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Soft Edge Smoothness Prior for Alpha Channel Super Resolution

Soft Edge Smoothness Prior for Alpha Channel Super Resolution. Shengyang Dai 1 , Mei Han 2 , Wei Xu 2 , Ying Wu 1 , Yihong Gong 2. EECS Department, Northwestern University, Evanston, IL NEC Laboratories America, Inc., Cupertino, CA. Prior is needed. Minimize the reconstruction error

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Soft Edge Smoothness Prior for Alpha Channel Super Resolution

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  1. Soft Edge Smoothness Prior for Alpha Channel Super Resolution Shengyang Dai1, Mei Han2, Wei Xu2, Ying Wu1, Yihong Gong2 • EECS Department, Northwestern University, Evanston, IL • NEC Laboratories America, Inc., Cupertino, CA

  2. Prior is needed • Minimize the reconstruction error • Degraded HR → LR input • Efficient solution by Back-projection (Irani’93) • However … • SR is under-determined (Baker&Kanade’02, Lin&Shum’04) • Image prior is needed for regularization

  3. What kind of prior? LR input Back-projection Bicubic interpolation Smooth edges are preferred

  4. What kind of smoothness? Hard edge vs. Soft edge binary value real value LR input Hard + Smooth Soft + Smooth Soft smoothness is preferred

  5. Questions • How to describe an edge? • How to obtain a soft smooth edge? Our solutions • Alpha channel edge description • Soft edge smoothness prior

  6. Questions • How to describe an edge? • How to obtain a soft smooth edge? Our solutions • Alpha channel edge description • Soft edge smoothness prior

  7. Alpha matting alpha matting - 1 + Image synthesis A closed form solution with smoothness assumption (Levin etc. ’06)

  8. Matting for SR HR patches alpha matting synthesis convolution down-sampling LR patches

  9. Matting for SR HR patches alpha matting synthesis SR? SR Bicubic Bicubic synthesis alpha matting convolution down-sampling LR patches

  10. Matting for SR ? SR

  11. Questions • How to describe an edge? • How to obtain a soft smooth edge? Our solutions • Alpha channel edge description • Soft edge smoothness prior

  12. Objective Regularity term prefers soft smooth edge Geocut Our method Hard edge Soft edge

  13. Objective Geocut Our method Hard edge Soft edge

  14. Pixel neighborhood

  15. Image grid graph

  16. Hard edge smoothness Geocut (Boykov&Kolmogorov’03) Curve C Cut metric: 1 0 : Binary indication function on grid : Neighborhood order of the image grid : Edge weight of the grid graph : Set of the pixels pairs of order k

  17. Hard edge smoothness • A regularity term prefers hard smooth edge • Application • Segmentation problem • Reducing the metrication artifact Cut metric Euclidean length

  18. Objective Geocut Our method Hard edge Soft edge

  19. Soft edge smoothness Level lines Soft edge Soft edge is equivalent to a set of image level lines

  20. Soft edge smoothness Geocut Our method Binary indication function Real-valued function Soft cut metric Cut metric

  21. Soft edge smoothness • A regularity term prefers soft smooth edge • Application • Super resolution • Reducing the jaggy effect

  22. … For SR • Objective function • Efficient optimization by steepest descent • Critical parameters • Two options • Alpha channel SR for each edge segment • Color channels SR over entire image

  23. …… Effect of Image size Zoom factor only upper plane is shown

  24. Effect of Back-projection Note: color channels are processed separately

  25. Color channels SR LR input Our result Bicubic interpolation

  26. Color channels vs. alpha channel Color channels SR on the entire image Alpha channel SR on edge segments

  27. Alpha channel SR Corner detection (He etc. 04) Process each edge segment separately

  28. Comparison Bicubic Our method Back-projection

  29. Comparison – reconstruction based Bicubic Our method Back-projection

  30. Comparison – exemplar based Our method Learning low level vision Neighbor embedding (courtesy to Bill Freeman) (courtesy to Dit-Yan Yeung)

  31. Conclusion • Soft smoothness prior • With specific geometric explanation • Applicable to super resolution • Alpha channel super resolution • Limitation • The smoothness prior may not hold for texture

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