1/5/2014. Bedrich Benes Purdue University Dec 6 th 2013 Prague. Modeling is an open problem in CG

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1 Berich Benes Purue University Dec 6 th 213 Prague Inverse Proceural Moeling (IPM) Motivation IPM Classification Case stuies IPM of volumetric builings IPM of stochastic trees Urban reparameterization IPM of 2D vector images Conclusions Moeling is an open problem in CG, sin, cos Traitional approaches Manually Scanning (an reconstruction) of real objects By a coe Parameters System Rules Structure 1

2 Can we fin a coe that generates a given structure? A) Nothing is given Fin the system, the rules, an the parameters Parameters System Structure?? Structure Rules? B) The system is given Fin the rules an their parameters C) The system an the rules are given Fin the parameters? System Structure? System Structure? Rules 2

3 D) The system an the parameter are given Fin the rules B) The system is given Fin the rules an their parameters Parameters System? Structure Vanegas, C.A., Aliaga, D.G., an Benes, B., Builing Reconstruction using Manhattan Worl Grammars, Proceeings of IEEE Conference on Computer Vision an Pattern Recognition (CVPR) 21 Automatically generate a 3D moel of a Manhattan worl builing Input: Geo reference bir s eye view photos Bouning box of the builing footprint Output: 3D moel of the builing represente as a grammar 3

4 A builing consists of a sequence of floors,,, The external profile of is a 2D polygon Generalize Rewriting Rule (GRR) Can be represente by a string of attribute letters prouce by a grammar c l a b c l a b Particular cases U shape ( an an ) Corner ( or an ) Pushback ( an an ) By image to geometry matching we etect turn signals that represent corners For each floor the parameters,, an are foun via optimization (it converges to one solution) The builing is then represente by a sequence of GRR,,, an their parameters 4

5 C) The system an the rules are given Fin the parameters Stava, O., Pirk, S., Benes, B., Mech, R., an Deussen, O., Inverse Proceural Moeling of Trees, In Computer Graphics Forum (214) 5

6 LiDAR Xfrog SpeeTree s Input Moel Similarity Measure Optimization Developmental Moel Convergence? No Yes Stop... Generate Moel Input Parameters The output is a 3D moel that is alive Novel (complicate) growth moel Enogenous an exogenous flow Uses 24 parameters Goo moeling capability 6

7 Monte Carlo Markov Chain optimization with Metropolis Hastings sampling strategy Similarity measure of two trees Geometric similarity metrics Graph istance Visual similarity The output allows for ranom variations The complex 3D geometry is represente by a set of 24 parameters of the proceural moel (goo compression) C) The system an the rules are given Fin the parameters Use them to re generate a city Vanegas, C, A., Garcia Dorao, I., Aliaga, D., Benes, B., an Waell, P., (212) Inverse Design of Urban Proceural Moels, in ACM Transactions on Graphics (TOG) 28 (5), 111 7

8 The objective is urban layout eiting The user is shiele from the proceural moel High level eiting changes by inicators Average istance to a park Sun exposure Lanscape visibility A combination of two approaches 1) Forwar proceural moeling by changing parameters, rules, an performing local changes 2) Inverse proceural moeling by eiting inicators 8

9 The problem is the amount of changes Can we provie better local control? How can we preict changes? Is it too high level? B) The system is given Fin the rules an their parameters Stava, O., Benes, B., Mech, R., Aliaga, D.,G., an Kristof, P., Inverse Proceural Moeling by Automatic Generation of s, Computer Graphics Forum (Eurographics), 29:2, 1 pages, 21. Input: Output: 2D vector image an Inspire by the previous work in symmetry etection 9

10 2D Vector Image Analysis Moifications Upate the affecte s De Similar vector elements are coe as terminals Similarity 1. Calculate terminal symbols by 2. Calculate s, fill spaces, an perform ing Distance Scaling Cluster size Seq. length 3. Analyze s an calculate significance P(3) P(m) A f(1) (3) P(m 1) 4. Create nonterminal symbols an rules A4 A3 A2 2 P1(m) [A] T 1 [B] S T s [P2(3)] A1 1

11 Compute similarity between all input elements Similar elements are represente by a terminal Transformation between two symbols A4 A3 A1 A2 2 P1(m) [A] T 1 [B] S T s [P2(3)] A4 A3 A1 A2 2 P1(m) [A] T 1 [B] P2(m) :m> [P1] T 2 P2(m 1) m= [P1] S T s [P2(3)] () f() (s) (β) Transformation between two coorinate systems Fin significant s Put all s into Transformation space Transformation = 4D Vector (2D transl., rotation, scale) A4 4D Transformation Space Clustering in the space Large s ~ significant s 4D Transformation Space A4 A3 A2 A3 A2 A1 A1 11

12 One space for each pair of terminal symbols 4x 4D Transformation Spaces A4 A A A B Cluster = Transformations between the same symbols 4x 4D Transformation Spaces A A A B A4 A3 A2 B A B B A3 A2 B A B B A1 A1 New rule ~ new non terminal symbol A A A B Clusters no longer vali Upate them using the new non terminal symbol Compute importance of upate s A A C C A B A4 C4 A3C3 A2 C2 A1C1 Non C : C4 C3 C2 C1 Non C : 12

13 Generate new rules until there are no s Axiom Last non terminal Final C4 C3 C2 C C C : D : C(m) [A] T 1 [B] D(m) :m> [C] T 2 D(m 1) m= [C] S T s [D(3)] C1 D1 Axiom: S T S D(3) A complex scene can have thousans of rules A post processing may be require A weighting function to give some preferences 13

14 What is a set of goo proceural rules? Minimal grammar problem Goo eiting properties What is the expression power of the IPM? What PM system shoul be use? Can the A case be solve? Proceural moeling is a very strong concept Dozens of ifferent PM for ifferent cases Hinere by the complexity of the rules Inverse methos can bring it to practical usage take a photograph of a tree/builing/clou an app will generate a PM that generates it 14