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study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
study Image Vectorization using Optimized Gradeint Meshes
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study Image Vectorization using Optimized Gradeint Meshes

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

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