1/5/2014 procedural modeling motivation ipm classification...

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Bedrich BenesPurdue UniversityDec 12th 2013INRIA ‐ Imagine

Inverse Procedural Modeling – Bedrich Benes – Dec 12th 2013

Inverse Procedural Modeling (IPM) MotivationIPM ClassificationCase studies

IPM of volumetric buildingsIPM of stochastic treesUrban reparameterizationIPM of 2D vector images

Conclusions


Modeling is an open problem in CG

Traditional approachesManuallyScanning (and reconstruction) of real objectsBy a code


SystemParameters Structure

Rules

, sin , cos

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Can we find a code that generates a given structure?


Rules


Kolmogorov complexity

Minimal grammar problem

Inverse problems in mathematics

…and others


A) Nothing is givenFind the system, the rules, and the parameters

?? Structure

?


B) The system is givenFind the rules and their parameters

System? Structure

?

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C) The system and the rules are givenFind the parameters

System? Structure

Rules


D) The system and the parameter are givenFind the rules


?



Vanegas, C.A., Aliaga, D.G., and Benes, B., Building Reconstruction using Manhattan‐World Grammars, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2010


Automatically generate a 3D model of a Manhattan‐world building

Input:Geo‐referenced bird’s‐eye view photosBounding box of the building footprint

Output:3D model of the building represented as a grammar

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Inverse Procedural Modeling – Bedrich Benes – Dec 12th 2013 Inverse Procedural Modeling – Bedrich Benes – Dec 12th 2013

A building consists of a sequence of floors , , … ,

The external profile of is a 2D polygon

Can be represented by a string of attributed letters produced by a grammar


Generalized Rewriting Rule (GRR)

→

l a

l‐a‐b

b

cc


Particular casesU‐shape ( 0 and 0 and 0) Corner ( 0 or 0 and 0)Pushback ( 0 and 0and 0)

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By image‐to‐geometry matching we detect “turn signals” that represent corners

For each floor the parameters , ,and are found via optimization (it converges to one solution)

The building is then represented by a sequence of GRR , , … , and their parameters



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C) The system and the rules are givenFind the parameters

Stava, O., Pirk, S., Benes, B., Mech, R., and Deussen, O., Inverse Procedural Modeling of Trees, In Computer Graphics Forum (2014)


LiDAR

Xfrog

SpeedTree

. . .

InputParameters

Developmental Model

SimilarityMeasure Optimization Convergence?

No

Yes

Stop

L‐systems

Input Model

GeneratedModel


The output is a 3D model that is “alive”

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Novel (complicated) growth model

Endogenous and exogenous flow

Uses 24 parameters

Good modeling capability


Monte Carlo Markov Chain optimizationwith Metropolis‐Hastings sampling strategy

Similarity measure of two treesGeometric similarity metricsGraph distanceVisual similarity


The output allows for random variations

The complex 3D geometry is represented by a set of 24 parameters of the procedural model(good compression)


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C) The system and the rules are givenFind the parametersUse them to re‐generate a city

Vanegas, C, A., Garcia‐Dorado, I., Aliaga, D., Benes, B., and Waddell, P., (2012) Inverse Design of Urban Procedural Models, in ACM Transactions on Graphics (TOG) 28 (5), 111


The objective is urban layout editing

The user is shielded from the procedural model

High‐level editing changes by indicatorsAverage distance to a parkSun exposureLandscape visibility


A combination of two approaches1) Forward procedural modeling

by changing parameters, rules, and performing local changes

2) Inverse procedural modelingby editing indicators

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What is the acceptable amount of changes?

Can we provide a better local control?

Can we predict the changes?

Is it too high‐level?



Stava, O., Benes, B., Mech, R., Aliaga, D.,G., and Kristof, P., Inverse Procedural Modeling by Automatic Generation of L‐systems, Computer Graphics Forum (Eurographics), 29:2, 10 pages, 2010.

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Input: 2D vector image

Output: an L‐system

Inspired by the previous work in symmetry detection


2D Vector Image Analysis L‐system Modifications


d

α

3. Analyze clusters and calculate

cluster significance

Update the affected clusters

4. Create non‐terminal

symbols and L‐system rules

2. Calculate transformations, fill

transformation spaces, and perform clustering

1. Calculate terminal symbols by inverse

instancing

Similarity

Distance

Cluster size

Seq. length

Scaling

P(m) →A f(1) ‐(30) P(m‐1)

P(3)

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cluster analysis

L‐system generation

transformationanalysis

inverse instancing

Deinstancing– Similar vector elements are coded as terminals

A2

A3

A4

B1A1

B2

B3B4

L‐system 2P1(m)→ [A] T 1 [B]

S → T s [P2(3)]


• Compute similarity between all input elements• Similar elements are represented by a terminal

A2

A3

A4

B1A1

B2

B3B4


S → T s [P2(3)]Terminals

A :

B :

cluster analysis



inverse instancing


cluster analysis



inverse instancing

• Transformation between two symbols

A2

A3

A4

B1A1

B2

B3B4


P2(m) :m>0 → [P1] T 2 P2(m‐1)m=0 → [P1]

S → T s [P2(3)]Terminals

A :

B :−(α) f(d)∗(s)−(β)

Transformation between two coordinate systems


cluster analysis



inverse instancing

• Find significant transformations– Put all transformations into Transformation space

Transformation = 4D Vector (2D transl., rotation, scale)

A2

A3

A4

B1A1

B2

B3B4

Terminals

A :

B :d

α

0

4D Transformation Space

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cluster analysis



inverse instancing

• Clustering in the transformation space– Large clusters ~ significant transformations

A2

A3

A4

B1A1

B2

B3B4

Terminals

A :

B :d

α

0

4D Transformation Space


cluster analysis



inverse instancing

• One transformation space for each pair of terminal symbols 4x 4D Transformation Spaces

d

α

0

A‐A

d

α

0

A‐B

d

α

0

B‐A

d

α

0

B‐BA2

A3

A4

B1A1

B2

B3B4

Terminals

A :

B :


cluster analysis



inverse instancing

• Cluster = Transformations between the same symbols

4x 4D Transformation Spaces

d

α

0

A‐A

d

α

0

A‐B

d

α

0

B‐A

d

α

0

B‐BA2

A3

A4

B1A1

B2

B3B4

Terminals

A :

B :


cluster analysis



inverse instancing

C1

C2

C3

C4

• New rule ~ new non‐terminal symbol

Terminals

A2

A3

A4

B1A1

B2

B3B4

Non‐TerminalsC :

A :

B :d

α

0

A‐A

d

α

0

A‐B

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cluster analysis



inverse instancing

C1

C2

C3

C4

• Clusters no longer valid– Update them using the new non‐terminal symbol– Compute importance of updated clusters

Terminals

Non‐TerminalsC :

A :

B :d

α

0

A‐A

d

α

0

A‐BC‐C


cluster analysis



inverse instancing

• Generate new rules until there are no clusters– Axiom → Last non‐terminal

Terminals

C1

C :

C2

C3

C4

D :

Axiom: S → TS D(3)D1

A :

B :d

α

0

C‐C


cluster analysis



inverse instancing

• Final L‐system

Terminals

A :

B :

L‐systemC(m)→ [A] T 1 [B]

D(m) :m>0 → [C] T 2 D(m‐1)m=0 → [C]

S → T s [D(3)]


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A complex scene can have thousands of rules

A post processing may be required

A weighting function to give some preferences


What is a set of good procedural rules?Minimal grammar problemGood editing properties

What is the expression power of the IPM?

What PM system should be used?

Can the A case be solved?


Procedural modeling is a very strong conceptDozens of different PM for different casesHindered by the complexity of the rulesInverse methods can bring it to practical usage

… take a photograph of a tree/building/cloudan app will fina a PM that generates it …

1/5/2014 procedural modeling motivation ipm classification...

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