1. Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일

2. Abstract Mesh quilting –Geometric texture synthesis algorithm –3D texture sample given in the form of a triangle inside a thin shell around an arbitrary surface Allow interactive and versatile editing and animation Based on stitching together 3D geometry elements On curved surfaces –Reduce distortion of geometry elements inside the 3D space of the thin shell –Low-distortion parameterization 2

3. Introduction Today’s commodity video cards –Exquisite details can be purely geometrically modeled Modeling such complex geometric details –A tedious process Creating mesh-based 3D geometric textures –Remains challenging 3

4. Mesh quilting To synthesize geometric details by stitching together small patches –of an input geometric texture sample Tools to further edit and animate –these geometric details 4

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6. Related work Modeling of Geometric Detail on Surfaces –Fur [Kajiya and Kay 1989] –Rendering fur with three dimensional textures. –In Proceedings of SIGGRAPH 89 –Volume textures [Neyret 1998] 6

7. More versatile representations –Geometric textures [Elber 2005] –Shell map [Porumbescu et al. 2005] 7

8. Limitations –Periodic textures Mesh-based creation –Of geometric textures on arbitrary meshes –[Fleischer et al. 1995] –Mostly restricted to the dissemination Of simple texture elements over the surface 8

9. Example-based Texture Synthesis Synthesis based on per-pixel non- parametric sampling –[Turk 2001;Wei and Levoy 2001; Ying et al. 2001; Tong et al. 2002; Zelinka and Garland 2003] Based on the L2-norm –a relatively poor measure of perceptual similarity, –such algorithms are not applicable to a large spectrum of textures. 9

10. Textures by directly copying small parts –of an input texture sample –alpha-blending [Praun et al. 2000] –quilting [Efros and Freeman 2001; Liang et al. 2001; Soler et al. 2002; Magda and riegman 2003; Kwatra et al. 2003; Wu and Yu 2004; Zhou et al. 2005] Searching for the “min-cut” seams –further enhance the smoothness across the seams [Efros and Freeman 2001; Kwatra et al. 2003; Zhou et al. 2005] 10

11. Feature matching –[Wu and Yu 2004] –Human visual system is so sensitive to edges, corners and other high-level features in textures Parallel controllable texture synthesis on GPU –[Lefebvre and Hoppe 2005] Texture synthesis using Expectation Maximization optimization –[Kwatra et al. 2005] 11

12. Graphcut textures 12

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15. Shell map 15

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18. Challenges Little work to provide tool –for 3D geometric texture synthesis. [Bhat et al. 2004; Lagae et al. 2005] 18 [Lagae et al. 2005]

19. [Bhat et al. 2004] –voxel-based approach [Lagae et al. 2005] –used distance fields 19 [Bhat et al. 2004]

20. Challenges Irregular mesh –The input texture sample is not a regular array of pixel values Geometry elements –Each being truly a small 3D object identified As a connected component in 3D Quilting is performed on curved surfaces –Severe distortion in the 3D space 20

21. Contributions Mesh-based geometric texture synthesis –Synthesized over the base mesh. Triangle meshes –Both the input geometry and output geometry Integrity –Maintains the integrity of geometry elements In the synthesized texture Texture editing and texture animation –can be easily performed 21

22. Aligns elements –through local deformation –And merges elements to connect texture patches Mesh quilting on curved surfaces –Low-distortion parameterization of the shell space 22

23. Mesh Quilting Synthesis Setup & Nomenclature 23

24. Algorithm Overview Seed Finding –Find a seed region R from which to grow the output mesh texture further out Geometry Matching –Find the best patch placement around region R using geometry matching to minimize mismatch between the new and the old patch Element Correspondences –Find correspondences between elements in the new patch and those in the old patch Element Deformation –Align the corresponding elements through local deformation Element Merging –Expand the output texture by merging the new patch into the output texture space 24

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26. Seed Finding Grid-based approach –The bounding boxes of both M out and M in are subdivided in finer regular grids These grids are only two-dimensional Initially, the cells of M out are tagged unprocessed Each time we wish to grow out the current mesh M out, –we look for an unprocessed cell with the largest number of adjacent cells that are already processed this will be the seed cell that we will try to process next. 26

27. Geometry Matching Find how to complete the mesh texture in the seed cell –and possibly add to its surroundings too. Using the nearby existing mesh texture available near the seed cell –Find a portion of the original swatch M in best matching this surrounding to extend M out. 27

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30. Restrict the translation t to be in –grid unit Element deformation described in Section 2.6 –will compensate for an imperfect element alignment Octree data structure for the input texture –Significant speed-up 30

31. Element Correspondences the overlapping region is usually larger than the small sub-patch P out –since the input mesh texture covers P out completely. 31

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33. Element Deformation 33

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36. Element Merging Every element (either from Cout or Cin) without correspondence –directly added to Mout. For every established correspondence (Cout,Cin) –If Cout is entirely within the overlapping region, Cout is ignored and Cin is instead added to the final results –if Cin is entirely within the overlapping region, Cin is ignored and Cout is added to Mout. 36

37. In all other cases stitch parts of Cin and Cout –to get a singly-connected, combined element –seek a cut path in each element –the graph cut algorithm [Boykov et al. 2001] 37

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41. Mesh Quilting Over Curved Surfaces Setup –Let M base be the base mesh that we wish to enhance with added geometric details. –M in the geometric texture mesh used as a swatch –seamlessly tile the base mesh –S the scale of the geometric details 41

42. From Planar to Curved 2D grid -> base mesh –Quilting process will stop Only when there are no more unprocessed triangles Define a local surface patch –By starting from the chosen triangle –Growing the region Using breadth-first traversal –Until we reach a certain depth –Or when the total area of the patch exceeds a user-defined threshold 42

43. Position of vertices located with respect to the base mesh Location of a vertex v –over a triangle Tbase –is defined by the barycentric coordinates –of its orthogonal projection on Tbase –along with the orthogonal distance (i.e., height) »from the triangle to v 43

44. discrete conformal mapping surface patch is flattened over the 2D plane –using a discrete conformal mapping DCM [Desbrun et al. 2002] 44

45. Local operations –Described for planar mesh quilting –Can be performed Over this parameterization plane Position of the newly synthesized vertices –Will be reprojected Onto the local mesh-based coordinate system 45

46. in very curved regions If the area distortion induced –by the local parameterization is too large –Reduce the area of the surface patch This will decrease –the size of the output-sub-patch Pout 46

47. Final Mesh Embedding Convert the vertex positions –Stored in local coordinates for now –Into a stand-alone, common embedding Self-intersections can be created Build a texture atlas for Mbase –Convert the above local representation of vertex positions to locations in a geometry texture space Then, construct a shell space around Mbase –Mapping the vertices from the geometry texture space to the shell space –will fix the location of the vertices in 3D space 47

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50. Shell Mapping Porumbescu et al. [2005] –Creates large distortion in curved regions We alleviate this! –By optimizing a stretch metric on this tetrahedral mesh –A natural extension of low-distortion parameterization –of triangle meshes [Sander et al. 2001] 50

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53. Minimization Algorithm Only update the u and v texture coordinates of the vertices on the offset surface Optimization of the stretch metric –along a randomly chosen search direction –in the (u, v) plane –as in [Sander et al. 2001]. 53

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58. Discussions Regions with very high curvature can be badly handled –parametric distortion of small surface patches may be high Cannot always achieve perfect matching –if the swatch is untileable even with major element deformation –Postprocessing step is performed to remove those visually-displeasing elements Figure 5(b) 58

59. Conclusions Mesh-based 3D texture synthesis algorithm 59