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

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mesh quilting for geometric texture synthesis

Mesh Quilting For Geometric Texture Synthesis

Kun Zhou et al.


발표 이성호

2009년 4월 15일

  • 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
  • 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
mesh quilting
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
related work
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]

More versatile representations

    • Geometric textures
      • [Elber2005]
    • Shell map
      • [Porumbescu et al. 2005]


    • 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
example based texture synthesis
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.

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]

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

[Lagae et al. 2005]


[Bhat et al. 2004]

    • voxel-based approach
  • [Lagae et al. 2005]
    • used distance fields

[Bhat et al. 2004]

  • 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
  • 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

Aligns elements

    • through local deformation
    • And merges elements to connect texture patches
  • Mesh quilting on curved surfaces
    • Low-distortion parameterization
      • of the shell space
mesh quilting synthesis
Mesh Quilting Synthesis
  • Setup & Nomenclature
algorithm overview
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
seed finding
Seed Finding
  • Grid-based approach
    • The bounding boxes of both Moutand Min are subdivided in finer regular grids
  • These grids are only two-dimensional
  • Initially, the cells of Moutare tagged unprocessed
  • Each time we wish to grow out the current mesh Mout,
    • 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.
geometry matching
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 Min best matching this surrounding to extend Mout .

Restrict the translation t to be in

    • grid unit
  • Element deformation described in Section 2.6
    • will compensate for an imperfect element alignment
  • Octreedata structure for the input texture
    • Significant speed-up
element correspondences
Element Correspondences
  • the overlapping region is usually larger than the small sub-patch Pout
    • since the input mesh texture covers Poutcompletely.
element merging
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 Cinis instead added to the final results
    • if Cin is entirely within the overlapping region,
      • Cinis ignored and Cout is added to Mout .
in all other cases
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]
mesh quilting over curved surfaces
Mesh Quilting Over Curved Surfaces
  • Setup
    • Let Mbase be the base mesh that we wish to enhance with added geometric details.
    • Minthe geometric texture mesh
      • used as a swatch
        • seamlessly tile the base mesh
    • S
      • the scale of the geometric details
from planar to curved
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

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

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
in very curved regions
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
final mesh embedding
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
shell mapping
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]
minimization algorithm
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].
  • 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-displeasingelements
      • Figure 5(b)
  • Mesh-based 3D texture synthesis algorithm