2. 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

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

6. Editable

7. Sclable

8. Easy to animate

9. Other fields
 Cartoon drawing vectorization
 skeletonization, tracing and approximation
 Triangulation-based Method
 Object-based Vectorization
 Bezier patch
 subdivision

10. Image Vectorization Method
Optimized Gradient Meshes
 Jian Sun, Lin Liang, Fang Wen, Heung-Yeung Shum
 Siggraph 2007

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

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

13. Flow Chart Process
Original Initial Mesh Optimized Mesh Final Rendering

14. Mesh Initialization
Clear View

15. 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

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

17. Mesh Optimization
Optimaized
input image initial rendering final rendering

18. 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

19. More Results
Initialize to process

20. THANK YOU ALL