Image Vectorization Cai Qingzhong 2007/11/01.

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Presentation transcript:

Image Vectorization Cai Qingzhong 2007/11/01

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

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

Why Vector Graphics Compact Scalable Editable Easy to animate

bicubic interpolation 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 Triangulation-based Method 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 Shum Siggraph 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

Ferguson Patch

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

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

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

Smoothness

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

Vector line guided optimized gradient mesh

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

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THE END. Thank you!