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Image Abstraction

This work addresses the challenge of simplifying complex scenes while maintaining crucial structures. We utilize Mean Curvature Flow (MCF) to smooth out curvature variations, enabling the drawing of isophotes and minimizing loss of detail in important features. The MCF evolution equation facilitates a refined approach, while techniques such as Shock Filtering and Laplacian-of-Gaussian help enhance edges. Integrating user inputs through Tangent Vector Fields (TVF) and layered maps allows for better control of feature directionality and structure preservation.

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Image Abstraction

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  1. Image Abstraction Chunsong Wang

  2. Image Abstraction: Main Problem • How to decrease the complexity of the scene while protecting important structures?

  3. Mean Curvature Flow • View Image I(x,y) as a height field, we are able to draw contours of the same color value(isophote). • Mean Curvature flow(MCF): Smooth the curvatures, high-curvature portion is smoothed faster

  4. MCF: Evolution Equation • Evolution Equation: • Where κ= local isophote curvature

  5. MCF: Evolution

  6. Shock Filtering • Edge Enhancement: • Filtering with Laplacian-of Gaussian function

  7. Constrained mean curvature flow • MCF+Shock filtering: still too aggressive • Tangent vector Field(TVF): denotes ‘desired’ feature direction

  8. CMCF: Evolution Equation • Evolution Equation: Where Where denotes the vector perpendicular to

  9. CMCF: Algorithm

  10. Incorporating user input

  11. Weighted Map

  12. Layered Map

  13. Layered Map

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