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# Vectorization

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### Vectorization

1. 1. What is Vectorization?  Vectorization is the term for converting a scalar program to a vector program. Vectorized programs can run multiple operations from a single instruction
2. 2. Image Vectorization  Goal  convert a raster image into a vector graphics  vector graphics include  points  lines  curves  polygons
3. 3. Why Vector Graphics  Compact  Scalable  Editable  Easy to animate
4. 4. Compact input raster image 37.5KB optimized gradient mesh 7.7KB
5. 5. Editable
6. 6. Sclable
7. 7. Easy to animate
8. 8. Other fields  Cartoon drawing vectorization  skeletonization, tracing and approximation  Triangulation-based Method  Object-based Vectorization  Bezier patch  subdivision
9. 9. Image Vectorization Method Optimized Gradient Meshes  Jian Sun, Lin Liang, Fang Wen, Heung-Yeung Shum  Siggraph 2007
10. 10. Surface Representation  A tensor product patch is defined as  Bezier bicubic, rational biquadratic, B-splines…  control points lying outside the surface
11. 11. Gradient Mesh  Control Point Attributes:  2D position  geometry derivatives  RGB color  color derivatives
12. 12. Flow Chart Process Original Initial Mesh Optimized Mesh Final Rendering
13. 13. Mesh Initialization Clear View
14. 14. Mesh Initialization  Decompose image into sub-objects  Divide the boundary into four segments  Fitting segments by cubic Bezier splines  Refine the mesh-lines  evenly distributed  interactive placement
15. 15. Mesh Optimization  To minimize the energy function P: number of patches
16. 16. Mesh Optimization Optimaized input image initial rendering final rendering
17. 17. Levenberg-Marquardt algorithm  Most widely used algorithm for Nonlinear Least Squares Minimization.  First proposed by Levenberg, then improved by Marquardt  A blend of Gradient descent and Gauss-Newton iteration
18. 18. More Results Initialize to process
19. 19. THANK YOU ALL