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

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


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


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 interpolation Bilinear interpolation


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


1-D Nearest-neighbor and bilinear interpolation

Rational resampling factor ( )

Number of interpolated pixels - 1RF

Number of original pixels - 1

Interpolation Definition Interpolation filter

Nearest-neighbor

interpolation

Bilinear interpolation

1

L L

2[ ]h n

n

1

L

2

L

2

L

1[ ]h n

n

1

1

[ ] [ ]* [ ].

1[ ] for ,

2 2 0 otherwise.

g n f n h n

L Lh n n

L

2

2

[ ] [ ]* [ ].

[ ] 1 for ,

0 otherwise.

g n f n h n

nh n n L

L

ARF =

B


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 image Periodic peaks in |First-order difference|

peakinterval


Basis for bilinear interpolation detection (RF=5)

Bilinear interpolated image

First-order difference

Periodic peaks in |Second-order difference|

peakinterval


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


Model for peak intervals in bilinear interpolation (RF=2.5)

, 1, 1 2, ...

2 4 1 3, 1, 1, 1 2, 1 2, 1 2, ...

5 5 5 5

S S S

S S S S S S

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


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

3 2 3 2 3

Peak location

Interpolated pixel

LegendSecond-order difference

Peak A Peak B1 Peak B2 Peak B3


Step-by-step illustration of vertical RF estimation for bilinear interpolation

(RF=4.5)

?Image

Interpolateby RF=4.5

JPEG-compression90% quality

Bilinear RFEstimationalgorithm

RFest


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

Vertical edge map

200 400 600 800 1000 1200

100

200

300

400

500

600

700

800



Step 5: Dilate the edge map to get a mask

Smooth regions do not provide a reliable reading of peak intervals

Vertical edge mask

200 400 600 800 1000 1200

100

200

300

400

500

600

700

800



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

1 2 3 4 5 6 7 8 9 100

20

40

60

80

Peak intervals

RFest=4.46

Histogram of detected peak intervals


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 4 is strongest)

Level 3 Level 1

Spread spectrum

watermarking

α=0.3 (not tested)

Adobe Photoshop

interpolaton + JPEG

(not tested) 10/12 quality


Test results(NN)

Tolerance for estimation accuracy: 15%

Reliable estimation for RF>1.5


Test results(NN with post-processing)

Reliable estimation for RF>2


Test results(BI)

Reliable estimation for RF>2


Test results(BI with post-processing)

For (BI, JPEG): Reliable estimation for RF>2


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


Thank you for listening

Documents

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