1. Image Vectorization
Cai Qingzhong
2007/11/01

2. What is Vectorization?

3. Image Vectorization Goal convert a raster image into a vector graphics
vector graphics include
points
lines
curves
polygons …

4. Why Vector Graphics
Compact
Scalable
Editable
Easy to animate

5. optimized gradient mesh
Compact
input raster image
37.5KB
optimized gradient mesh
7.7KB

6. Why Vector Graphics
Compact
Scalable
Editable
Easy to animate

7. bicubic interpolation
Scalable
original image
vector form
bicubic interpolation

8. Why Vector Graphics
Compact
Scalable
Editable
Easy to animate

9. Editable

10. Why Vector Graphics
Compact
Scalable
Editable
Easy to animate

11. Easy to animate

12. Related Work Cartoon drawing vectorization Triangulation-based Method
skeletonization, tracing and approximation
Triangulation-based Method
Object-based Vectorization
Bezier patch
subdivision

13. Image Vectorization using Optimized Gradient Meshes
Jian Sun, Lin Liang, Fang Wen, Heung-Yeung Shum
Siggraph 2007

14. About the author --- Jian Sun
Lead Researcher, Visual Computing Group, Microsoft Research Asia
Research interests in
stereo matching
interactive computer vision
computational photography

15. Surface Representation
A tensor product patch is defined as
Bezier bicubic, rational biquadratic, B-splines…
control points lying outside the surface

16. Ferguson Patch

17. Gradient Mesh Control Point Attributes: 2D position
geometry derivatives
RGB color
color derivatives

18. Flow Chart
Original
Initial Mesh
Optimized Mesh
Final Rendering

19. Mesh Initialization

20. 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

21. Mesh Optimization
input image
initial rendering
final rendering

22. Mesh Optimization
To minimize the energy function
P: number of patches

23. 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

24. Smoothness

25. Smoothness Constraint
Add a smoothness term into the energy
which minimizes the second-order finite difference.

26. Vector line guided optimized gradient mesh

27. Vector line guided optimized gradient mesh
Given vector fields Vu and Vv, we optimize

28. More Results

29. More Results

30. THE END.
Thank you!