1. IMAGE UPSAMPLING VIA IMPOSED EDGE STATISTICS Raanan Fattal. ACM Siggraph 2007 Presenter: 이성호

2. Previous work Classical approach  Nearest-Neighbor, Bilinear, Bicubic, Hann, Hamming, and Lanczos interpolation kernels.  assumption that the image data is either spatially smooth or band-limited

3. More sophisticated methods  [Su and Willis 2004]  Reduce the number of variables that are averaged  forms a noticeable block-like effect BicubicSu and Willis 2004

4. [Li and Orchard 2001]  Arbitrary edge orientation is implicitly matched  By estimating local intensity covariance from the low-resolution image  Generating smooth curves and of reducing jaggies  Not sharp edges

5. [Hertzmann et al. 2001]  Image Analogies

6. [Freeman et al. 2002]  adding high-frequency patches  from a non-parametric set of examples relating low and high resolutions  Sharpens edges and yields images with a detailed appearance  tends to introduce some irregularities into the constructed image

7. [Osher et al. 2003]  invert a blurring process  measures the L 1 norm of the output image

8. Assumptions on image upsampling  different upsampling techniques correspond to different assumptions:  images are smooth enough to be adequately approximated by polynomials yields analytic polynomial-interpolation formulas  images are limited in band yields a different family of low-pass filters  these assumptions are highly inaccurate  suffer from excessive blurriness and the other visual artifacts

9. Edge-Frame Continuity Moduli  predict the spatial intensity differences  at the high-resolution based on the low-resolution input image

10. Approach  Statistics of intensity differences  intensity conservation constraint  we discuss only gray scale images  later extend to handle color images

11. Derivatives

12. Image statistics

14. edge-frame continuity modulus (EFCM)

16. Upsampling using the EFCM

17. Gauss-Markov Random Field model

18. Color images  First we upsample the luminance channel  of the YUV color space  compute the absolute value of its luminance difference d1d2 d3d4

19. Results High-res originalDownsampled

20. BilinearOurs

21. Simple Edge SensitiveNew Edge-Directed

22. magnified by a factor of 4

26. magnified by a factor of 8

29. magnified by a factor of 16

31. objective error measurements between an upsampled image and the original ground-truth image (i.e., before downsampling). Structural Similarity Image Quality (SSIQ) described in [Wang et al. 2004]

32. Implementations  implemented in C++  Mobile Pentium-M, running at 2.1MHz  Upsample an image of 128 2 pixels  to twice its resolution (256 2 ).  2 seconds  To a resolution of 1024 2 pixels  22 seconds.

33. Conclusions  Drawbacks:  Emphasize lack of texture and absence of fine-details  The jaggies artifact  Acutely twisted edges  involves more computations than some of the existing techniques  generic behavior of edges does not accurately describe every particular case.  Further improve  Using higher-order edge properties Such as curvature

35. Numerical analysis on EFCM upsampling Appendix

36. Lagrange multipliers

37. Apply to the formula in this paper  Solve this linear system  with Conjugate Gradient-based Null Space method