1. Lapped Textures Emil Praun Adam Finkelstein Hugues Hoppe Emil Praun Adam Finkelstein Hugues Hoppe Princeton University Microsoft Research Princeton University Microsoft Research

2. Goal “example” image textured surface mesh geometry ?

3. Goal Little user effort No apparent seams No obvious periodicity Low distortion Local texture control Anisotropy Little user effort No apparent seams No obvious periodicity Low distortion Local texture control Anisotropy

4. Previous 2D Texture Synthesis Histogram equalization [Heeger ’96] Laplacian block shuffling [de Bonet ’97] Pixel template matching [Efros ’99] [Wei ’00] Histogram equalization [Heeger ’96] Laplacian block shuffling [de Bonet ’97] Pixel template matching [Efros ’99] [Wei ’00]

5. Histogram equalization [Heeger ’96] Laplacian block shuffling [de Bonet ’97] Pixel template matching [Efros ’99] [Wei ’00] Random pasting of image blocks [Xu ’00] Histogram equalization [Heeger ’96] Laplacian block shuffling [de Bonet ’97] Pixel template matching [Efros ’99] [Wei ’00] Random pasting of image blocks [Xu ’00] Previous 2D Texture Synthesis

6. Previous 3D Texturing Volumetric textures: Noise functions [Perlin ’85, Worley ’96] Noise functions [Perlin ’85, Worley ’96] Solid textures by example [Ghazanfarpour ’96] Solid textures by example [Ghazanfarpour ’96] Synthesizing texture on a surface: Reaction-diffusion [Turk ’91, Witkin ’91] Reaction-diffusion [Turk ’91, Witkin ’91] Cellular textures [Fleischer ’95] Cellular textures [Fleischer ’95] Covering surface with triangular tiles [Neyret ’99] Covering surface with triangular tiles [Neyret ’99] Volumetric textures: Noise functions [Perlin ’85, Worley ’96] Noise functions [Perlin ’85, Worley ’96] Solid textures by example [Ghazanfarpour ’96] Solid textures by example [Ghazanfarpour ’96] Synthesizing texture on a surface: Reaction-diffusion [Turk ’91, Witkin ’91] Reaction-diffusion [Turk ’91, Witkin ’91] Cellular textures [Fleischer ’95] Cellular textures [Fleischer ’95] Covering surface with triangular tiles [Neyret ’99] Covering surface with triangular tiles [Neyret ’99]

7. Approach texture patch surface

8. Key Idea: Patch Pasting texture patch surfacesurface “lapped textures”

9. PROCESS

10. Algorithm texture patch surface

11. Algorithm texture patch surface

12. Algorithm texture patch surface

13. Algorithm texture patch surface

14. Issues 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering

15. Issues 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering

16. Texture Patch Creation

17. Less Structure  Splotch

18. Issues 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering

19. Direction Field: User-specified

20. Direction Field: Local to Patch

21. Issues 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering

22. Patch Growth

29. Issues 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering

30. Align Patch to Direction Field texture patch surface

31. Tangential Vector Field

32. Optimizing the Parametrization Least squares best match to unit axes Sparse linear system. No explicit fairness functional Least squares best match to unit axes Sparse linear system. No explicit fairness functional

33. Result of Optimization

34. Issues 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering

35. Coverage estimation off-screen buffer Render patch triangles Flag covered triangles Remember 1 pixel per uncovered triangle per uncovered triangle Render patch triangles Flag covered triangles Remember 1 pixel per uncovered triangle per uncovered triangle

36. Coverage estimation off-screen buffer Render patch triangles Flag covered triangles Remember 1 pixel per uncovered triangle per uncovered triangle Render patch triangles Flag covered triangles Remember 1 pixel per uncovered triangle per uncovered triangle

37. Coverage estimation off-screen buffer Render patch triangles Flag covered triangles Remember 1 pixel per uncovered triangle per uncovered triangle Render patch triangles Flag covered triangles Remember 1 pixel per uncovered triangle per uncovered triangle

38. Issues 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering 1.Texture patch creation 2.Specifying direction field 3.Surface patch growth 4.Patch parametrization 5.Face coverage estimation 6.Texture storage and rendering

39. Texture Storage and Rendering Method 1: Texture Atlas Pre-composite into a global texture map. Pre-composite into a global texture map. -- OR -- Method 2: Runtime pasting Composite at run-time using hardware Composite at run-time using hardware Method 1: Texture Atlas Pre-composite into a global texture map. Pre-composite into a global texture map. -- OR -- Method 2: Runtime pasting Composite at run-time using hardware Composite at run-time using hardware

40. Method 1: Texture Atlas Patches of triangles with similar normals 2D packing problem for arbitrary polygons Patches of triangles with similar normals 2D packing problem for arbitrary polygons

41. Method 2: Runtime Pasting Store vertex coordinates for each patch Composite at run-time using hardware May render triangles several times Store vertex coordinates for each patch Composite at run-time using hardware May render triangles several times

42. Atlas vs. Runtime Pasting Atlas + Faster rendering, more portable + Easy to paint unique details (eyes, nose on bunny) – Sampling artifacts; user effort Pasting – Increases model complexity (   1.6 –3) + Huge effective resolution + Reuse splotch parameterization for many textures Atlas + Faster rendering, more portable + Easy to paint unique details (eyes, nose on bunny) – Sampling artifacts; user effort Pasting – Increases model complexity (   1.6 –3) + Huge effective resolution + Reuse splotch parameterization for many textures

43. RESULTS

44. Results: Splotches (completely automatic: no direction field)

45. Results: Anisotropic

46. Controlling Direction and Scale

47. 25 frames per sec! 256 x 256 texture (282 times) 256 x 256 texture (282 times) 15,000 faces

48. Limitations low-frequencycomponentsboundarymismatches direction field singularities

49. Video

50. Interactive Paint Demo

51. Timings Texture patch creation: 1 min Specifying direction field: 15 min Surface patch growth Patch parameterization Face coverage estimation Rendering: 25fps @ 1024 2 Texture patch creation: 1 min Specifying direction field: 15 min Surface patch growth Patch parameterization Face coverage estimation Rendering: 25fps @ 1024 2 Preprocessing: 20sec – 6 min Preprocessing: Pentium III 733MHz, GeForce graphics Human effort

52. Conclusions Effective texture-by-example through:  Overlapping texture patches  Minimal edge blending Aligning to direction field  fast optimization Runtime pasting  high effective resolution Effective texture-by-example through:  Overlapping texture patches  Minimal edge blending Aligning to direction field  fast optimization Runtime pasting  high effective resolution

53. Future Work Other texture types: Animated Animated “Thick” (volumetric) textures  fur “Thick” (volumetric) textures  fur NPR rendering NPR rendering Greater automation Fine-tuning patch placement Other texture types: Animated Animated “Thick” (volumetric) textures  fur “Thick” (volumetric) textures  fur NPR rendering NPR rendering Greater automation Fine-tuning patch placement

54. “X Covers Y”? Flattening covers texture patch Texture patch covers triangle Use inner / outer hulls of texture unit OR scan - convert (use hardware) Flattening covers texture patch Texture patch covers triangle Use inner / outer hulls of texture unit OR scan - convert (use hardware)

55. Polygonal Hulls Start w/ boundary pixels, edges between neighbors Conservatively simplify polygons Start w/ boundary pixels, edges between neighbors Conservatively simplify polygons

56. Algorithm Cut texture patches from input texture [Specify texture direction & scale on mesh] REPEAT Pick texture patch T, mesh point P Grow surface patch S around P to size(T) Flatten S over T; paste T on mesh Update mesh coverage info UNTIL mesh is covered Cut texture patches from input texture [Specify texture direction & scale on mesh] REPEAT Pick texture patch T, mesh point P Grow surface patch S around P to size(T) Flatten S over T; paste T on mesh Update mesh coverage info UNTIL mesh is covered

57. Patch Growth Guess initial parametrization Want to cover texture patch Overlaps ok Prevent excessive distortion Surface patch homeomorphic to a disc Guess initial parametrization Want to cover texture patch Overlaps ok Prevent excessive distortion Surface patch homeomorphic to a disc

58. Optimizing the Parametrization TT SS BB CC AA (T)(T)(T)(T) (T)(T)(T)(T) (S)(S)(S)(S) (S)(S)(S)(S) (A)(A)(A)(A) (A)(A)(A)(A) (B)(B)(B)(B) (B)(B)(B)(B) (C)(C)(C)(C) (C)(C)(C)(C)  tt^^ss ^^ face in 3D 2D texture space

59. Optimizing the Parametrization Scale control given by || S ||, || T || Solution unique up to a translation (fix patch center) No explicit fairness term No flipped triangle ambiguity as in methods using meshes of springs Patch may require further growth Scale control given by || S ||, || T || Solution unique up to a translation (fix patch center) No explicit fairness term No flipped triangle ambiguity as in methods using meshes of springs Patch may require further growth