N Color Depth

Color depth describes the number of possible colors in a digital image. For example a PGM image can have the possible color depths:

                                                       Bit Depth , Color Depth
                                                           1 bits           2
                                                           2 bits           4
                                                           3 bits           8
                                                           4 bits         16
                                                           5 bits         32
                                                           6 bits         64
                                                           7 bits         128
                                                           8 bits         256

The following results were obtained from varying color depth within the above bound using Ifranview.

Figure #4: Xie N Color Depth

Figure #5: Cox N Color Depth

Figure #6: 256 and 2 Color Depth Images

From the above results we see that both algorithms give excellent correlation with little change until the image has a color depth of 2. Cox's algorithm gives a correlation of about 0.5 where as Xie's gives a correlation of 0 for when the color depth is 2.

JPEG Compression

The `Joint Photographic Experts Group' (JPEG) compression algorithm works by reducing the amount of information contained in an image. JPEG uses the Discrete Cosine Transform to compress the image. JPEG compression was applied to the smoking lady image with quality factor ranging from 90 to 10. As noted by the authors of Stirmark, most existing algorithms breakdown towards a quality factor of 50, but most images still look fine at 30. For a quality factor of 10 most pictures look pixilated and loss of image quality is quite noticeable.

Figure #7: Xie JPEG Compression

Figure #8: Cox JPEG Compresion

Figure #9: JPEG Compression with Quality Factors 90 and 10

Both algorithms are robust against JPEG compression with Xie's correlations varying more than Cox's for the image tested. For this image it appears as though Cox was correct in assuming that if the watermark is stored in the most significant coefficients of the DCT that the watermark will not be lost during JPEG compression.

Image Cropping

Cropping a watermarked image is another way of attacking the watermark and can make it unrecognizable. Cropping a watermarked image can remove the majority of the watermark or make the extraction process invalid depending on the algorithm. The smoking lady image was center cropped for the following percentages: 1, 2, 5, 10, 15, 20, 25, 50 and 75.

Figure #10: Xie Image Cropping

Figure #11: Cox Image Cropping

Figure #12: 1% and 75% Center Cropped Image

As can be seen from the above results cropping attacks are a very effective way to destroy the watermark for both algorithms. The Xie's watermark is destroyed with a 1% crop to the image. The majority of the watermark is still embedded in the image but the cropping affects the reconstruction point for extracting the watermark. This was found to be the best and easiest attack for destroying the recovery of the Xie watermark. The Cox watermark faired a bit better than the Xie watermark but not by much. A greater than 15% crop to the image destroys the Cox watermark making it recoverable with a correlation of less than 0.2, which is less than satisfactory. For this picture the majority of the watermark was embedded in the background so as the image is cropped more and more of the watermark is lost. This explains why we get such a low correlation when the image is cropped down to her face. Both algorithms perform undesirably when the watermarked image is cropped. Depending on the image watermarked the Cox algorithm may perform better. The Xie algorithm is found to be unsuitable when cropped for all images because of its extraction method.