Vectorization

Presented byMd. Solaiman sikder

Amit KumarMd.Shariful Islam

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

Image VectorizationGoal

convert a raster image into a vector graphics

vector graphics includepointslinescurvespolygons

Why Vector GraphicsCompactScalableEditableEasy to animate

Compact

input raster image

37.5KB

optimized gradient mesh

7.7KB

Editable

Sclable

Easy to animate

Other fieldsCartoon drawing vectorization

skeletonization, tracing and approximationTriangulation-based MethodObject-based Vectorization

Bezier patchsubdivision

Image Vectorization MethodOptimized Gradient Meshes

Jian Sun, Lin Liang, Fang Wen, Heung-Yeung Shum

Siggraph 2007

Surface RepresentationA tensor product patch is defined as

Bezier bicubic, rational biquadratic, B-splines…control points lying outside the surface

Gradient MeshControl Point Attributes:

2D positiongeometry derivativesRGB colorcolor derivatives

Flow ChartProcess

Original Initial Mesh Optimized Mesh Final Rendering

Mesh InitializationClear View

Mesh InitializationDecompose image into sub-objectsDivide the boundary into four segmentsFitting segments by cubic Bezier splinesRefine the mesh-lines

evenly distributedinteractive placement

Mesh OptimizationTo minimize the energy function

P: number of patches

Mesh OptimizationOptimaized

input image initial rendering

final rendering

Levenberg-Marquardt algorithmMost widely used algorithm for Nonlinear

Least Squares Minimization.First proposed by Levenberg, then improved

by MarquardtA blend of Gradient descent and Gauss-

Newton iteration

More ResultsInitialize to process

THANK YOU ALL