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!