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Projective Texture Atlas for 3D Photography

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

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Projective Texture Atlas for 3D Photography

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  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)

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