1. Example-Based Fractured Appearance L. Glondu, L. Muguercia, M. Marchal, C. Bosch, H. Rushmeier, G. Dumont and G. Drettakis

2. Introduction Reproducing a specific fracture pattern with simulation can be a tedious task Obtaining the same pattern is often not necessary Similarity between two fracture patterns not well defined PhotographSimulation

3. Our goal Estimate fracture simulation parameters from photographs (of cracks) Match statistics rather than exact patterns – Fragment areas, edge lengths, junctions, … Determine which statistics influence similarity – Use this as a metric during optimization Adapt existing simulation approach

4. Contributions User study to determine similarity between fracture patterns based on statistics Optimization process using this metric Extended RT fracture simulation approach Interactive modeling interface

5. Related work (I) Aging and weathering – Physically-based simulation [DORSEY et al. 1996, MÉRILLOU et al. 2008] – Data driven [WANG et al. 2006, GU et al. 2006] – Example-based simulation (stains) [BOSCH et al. 2011]

6. Related work (II) Fracture simulation – Continuum mechanics [O’BRIEN et al. 1999, MULLER et al. 2004] – RT + implicit approach [GLONDU et al. 2012] – Stress field [IBEN and O’BRIEN 2006] – Procedural [MOULD 2005, GOBRON and CHIBA 2001, DESBENOIT et al. 2005]

7. Related work (III) Statistical models for fracture – Validate simulation [VALETTE et al. 2008] – Matching of fragments [SHIN et al. 2010]

8. Outline 1.Processing of input patterns 2.User study on statistical pattern similarity 3.Fracture simulation approach 4.Optimization of parameters 5.Results

9. Processing input patterns 1)Extract cracks location 2)Process features: fragments, edges, junctions 3)Obtain statistics: areas, lengths, angles, … PhotographCracksFeaturesStatistics

10. User study (I) Which simulated pattern is the most similar to the reference pattern ? (2-AFC) Reference pattern (from photo) Choice 2 (simulation) Choice 1 (simulation)

11. User study (II) 5 reference images 7 simulation conditions – Matching fragment statistics (S1) – Matching crack statistics (S2) – Matching junction statistics (S3) – Combinations of S1, S2 and S3 (S1+S2, S2+S3, …) 20 participants (14 males, 6 females) 212 comparisons (~20 min.)

12. Images for the user study

13. Demo

14. User study results Fragment statistics (S1) as predominant choice (except S1 + S3) Statistics relevant for defining visual similarity S1S2S3S1 + S3 S19179.550 S292722 S320.57327.5 S1 + S3507872.5

15. Fracture simulation FEM based on modal analysis [GLONDU et al. 2012] – Fast + volumetric approach Stress map evolving over time [IBEN and O’BRIEN 2006] – Initial stress computed from loading forces – Opening based on resistance threshold R c (per-element) t=0 (no stress) t > 0 resulting fracture

16. Crack propagation Implicit fracture surface [GLONDU et al. 2012] We incorporate stress relaxation around cracks – Smoothing kernel based on distance (+ radius) – Combine with tensor to model preferred orientations Omni-directional relaxation Directional relaxation

17. Relaxation results Selection based on input pattern statistics (mean junction angle) Omni-directional relaxation (no preferred orientation) Directional relaxation (preferred orientations)

18. Parameters to optimize Parameter symbol DescriptionRelative to Loading force magnitudeBody mass Stress increase rateResistance to fracture Resistance to fracture variance Resistance to fracture Stress relaxation rateResistance to fracture Stress relaxation radius Input material properties: E, v, ρ, R c m Others: age, path noise

19. Optimization

20. Error metric Fragment statistics Crack statistics Junction statistics EMD : Earth Mover’s Distance (w f, w c, w j ) : weighting coefficients = (3,1,1) based on user study

21. Optimization approach Approximate Bayesian Computation [BEAUMONT et al. 02] – Takes into account randomness of R c and force position Run N = 20k simulations (~15 min.) Take the parameter set with lowest error

22. Results

23. Complex scenes

24. Fracture evolution Increasing age parameter

25. Volumetric approach True 3-D fracture surfaces

26. Interactive Fracture Modeling (1/3)

27. Interactive Fracture Modeling (2/3) Applying a similar pattern on a large scene

29. Performance Simulation – Timings: 16 ms - 264 ms – Model size: 7K elements (tile) to 54K (road) Interactive editor: 30-100 fps Optimization: 15 min. (60 ms/iteration) Intel Core 2 Extreme, 2.3GHz, 4GB RAM + nVidia Quadro FX 3700M

30. Conclusion Fracture similarity metric based on statistics and user study – 2D statistics better than 1D Optimization method for fitting parameters based on this metric Efficient simulation allowing interactive application of fractured appearance Main limitation: no internal information – Thickness, texture, …

31. Thank you! Acknowledgments TIN2010-20590-C02-02 grant NSF-1064412 grant Donations: Autodesk, Adobe, nVidia