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Ariawan Suwendi Prof. Jan P. Allebach Purdue University - West Lafayette, IN

Nearest-neighbor and Bilinear Resampling Factor Estimation to Detect Blockiness or Blurriness of an Image*. Ariawan Suwendi Prof. Jan P. Allebach Purdue University - West Lafayette, IN. *Research supported by the Hewlett-Packard Company. Outline. Introduction

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Ariawan Suwendi Prof. Jan P. Allebach Purdue University - West Lafayette, IN

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  1. Nearest-neighbor and Bilinear Resampling Factor Estimation to Detect Blockiness or Blurriness of an Image* Ariawan Suwendi Prof. Jan P. Allebach Purdue University - West Lafayette, IN *Research supported by the Hewlett-Packard Company

  2. Outline • Introduction • 1-D Nearest-neighbor and bilinear interpolation • The basis for interpolation detection (RF>1) • Step-by-step illustration of the resampling factor estimation algorithm • Robustness evaluation • Conclusions

  3. Original Low-Res Image NN interpolation Bilinear interpolation Introduction • Nearest-neighbor and bilinear interpolation are widely used • Popescu and Farid (IEEE T-SP, 2005): Detect resampled images by analyzing statistical correlations • Not able to detect the resampling amount • Ineffective to some common post-processings

  4. Introduction (cont.) • How to detect and estimate resampling factor (RF) for nearest-neighbor and bilinear interpolation • Since both interpolations are separable, most of the things will be explained in 1-D space

  5. 1-D Nearest-neighbor and bilinear interpolation • Rational resampling factor ( )

  6. peak interval Basis for nearest-neighbor interpolation detection (RF=5) Nearest-neighbor interpolated image • Periodic peaks in first-order difference image • Peak intervals contain information about the RF applied Periodic peaks in |First-order difference|

  7. Basis for bilinear interpolation detection (RF=5) Bilinear interpolated image Periodic peaks in |Second-order difference| peak interval First-order difference

  8. Basis for interpolation detection • In nearest-neighbor interpolated images, the first-order difference image should contain peaks with peak intervals equal floor(RF) or ceil(RF) • In bilinear interpolated images, the second-order difference image should contain peaks with peak intervals equal floor(RF) or ceil(RF) • Resampling factor RF can be estimated as the average of the detected peak intervals • Smooth regions in the difference image do not provide a reliable reading of peak intervals and, hence, should be ignored

  9. Model for peak intervals in bilinear interpolation (RF=2.5) Uninterpolated pixel values: Interpolated pixel values: • Assume that the increment term (Δn) is uniformly distributed in [-255,255] • Periodic second-order difference coefficient sequence: 0,1,1,0,2,0,1,1,0,2,0,1,1,0,2,… one period

  10. Peak detection (RF=2.5) • Assignment of peak location for 4 possible peaks: • Peak intervals for the second-order diff. coeff. sequence: • 0,1,1,0,2, 0,1,1,0,2, 0,1,1,0,2,0,… • RFest = Average of detected peak intervals = 2.5 Second-order difference Legend Peak A Peak B1 Peak B2 Peak B3 Peak location Interpolated pixel 3 2 3 2 3

  11. Step-by-step illustration of vertical RF estimation for bilinear interpolation (RF=4.5) ? Image Interpolate by RF=4.5 JPEG-compression 90% quality Bilinear RF Estimation algorithm RFest

  12. Step-by-step illustration (cont.) • Step 1: Compute luminance plane using YCbCr model • Step 2: Compute |second difference image| • Step 3: Scale the difference image to [0,255] • Step 4: Apply the horizontal Sobel edge detection filter

  13. Step-by-step illustration (cont.) • Step 5: Dilate the edge map to get a mask • Smooth regions do not provide a reliable reading of peak intervals

  14. RFest=4.46 Step-by-step illustration (cont.) • Step 6: Mask the difference image, project, and average to get a 1-D projection array • Step 7: Detect peaks and measure peak intervals • Step 8: Use histogram to extract resampling factor • Step 9: Detect possible false alarms Histogram of detected peak intervals

  15. Robustness evaluation(30 Images, 26 resampling factors)

  16. Test results(NN) • Tolerance for estimation accuracy: 15% • Reliable estimation for RF>1.5

  17. Test results(NN with post-processing) • Reliable estimation for RF>2

  18. Test results(BI) • Reliable estimation for RF>2

  19. Test results(BI with post-processing) • For (BI, JPEG): Reliable estimation for RF>2

  20. Conclusions • The NN resampling factor estimation algorithm works well for RF>2 • It can withstand significant post-processing • The bilinear resampling factor estimation algorithm works well for RF>2 except in sharpening and watermarking tests • It can only withstand mild post-processing • One weakness is that bilinear interpolation with 1<RF<2 tends to be overestimated with 2<RFest≤3

  21. Thank you for listening

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