Rotation with Cropping Not Kept to Scale

Images used for this test were generated with Stirmark and are much like that used for the testing in the section above. The image is rotated followed by cropping and then randomly scaled. The rotated angles are the same as in the test above: 5, 10, 15, 30, 45, and 90.

Figure #21: Xie Rotation with Cropping and Random Scale


Figure #22: Cox Rotation with Cropping and Random Scale

Figure #23: 10 and 90 Degree Rotation with Cropping and Random Scale

Results are similar to that of rotation with cropping kept to scale as should be expected.


General Linear Geometric Transformation

A general linear geometric transformation was applied to the watermarked images with Stirmark according to the following formula:

|x'| = |a b| |x|
|y'| |c d| |y|

with the following parameters:

(a, b, c, d) = (1.010, 0.013, 0.009, 1.011)
(1.007, 0.010, 0.010, 1.012)
(1.013, 0.008, 0.011, 1.008)

The following results were obtained:

                                 Xie Linear Geometric Transformation
                                   a         b           c          d             Correlation
                              1.007      0.01        0.01      1.012            0.055556
                              1.01        0.013      0.009    1.011             0.062131
                              1.013      0.008       0.011   1.008            0.069444
                                Cox Linear Geometric Transformation
                                   a         b            c          d            Correlation
                               1.007      0.01        0.01     1.012            0.564686
                               1.01        0.013      0.009   1.011            0.522842
                               1.013      0.008      0.011   1.008            0.602232 

Symmetric and Asymmetric Column and Row Removal

The images for this test were generated with Stirmark. The following images were generated: (1,1), (1, 5), (5, 1), (5, 17), (17, 5) where the first component is the number of columns removed and the second is the number of rows. The following X values on the graphs correspond to:

Row Column X points
1 1 1
1 5 2
17 5 3
5 1 4
5 17 5

Figure #24: Xie Row and Column Removal


Figure #25: Cox Row and Column Removal

Shearing

Stirmark was used to shear the images tested. Symmetric and asymmetric shearing in the X and/or Y direction was done as follows: (0, 1), (0, 5) (1, 0), (5, 0), (1, 1) and (5, 5). The first component is the shift in X direction (% of width) and the second is the shift in the Y direction (% of height). The following results were obtained:


Figure #26: Xie Image Shearing


Figure #27: Cox Image Shearing

 


Re-watermarking Watermarked Image

If an attacker has knowledge of watermarking algorithm used they may try to re-watermark the image to attack the watermark. Different watermarks were embedded in the image "overtop" of the original and then the original was extracted and correlated. This was the only malicious attack tested and the results are as follows:


Xie Re-watermarking
Re-watermarking # Correlation
1 -0.291667
2 -0.180556

Cox Re-watermarking
Re-watermarking Correlation
1 0.736621
2 0.58651
3 0.534329
4 0.443726
5 0.432266
6 0.42009

From above results re-watermarking an image with the Xie watermark completely destroys the original watermark. The most recent embedded watermark still gives a high correlation because it rearranges and manipulates the bits according to the new watermark hence overwriting the old watermark. Re-watermarking an original Cox watermarked image degrades the watermark correlation but is still satisfactory. As can be seen above we still get a decent correlation even after the sixth time the image has been re-watermarked. After six times watermarked the watermark is very noticeable and the image has been visually degraded as can be seen below.


Figure #28: Cox Re-watermarked 1 and 6 Times

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