1. EI 2006 - San Jose, CA Slide No. 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. EI 2006 - San Jose, CA Slide No. 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. EI 2006 - San Jose, CA Slide No. 3 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 Original Low-Res Image NN interpolationBilinear interpolation

4. EI 2006 - San Jose, CA Slide No. 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. EI 2006 - San Jose, CA Slide No. 5 1-D Nearest-neighbor and bilinear interpolation Rational resampling factor ( ) InterpolationDefinitionInterpolation filter Nearest-neighbor interpolation Bilinear interpolation

6. EI 2006 - San Jose, CA Slide No. 6 Basis for nearest-neighbor interpolation detection (RF=5) Periodic peaks in first-order difference image Peak intervals contain information about the RF applied Nearest-neighbor interpolated imagePeriodic peaks in |First-order difference| peak interval

7. EI 2006 - San Jose, CA Slide No. 7 Basis for bilinear interpolation detection (RF=5) Bilinear interpolated image First-order difference Periodic peaks in |Second-order difference| peak interval

8. EI 2006 - San Jose, CA Slide No. 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. EI 2006 - San Jose, CA Slide No. 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. EI 2006 - San Jose, CA Slide No. 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,… RF est = Average of detected peak intervals = 2.5 32323 Peak location Interpolated pixel Legend Second-order difference Peak APeak B 1 Peak B 2 Peak B 3

11. EI 2006 - San Jose, CA Slide No. 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 RF est

12. EI 2006 - San Jose, CA Slide No. 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. EI 2006 - San Jose, CA Slide No. 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. EI 2006 - San Jose, CA Slide No. 14 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 RF est =4.46 Histogram of detected peak intervals

15. EI 2006 - San Jose, CA Slide No. 15 Robustness evaluation (30 Images, 26 resampling factors) Test description Parameters for NN tests Parameters for BI tests No post-processing-- JPEG compression70% quality90% quality Sharpening (Unsharp Masking) same Digimarc’s watermarking (Level 4 is strongest) Level 3Level 1 Spread spectrum watermarking α=0.3 (not tested) Adobe Photoshop interpolaton + JPEG (not tested)10/12 quality

16. EI 2006 - San Jose, CA Slide No. 16 Test results (NN) Tolerance for estimation accuracy: 15% Reliable estimation for RF>1.5

17. EI 2006 - San Jose, CA Slide No. 17 Test results (NN with post-processing) Reliable estimation for RF>2

18. EI 2006 - San Jose, CA Slide No. 18 Test results (BI) Reliable estimation for RF>2

19. EI 2006 - San Jose, CA Slide No. 19 Test results (BI with post-processing) For (BI, JPEG): Reliable estimation for RF>2

20. EI 2006 - San Jose, CA Slide No. 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<RF est ≤3

21. EI 2006 - San Jose, CA Slide No. 21 Thank you for listening