, SIAT, NUDT, TAU

  10. Symmetry-driven analysis How good is the decomposition? How symmetric are the two substructures? Symmetry maximization at each decomposition SFU, SIAT, NUDT, TAU

  11. Symmetry-driven analysis Objective: sum of symmetry measure of all internal nodes SFU, SIAT, NUDT, TAU

  12. Related works Symmetry hierarchy [Wang et al. 2007] Folding mesh [Simariet al. 06] Structuring 3D Geometry [Martinet 2007] Structuring symmetry SFU, SIAT, NUDT, TAU

  13. Related works Adaptive Partitioning [Shen et al. 2011] Instant architecture [Wonka et al. 2003] Symmetry-summarization [Wu et al. 2011] Shape grammar parsing [Teboulet al. 2011] Layering has so far not been considered. Façade analysis SFU, SIAT, NUDT, TAU

  14. Related works Inverse L-system [Stava et al. 2010] Partial symmetry and inverse procedural modeling [Bokeloh et al. 2010] We do not produce a shape grammar. Inverse procedural modeling SFU, SIAT, NUDT, TAU

  15. Overview – Key components Element groups … … … … Hierarchy optimization Box abstraction Candidate selection SFU, SIAT, NUDT, TAU

  16. Interactive box abstraction SFU, SIAT, NUDT, TAU

  17. Element groups • Must be maximal: not contained by any other one A set of well-aligned boxes whose content repeats SFU, SIAT, NUDT, TAU

  18. Candidate decomposition selection • Given a box pattern, find all candidates of split and layering … Split cand. 1 Split cand. 2 … Input Layering cand. 1 Layering cand. 2 SFU, SIAT, NUDT, TAU

  19. Candidate decomposition selection Some examples … Principle 1: An element group can not divided into two components by a valid decomposition SFU, SIAT, NUDT, TAU

  20. Candidate decomposition selection Invalid split Becomes valid after layering Examples SFU, SIAT, NUDT, TAU

  21. Candidate decomposition selection Invalid split Becomes valid after split Examples SFU, SIAT, NUDT, TAU

  22. Candidate decomposition selection Invalid layering Becomes valid after layering Examples SFU, SIAT, NUDT, TAU

  23. Candidate decomposition selection Combinatorial search! … … Split cand. 1 Split cand. 1 Split cand. 2 … … Substructure Input Layering cand. 1 Layering cand. 1 Layering cand. 2 Principle 2: Candidate selection is carried out recursively SFU, SIAT, NUDT, TAU

  24. Finding the optimal hierarchy Crossover Mutation Split Layering Altering decomposition Swapping sub-trees • Genetic algorithm with tree representation • Sample and evolve population of hierarchies • Genetic operators: SFU, SIAT, NUDT, TAU

  25. Finding the optimal hierarchy: Genetic algorithm Symmetry measure of a node (a substructure) Fitness function: SFU, SIAT, NUDT, TAU

  26. Symmetry measure at a node X Y Perfectly symmetric asymmetric • Requirements: • Continuousmeasure for a discrete box pattern • Behaves well at both ends of the symmetry spectrum • Integral Symmetry (IS): • Integral of symmetry profiles along two directions SFU, SIAT, NUDT, TAU

  27. Symmetry measure of a discrete pattern Symmetry profile – Intra-box profile SFU, SIAT, NUDT, TAU

  28. Symmetry measure of a discrete pattern Symmetry profile – Intra-box profile SFU, SIAT, NUDT, TAU

  29. Symmetry measure of a discrete pattern Symmetry profile – Intra-box profile SFU, SIAT, NUDT, TAU

  30. Symmetry measure of a discrete pattern Symmetry profile – Inter-box profile SFU, SIAT, NUDT, TAU

  31. Symmetry measure of a discrete pattern Integral Symmetry Combining inter-box andintra-box profiles: SFU, SIAT, NUDT, TAU

  32. An application – Façade retargeting Top-down propagation SFU, SIAT, NUDT, TAU

  33. An application – Façade retargeting Top-down propagation SFU, SIAT, NUDT, TAU

  34. An application – Façade retargeting Top-down propagation SFU, SIAT, NUDT, TAU

  35. An application – Façade retargeting input retargeted Top-down propagation SFU, SIAT, NUDT, TAU

  36. Structure-aware façade retargeting SFU, SIAT, NUDT, TAU

  37. Input User interactive structural analysis [Lin et al. 2011] Seam carving Structure-aware SFU, SIAT, NUDT, TAU

  38. Evaluation I: Integral symmetry A B Symmetry ranking tests SFU, SIAT, NUDT, TAU

  39. Evaluation I: Integral symmetry • The accuracy score obtained is 88% • Consistent with human perception SFU, SIAT, NUDT, TAU

  40. Evaluation II: Symmetry-driven decomposition max. Our method SFU, SIAT, NUDT, TAU

  41. Evaluation II: Symmetry-driven decomposition Alternative 1: Alternative 2: Global reflectional symmetry Graph-cut segmentation Compare to two alternatives SFU, SIAT, NUDT, TAU

  42. Evaluation II: Symmetry-driven decomposition Please select which one, A or B, appears to offer the best high-level explanation of the facade structure: SFU, SIAT, NUDT, TAU

  43. Evaluation II: Symmetry-driven decomposition • On 600 questions • Obtain a winning percentage • of 73% against Alternative 1 • of 79% against Alternative 2 SFU, SIAT, NUDT, TAU

  44. Limitations • Box abstraction and element grouping carried out with user assistance • Limited to axis-aligned structures • Limited to binary decompositions • Human perception related • learning/crowdsourcing? SFU, SIAT, NUDT, TAU

  45. Conclusion • Hierarchical and layered analysis of irregular facades • Generative model: hierarchy of decompositions • A clearly defined objective: symmetry maximization • Applications: • Structure-aware façade retargeting/editing/exploration SFU, SIAT, NUDT, TAU

  46. Acknowledgement • Anonymous reviewers • Yangyan Li, NiloyMitra, and Ariel Shamir • Participants of our user studies • Research grants • NSERC Canada, NSFC China, Guangdong Sci. and Tech. Program, Shenzhen Sci. and Inno. Program, CPSF, and the Israel Science Foundation. SFU, SIAT, NUDT, TAU

  47. Thank you! Code and data are available: kevinkaixu.net SFU, SIAT, NUDT, TAU

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