study Image Vectorization using Optimized Gradeint Meshes
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  • 1. Image Vectorization using Gradient Meshes
    Jian Sun, Lin Liang, Fang Wen, Heung-Yeung Shum
    Microsoft Research Asia
    ACM SIGGRAPH 2007
  • 2. Cutout tool
    Initial mesh
    Input image
    Optimized gradient mesh
    Reconstruction
  • 3. Outline
    Introduction
    Background
    Gradient Mesh
    Optimized Gradient Mesh
    Result
    Conclusions
  • 4. Introduction
  • 5. Image Vectorization
    Goal : convert a raster image into a vector graphics
    Compact
    Scalable
    Easy to animate
    Requirements
    Vector-based contents (eg. Flash or SVG) on the Internet
    Vector-based GUIs used in Windows Vista
  • 6. Gradient mesh
    Gradient mesh, adrawing tool of commercial vector graphics editors
    Tracing photograph
    Start adding mesh points
    Selecting mid value skin tone
    Sampling colors from face mesh to hide seam
    Sampling colors from photo
    Sampling colors from within the mesh
    Finished eye/eye socket
    http://www.creativebush.com/tutorials/mesh_tutorial.php
  • 7. Image represented by gradient mesh
    gradient mesh
    http://www.creativebush.com/tutorials/mesh_tutorial.php
  • 8. Image vectorization tools
    Adobe Illustrator, “Live Trace”
    Corel CoreDraw, “CorelTrace”
    AutoTrace, “AutoTrace”
    Input image
    Adobe, Live Trace
  • 9. Optimized gradient mesh
    Blend surface colors according to the control points color as constructing surface by the control points
    Optimize the gradient mesh as an energy minimization problem
    Advantages
    Efficiency of use
    Easy to edit – modify, animation
    Scalability
    Compact representation
    JPEG, 37.5 KB
    Optimized, 7.7KB
  • 10. Background
  • 11. Object-based vectorization
    Object-based vectorization [Price and Barrett 06]
    Hierarchically segmentation of object and sub-objects by a recursive graph cut algorithm
    Subdivide meshes until the reconstruct error is below a threshold
    Input image
    Subdivision mesh
  • 12. RaveGrid
    [Swaminarayan and Prasad 06]
    Constrained Delaunay triangulation of the edge contour set
  • 13. cont.
  • 14. Ardeco
    Automatic Region Detection and Conversion algorithm [Lecot and Levy 06]
    Cubic splines
    Each region filled with a constant color, or a linear or circular gradient
  • 15. cont.
  • 16. Gradient Mesh
  • 17. Overview
    Cutout tool
    Input raster image
    Initial mesh
    (Coons mesh)
    E(M) Constrains:
    Smoothness
    User guidedvector
    Boundary
    min argEnergy(Mesh)
    non-linear least squares (NULL) problem
    Levenberg-Marquardt (LM) algorithm
    Optimized gradient mesh
    (Ferguson patch)
    Reconstruction image
    • Color fitting: monotonic cubic spline interpolation
    • 18. Coherent matting method: sample object boundary color from the estimated foreground colors
  • Mesh initialization (manually)
    Decompose the input image into sub-objects using Cutout tool [Li et al. 04]
    Divide each sub-objects with 4 segments manually as Coons patches
    m(u,v): the position vector of a point (u,v)
    Q : control points el al.
    F : basis functions
  • 19. Ferguson patch
    TA
    TB
    [Ferguson 1964]
    P(0)=A
    Basic Curve Segmentation
    P(1)=B
  • 20. Ferguson patch
    Basic Surface Segmentation
    0
  • 21. Ferguson patch
    Basic Surface Segmentation
    0
  • 22. Gradient mesh
    A gradient mesh consists of topologically planar rectangular Ferguson patches with mesh-lines
    For each point q
    • Position: {xq,yq}
    Derivatives: {mqu,mqv, αqumqu, αqvmqv}
    RGB color: cq = {cq(r), cq(g), cq(b)}
  • 23. Ferguson patches are lack of Cv and Cu !
    Color interpolation
  • 24. [Wolberg and Alfy 99]
    Determine the smoothest possible curve that passes through its control points and satisfy monotonic constraint
    The seven data points are monotonically increasing in f(xi) for 0 ≦i ≦ 6, the cubic spline is not monotonic
    Monotonic cubic spline
  • 25. Rendering Ferguson patches
    Sample color of control points
    Estimate Cu, Cv by Monotoic Cubic Spline algorithm
    Render Ferguson patches
  • 26. Scalability
    A gradient mesh
    • original resolution (x 1)
    Scaling result (x8)
    • shape edges are well preserved
    Bi-cubic raster scaling (x8)
    • Blocky artifacts appear
  • Optimized gradient mesh
  • 27. Minimize E(M)
    min arg.
  • 28. Solve NULL problem using LM algorithm
    Minimizing E(M) is a non-linear least squares (NULL) problem
    Energy function
    z: vector form of unknowns in M
    Levenberg-Marquardt (LM) algorithm is the most successful solver for NULL
    [Levenberg 44], [Nocedal and Wright 99]
  • 29. cont.
    • Gaussian pyramid from the input image and apply coarse-to-fine optimization for LM
  • Optimization
    Gradient mesh of Adobe Illustrator
    Optimized gradient mesh
    • 0.7/pixel reconstruction error
    • 30. 40 iterations
  • Smooth constraint
    Opt. gradient mesh without smooth(err. 1.8/pixel)
    Opt. gradient mesh with smooth (err. 0.9 pixel)
    Input image
    Smooth neighboring patches also,
    mp(- △s, t) = mp-1(1- △s, t)
  • 31. Vector line guided optimized gradient mesh
    User guided vector, V
    Initial mesh
    Opt. gradient mesh with user guided vector
    (err. 0.5/pixel)
    Directly optimized gradient mesh
    (err. 2.5/pixel)
  • 32. Vector line guided optimized gradient mesh
    w = 1/5 L
    Initial mesh
    Opt. gradient mesh with V
  • 33. Boundary constraint
    The boundary of a gradient – one or more cubic Bezier spline
    The control points on the boundary only move along the spline
    Ex: control point q on the spline S in u direction
  • 34. Results
  • 35. Red pepper
    Optimized
    the highlight and shadow regions are reconstructed
    Initial
    gradient meshes
    Gradient meshes by an artist (354 patches)
  • 36. Sculpture
    Optimized gradient mesh
    Input image
    Reconstruction
  • 37. Face
    Optimized gradient mesh
    Input image
    Reconstruction
  • 38. Conclusions
    Input image
    Introduce the gradient mesh as an image representation tool first
    Present optimized gradient mesh
    Limitations
    A fine image details and highly textured image
    Boundaries or topologies are too complicated
    Reconstructed image
    Optimized gradient meshes
  • 39. END