image vectorization cai qingzhong 2007/11/01. what is vectorization?
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Image Vectorization
Cai Qingzhong2007/11/01
What is Vectorization?
Image Vectorization Goal
convert a raster image into a vector graphics
vector graphics include points lines curves polygons …
Why Vector Graphics
Compact Scalable Editable Easy to animate
Compact
input raster image
37.5KB
optimized gradient mesh
7.7KB
Why Vector Graphics
Compact Scalable Editable Easy to animate
Scalable
original image
vector form bicubic interpolation
Why Vector Graphics
Compact Scalable Editable Easy to animate
Editable
Why Vector Graphics
Compact Scalable Editable Easy to animate
Easy to animate
Related Work
Cartoon drawing vectorization skeletonization, tracing and
approximation Triangulation-based Method Object-based Vectorization
Bezier patch subdivision
Image Vectorization using Optimized Gradient Meshes
Jian Sun, Lin Liang, Fang Wen, Heung-Yeung ShumSiggraph 2007
About the author --- Jian Sun Lead Researcher, Visual
Computing Group, Microsoft Research Asia
Research interests in stereo matching interactive computer
vision computational
photography
Surface Representation
A tensor product patch is defined as
Bezier bicubic, rational biquadratic, B-splines… control points lying outside the surface
( , ) ( ) ( )Tm u v F u QF v
Ferguson Patch
( , ) T Tm u v UCQC V0 2 0 2
1 3 1 3
0 2 0 2
1 3 1 3
v v
v v
u u uv uv
u u uv uv
m m m m
m m m mQ
m m m m
m m m m
1 0 0 0
0 0 1 0
3 3 2 1
2 2 1 1
C
2 31U u u u 2 31V v v v
Gradient Mesh
Control Point Attributes: 2D position geometry derivatives RGB color color derivatives
( , ) f T Tf u v UCQ C V
Flow Chart
Original Initial Mesh Optimized Mesh Final Rendering
Mesh Initialization
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
Mesh Optimization
input image initial rendering final rendering
Mesh Optimization
To minimize the energy function
P: number of patches
2
1 ,
( ) ( ( , )) ( , )P
p pp u v
E M I m u v f u v
Levenberg-Marquardt algorithm Most widely used algorithm for Nonlin
ear Least Squares Minimization. First proposed by Levenberg, then im
proved by Marquardt A blend of Gradient descent and Gaus
s-Newton iteration
Smoothness
Smoothness Constraint
Add a smoothness term into the energy
which minimizes the second-order finite difference.
'
2
1 ,
2
( ) ( )
{ ( , ) 2 ( , ) ( , )
( , ) 2 ( , ) ( , ) }
P
p s t
E M E M
m s s t m s t m s s t
m s t t m s t m s t t
Vector line guided optimized gradient mesh
Vector line guided optimized gradient mesh
Given vector fields Vu and Vv, we optimize
2'' '
1 ,
2
( , )( ) ( ) { ( ( , )) , ( ( , ))
( , )( ( , )) , ( ( , ))
P
u up u v
v v
m u vE M E M w m u v V m u v
u
m u vw m u v V m u v
v
More Results
More Results
THE END.Thank you!