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Edge-Directed Image Interpolation

Edge-Directed Image Interpolation. Nickolaus Mueller, Yue Lu, and Minh N. Do. “In theory, there is no difference between theory and practice; In practice, there is.” -Chuck Reid. Outline of the Talk. Description of Problem Examples One-Dimensional Signals Two-Dimensional Images

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Edge-Directed Image Interpolation

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  1. Edge-Directed Image Interpolation • Nickolaus Mueller, Yue Lu, and Minh N. Do “In theory, there is no difference between theory and practice; In practice, there is.” -Chuck Reid

  2. Outline of the Talk • Description of Problem • Examples • One-Dimensional Signals • Two-Dimensional Images • State of the Art • Description of Methods • Results • Wavelet Algorithms • Regularity Preserving Image Interpolation • Proposed Method using Contourlets

  3. Basic Image Interpolation • Given a low-resolution image, increase resolution by a factor of 2 or larger

  4. Description of Problem • Problem: Basic interpolation techniques cause “jagged” or “blurred” edges • Goal: Reduce artifacts using edge information • Simple image model: continuous, smooth objects piecewise continuous, smooth edges

  5. Examples of Edge Artifacts Original Original Original Bilinear Bilinear Bicubic

  6. One-Dimensional Problem

  7. Images: A More Difficult Task • 2-D Edges - Magnitude and directional component • Edges have “Geometric Regularity” • Challenge: Estimate orientation so that edges are both sharp and free from artifacts.

  8. State of the Art Methods • Sub-pixel Edge Localization • Kris Jensen and Dimitris Anastassiou, 1995 • New Edge Directed Interpolation • Xin Li and Michael T. Orchard, 2001 • Canny Edge Based Interpolation • Hongjian Shi and Rabab Ward, 2002 • Data-Dependent Triangulation • Dan Su and Phillip Willis, 2004 • Edge-Guided Interpolation • Lei Zhang and Xiaolin Wu, 2006

  9. Sub-pixel Edge Localization • Explicitly calculate edges in 3 x 3 window of image • Ideal step edge assumption • Calculating the parameters: • Develop continuous space theory - projections onto an orthonormal basis • Use discrete approximations to inner products. A B

  10. New Edge-Directed Interpolation • Classical Wiener theory to develop MMSE weighting scheme for interpolation • Estimate high resolution covariances from low resolution image. • y is the data vector, C is a matrix used to estimate the high resolution covariance matrix Dark Pixels: Low Resolution Lattice Red Pixel: Pixel to be Interpolated in Step 1 Green Pixels: Pixels Interpolated in Step 2

  11. Canny Edge Based Expansion • First, expand image using bilinear or bicubic interpolation • Run Canny edge detector on expanded image • Determine if magnitude of gradient is larger vertically or horizontally at each edge pixel • Modify pixels on either side of edge in vertical or horizontal direction

  12. Data-Dependent Triangulation • For each set of four low resolution pixels, estimate edge as dividing pixels into two triangles • Create an image mesh which stores the direction of each edge • Use linear interpolation within triangles Image Mesh

  13. Edge Guided Image Interpolation • More general triangulation technique • Use directional variances to produce weighting scheme • Perform interpolation using both triangles, fuse with weighting scheme

  14. Comparison of Methods Original Bilinear Sub-pixel Edge Loc. NEDI Canny Edge Based DDT

  15. Comparison of Methods Original Bilinear Sub-pixel Edge Loc. NEDI Canny Edge Based DDT

  16. Comparison of Methods Original Bilinear Sub-pixel Edge Loc. NEDI Canny Edge Based DDT

  17. Factor of Four Interpolation Original Bilinear NEDI Canny Edge Based DDT

  18. Lena Lena Gaussian Disc Gaussian Disc Bilinear 32.42 39.58 Bilinear 0.287 0.314 SEL 33.09 46.04 NEDI 37.37 42.76 SEL 2.047 3.026 Canny 37.29 40.37 DDT 37.42 41.68 NEDI 42.5 36.1 Edge Guided 37.37 41.68 Canny 1.386 1.299 DDT 0.945 0.982 Edge Guided 1.124 1.230 Algorithm Comparison Speed in Seconds PSNR

  19. Regularity Preserving Image Interpolation • High similarity between different wavelet scales in regions of low regularity • Convergence of series of features across scales for edge detection • Goal: Synthesize a new sub-band by extrapolating from rate of decay of features across known sub-bands • Apply algorithm separably along rows and columns

  20. Regularity Preserving Image Interpolation

  21. Take Home Message • Higher cost methods can result in significant improvement • Still room for improvement using low-cost algorithms • Current wavelet techniques still have room for improvement • Proposed Method: Edge-Directed Interpolation using Multiscale Geometric Representations • Questions?

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