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Image Processing and Reconstructions Tools

Explore gradient domain operations, tone mapping, fusion, and more for image processing. Learn about graph cuts, segmentation, denoising, and filters to enhance image quality.

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Image Processing and Reconstructions Tools

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  1. Image Processing and Reconstructions Tools Ramesh Raskar Mitsubishi Electric Research Labs Cambridge, MA

  2. Image Tools • Gradient domain operations, • Tone mapping, fusion and matting • Graph cuts, • Segmentation and mosaicing • Bilateral and Trilateral filters, • Denoising, image enhancement

  3. Intensity Gradient in 1D Intensity Gradient 105 105 1 1 I(x) G(x) Gradient at x,G(x) = I(x+1)- I(x)Forward Difference

  4. Reconstruction from Gradients Gradient Intensity 105 105 ? ? 1 1 G(x) I(x) For n intensity values, about n gradients

  5. Reconstruction from Gradients Gradient Intensity 105 105 ? 1 1 G(x) I(x) 1D Integration I(x) = I(x-1) + G(x) Cumulative sum

  6. Intensity Gradient in 2D Gradient at x,y as Forward Differences Gx(x,y) = I(x+1 , y)- I(x,y) Gy(x,y) = I(x , y+1)- I(x,y) G(x,y) = (Gx , Gy) Grad X Grad Y

  7. Intensity Gradient Vectors in Images Gradient Vector

  8. Image Intensity Gradients in 2D Sanity Check: Recovering Original Image 2D Integration Grad X Solve Poisson Equation, 2D linear system Grad Y

  9. Intensity Gradient Manipulation A Common Pipeline 2D Integration Grad X New Grad X Gradient Processing New Grad Y Grad Y Modify Gradients

  10. Graph and Images Credits: Jianbo Shi

  11. Agrawala et al, Digital Photomontage, Siggraph 2004

  12. Source images Brush strokes Computed labeling Composite

  13. i Wij j Wij Segmentation = Graph partition V: graph node E: edges connection nodes Wij: Edge weight Image pixel Link to neighboring pixels Pixel similarity

  14. Minimum Cost Cuts in a graph Cut: Set of edges whose removal makes a graph disconnected Si,j : Similarity between pixel i and pixel j Cost of a cut, A A

  15. Graph Cuts for Segmentation and Mosaicing Cut ~ String on a height field Brush strokes Computed labeling

  16. Bilateral Filtering Gaussian Smoothing Input Log(Intensity) Bilateral Smoothing [Ben Weiss, Siggraph 2006]

  17. Start with Gaussian filtering • Here, input is a step function + noise output input

  18. Start with Gaussian filtering • Spatial Gaussian f output input

  19. Start with Gaussian filtering • Output is blurred output input

  20. Gaussian filter as weighted average • Weight of x depends on distance to x output input

  21. The problem of edges • Here, “pollutes” our estimate J(x) • It is too different output input

  22. Principle of Bilateral filtering [Tomasi and Manduchi 1998] • Penalty g on the intensity difference output input

  23. Bilateral filtering [Tomasi and Manduchi 1998] • Spatial Gaussian f output input

  24. Bilateral filtering [Tomasi and Manduchi 1998] • Spatial Gaussian f • Gaussian g on the intensity difference output input

  25. [Tomasi and Manduchi 1998] • The weights are different for each output pixel output input

  26. Bilateral filtering is non-linear [Tomasi and Manduchi 1998] • The weights are different for each output pixel output input

  27. Bilateral Filtering • Unilateral filtering • Smoothing using filtering • Bilateral filtering • Edge-preserving smoothing Gaussian Smoothing Input Log(Intensity) Bilateral Smoothing [Ben Weiss, Siggraph 2006]

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