Hao Zhang Kai Xu Wei Jiang Jinjie Lin Daniel CohenOr Baoquan Chen Simon Fraser University Shenzhen Institutes of Advanced Technology National University of Defense Technology Tel Aviv University ID: 279004
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Slide1
Layered Analysis of Irregular Facades via Symmetry Maximization
Hao Zhang, Kai Xu, Wei Jiang, Jinjie Lin, Daniel Cohen-Or, Baoquan Chen
Simon Fraser University
Shenzhen Institutes of Advanced Technology
National University of Defense Technology
Tel Aviv UniversitySlide2
Façade
Rich interesting structure to analyze
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Our goal
A high-level understanding of the structure of irregular facadesA generative modelAn explanation of how the input facade was seemingly generated
Layering
Split
Decomposition
2. Instantiation
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Generative model
A hierarchy of decompositions
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Generative model
Two decomposition operations: split + layering
Input
+
Two substructures
Split
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Generative model
Input
Layering
+
Two substructures (layers)
Structure completion
Two decomposition operations: split + layering
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More compact generative model
input
split only
8 ops.
split +
layering
4 ops.
Two decomposition operations: split + layering
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A good generative model
Two objectivesStructural: Occam’s Razor (Simplest explanation)
min.
# ops.
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A good generative model
Two objectivesStructural: Occam’s Razor (Simplest explanation)Perceptual: Law of Gestalt (Symmetry
maximization)The two objectives can be optimized simultaneously.
Two substructures are most symmetric!
Symmetry maximization
decomposition terminates
the fastest
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Symmetry-driven analysis
Symmetry maximization at each decompositionHow symmetric are the two substructures?How good is the decomposition?
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Symmetry-driven analysis
Objective: sum of symmetry measure of all internal nodes
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Related works
Structuring symmetry
Folding mesh
[
Simari et al. 06]
Structuring 3D
Geometry
[Martinet 2007]
Symmetry hierarchy[Wang et al. 2007]SFU, SIAT, NUDT, TAUSlide13
Related works
Façade analysisSymmetry-summarization[Wu et al. 2011]Shape grammar
parsing[Teboul et al. 2011]
Adaptive Partitioning
[Shen et al. 2011]
Instant
architecture
[
Wonka
et al. 2003]
Layering has so far not been considered.
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Related works
Inverse procedural modelingPartial symmetry and inverse procedural modeling[Bokeloh et al. 2010]
Inverse L-system[Stava et al. 2010]
We do not produce a shape grammar.
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Overview – Key components
Box
abstraction
Element
groups
Candidate
selection
…
…
…
…
Hierarchy
optimization
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Interactive box abstraction
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Element groups
A set of well-aligned boxes whose content repeats
Must be maximal: not contained by any other one
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Candidate decomposition selection
Split
cand
. 1
Split
cand
.
2
Layering
cand
. 1
Layering
cand
. 2
Input
…
…
Given a box pattern, find all candidates of split and
layering
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Candidate decomposition selection
Principle 1: An element group can not divided into two components by a valid decompositionSome examples …SFU, SIAT, NUDT, TAUSlide20
Candidate decomposition selection
ExamplesInvalid split
Becomes valid after layering
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Candidate decomposition selection
ExamplesInvalid splitBecomes valid after split
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Candidate decomposition selection
ExamplesInvalid layeringBecomes valid after layering
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Candidate decomposition selection
Principle 2: Candidate selection is carried out recursivelyCombinatorial search!
Split
cand
. 1
Split
cand
.
2
Layering
cand
. 1
Layering
cand
. 2
Layering
cand
. 1
Split
cand
. 1
Input
Substructure
…
…
…
…
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Finding the optimal hierarchy
Genetic algorithm with tree representationSample and evolve population of hierarchiesGenetic operators:
Altering decomposition
Crossover
Split
Layering
Swapping sub-trees
Mutation
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Finding the optimal hierarchy: Genetic algorithm
Fitness function:
Symmetry measure of a node (a substructure)
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Symmetry measure at a node
Requirements:Continuous measure for a discrete box patternBehaves well at both ends of the symmetry spectrumIntegral Symmetry (IS):Integral of
symmetry profiles along two directions
X
Y
Perfectly symmetric
asymmetric
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Symmetry measure of a discrete pattern
Symmetry profile – Intra-box profile
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Symmetry measure of a discrete pattern
Symmetry profile – Intra-box profile
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Symmetry measure of a discrete pattern
Symmetry profile – Intra-box profile
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Symmetry measure of a discrete pattern
Symmetry profile – Inter-box profile
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Symmetry measure of a discrete pattern
Combining inter-box and intra-box profiles:
Integral Symmetry
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An application – Façade retargeting
Top-down propagation
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An application – Façade retargeting
Top-down propagation
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An application – Façade retargeting
Top-down propagation
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An application – Façade retargeting
Top-down propagation
input
retargeted
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Structure-aware façade retargeting
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Input
Seam carving
Structure-aware
User interactive structural analysis [Lin et al. 2011]
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Evaluation I: Integral symmetry
Symmetry ranking tests
A
B
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Evaluation I: Integral symmetry
The accuracy score obtained is 88%Consistent with human perceptionSFU, SIAT, NUDT, TAUSlide40
Evaluation II: Symmetry-driven decomposition
max.
Our
method
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Evaluation II: Symmetry-driven decomposition
Compare to two alternatives
Global
reflectional
symmetry
Alternative 1:
Graph-cut segmentation
Alternative 2:
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Evaluation II: Symmetry-driven decomposition
Please select
which one, A or B, appears to
offer
the best high-level explanation of the facade structure:
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Evaluation II: Symmetry-driven decomposition
On 600 questionsObtain a winning percentageof 73% against Alternative 1of 79% against Alternative 2SFU, SIAT, NUDT, TAUSlide44
Limitations
Box abstraction and element grouping carried out with user assistanceLimited to axis-aligned structuresLimited to binary decompositionsHuman perception relatedlearning/crowdsourcing?
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Conclusion
Hierarchical and layered analysis of irregular facadesGenerative model: hierarchy of decompositionsA clearly defined objective: symmetry maximizationApplications:Structure-aware façade retargeting/editing/explorationSFU, SIAT, NUDT, TAUSlide46
Acknowledgement
Anonymous reviewersYangyan Li, Niloy Mitra, and Ariel ShamirParticipants of our user studiesResearch grantsNSERC Canada, NSFC China, Guangdong Sci. and Tech.
Program, Shenzhen Sci. and Inno. Program, CPSF, and the Israel Science Foundation.
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Thank you!
Code and data are available:
kevinkaixu.net
SFU, SIAT, NUDT, TAU