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 EI 2006 - San Jose, CA Slide No. 1
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 EI 2006 - San Jose, CA Slide No. 2
Introduction Original Low-Res Image NN interpolation Bilinear interpolation 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 EI 2006 - San Jose, CA Slide No. 3
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 EI 2006 - San Jose, CA Slide No. 4
1-D Nearest-neighbor and bilinear interpolation Interpolation Definition Interpolation filter Nearest-neighbor interpolation Bilinear interpolation Rational resampling factor ( ) EI 2006 - San Jose, CA Slide No. 5
Basis for nearest-neighbor interpolation detection (RF=5) Nearest-neighbor interpolated image Periodic peaks in First-order difference peak interval Periodic peaks in first-order difference image Peak intervals contain information about the RF applied EI 2006 - San Jose, CA Slide No. 6
Basis for bilinear interpolation detection (RF=5) Bilinear interpolated image Periodic peaks in Second-order difference First-order difference peak interval EI 2006 - San Jose, CA Slide No. 7
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 EI 2006 - San Jose, CA Slide No. 8
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 EI 2006 - San Jose, CA Slide No. 9
Peak detection (RF=2.5) Assignment of peak location for 4 possible peaks: Second-order difference Peak A Peak B 1 Peak B 2 Peak B 3 Legend Peak location Interpolated pixel 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, 3 2 3 2 3 RF est = Average of detected peak intervals = 2.5 EI 2006 - San Jose, CA Slide No. 10
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 EI 2006 - San Jose, CA Slide No. 11
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 EI 2006 - San Jose, CA Slide No. 12
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 EI 2006 - San Jose, CA Slide No. 13
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 Histogram of detected peak intervals RF est =4.46 Step 9: Detect possible false alarms EI 2006 - San Jose, CA Slide No. 14
Robustness evaluation (30 Images, 26 resampling factors) Test description Parameters for NN tests Parameters for BI tests No post-processing - - JPEG compression 70% quality 90% quality Sharpening (Unsharp Masking) same same Digimarc s watermarking Level 3 Level 1 (Level 4 is strongest) Spread spectrum watermarking Adobe Photoshop interpolaton + JPEG α=0.3 (not tested) (not tested) 10/12 quality EI 2006 - San Jose, CA Slide No. 15
Test results (NN) Tolerance for estimation accuracy: 15% Reliable estimation for RF>1.5 EI 2006 - San Jose, CA Slide No. 16
Test results (NN with post-processing) Reliable estimation for RF>2 EI 2006 - San Jose, CA Slide No. 17
Test results (BI) Reliable estimation for RF>2 EI 2006 - San Jose, CA Slide No. 18
Test results (BI with post-processing) For (BI, JPEG): Reliable estimation for RF>2 EI 2006 - San Jose, CA Slide No. 19
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 EI 2006 - San Jose, CA Slide No. 20
Thank you for listening EI 2006 - San Jose, CA Slide No. 21