Projective Texture Atlas for 3D Photography

1. Projective Texture Atlas for 3D Photography Jonas Sossai Júnior Luiz Velho • IMPA

2. Motivation • Texture maps describe surface properties • Important for Visualization and Modelling • Surface parameterization(Mapping a 2D domain to a 3D surface) • Difficult to compute / Introduces distortion • Solution: use an atlas structure(set of charts individually parameterized)

3. Problem Description • Our work: Build texture atlas for 3D photography • Strategy: • Projective atlas • Variational optimization • Applications: • 3D photography • Attribute editing

4. Related Work • 3D photography (Scopigno et al. 2002) • Surface representation (Sander et al. 2003) • Variational approximation (Desbrun et al. 2004)

5. Contributions Projective texture atlas: • 3D Photography Application • Optimal Patch Construction • Texture Compression and Smoothing

6. Texture for 3D Photography • The problem: Construct a good texture map from photographs • Requirements: • Minimize texture distortion • Space-optimized texture • Reduce color discontinuity • Variational projective texture atlas: • Surface partitioning (distortion and frequency-based) • Parametrization, discretization and packing • PDE-based color diffusion • Texture smoothing

7. Overview Partitioning Parameterization Packing • Techniques: • Partitioning: Variational minimization of texture distortion and space • Parameterization: Projective mapping • Packing: Simple algorithm

8. Variational Surface Partitioning • Given a surface S, a desired number of regions n, andan error metric E • An optimal atlas A with a partition R over S,is a set of regions Ri, associated with charts Ci, that minimizes the total error: E(R, A) = ∑ E(Ri, Ci) • Error Metrics • Texture Distortion • Frequency Dissimilarity

9. Lloyd’s Algorithm • Clustering by Fixed Point Iteration Repeat until done: • Assign points to regions according to centers • Update centers • Scheduling • Chart adding • Chart growing • Chart merging

10. Minimizing Texture Distortion • Texture Distortion • Visibility Ci – Chart ci – Camera associate to chart Ci ni – camera direction n(x) – surface normal

11. Maximizing Frequency Coherency • Texture has different levels of detail • Algorithm: • Compute frequency content using wavelet analysis • Make charts based on frequency similarity • Scale images according to frequency

12. Color Compatibilization • Problem: Color discontinuity between images (different exposure) • Solution:Frontier faces share an edge(color from two images)

13. PDE-based Diffusion • Algorithm: • For each frontier edge compute the color difference between corresponding texels • Multigrid diffusion of differences over charts

14. Parameterization and Discretization • Parameterization of each chart is the projective mapping of its associated camera • The discretization is obtained by projecting the chart boundary onto its associated image

15. Packing • Output Texture Map • Simple Algorithm: • For each chart clip the bounding box • Sort these clipped regions by height • Place sequentially into rows • OBS: Could use better packing, but frequency analysis makes the size of the texture atlas small enough

16. Results I (5 charts, distortion=5875.18) 220 x 396 (39 charts, distortion=4680.54) 750 x 755

17. Results II 39 charts 750 x 755 70 charts 320 x 433

18. Comparison I Real photograph Scopigno et al. 2002 Our results 6 charts, 256 x 512 5 charts, 220 x 396

19. Comparison II Real photograph Scopigno et al. 2002 Our results 73 charts, 512 x 1024 39 charts, 750 x 755

20. Conclusions and Future Work • Projective texture atlas: • Powerful structure for 3D photography • Foundation for attribute editing • Improvements: • Better packing algorithm • Other surface attributes(normal and displacement)