6. RESULTS
The above scheme of fragile watermarking based on wavelet has been implemented and the original image and watermarked image is shown in Fig 4 and Fig 5. It can be seen that there is almost no perceptual difference between the two. To assess the extent of tampering, the following function which is called the tamper assessment function (TAF) is calculated:

where w is the true author watermark, w is the extracted mark, and Nw is the length of the watermark. The value of TAF ranges between zero and one. The presence of tampering is determined if TAF(w,w)≥, where 0 ≤ ≤ 1 a pre-specified threshold. If TAF(w,w)< , then the modifications on the image is considered to be negligible.

An averaging attack on the watermarked image using a 2-D 3×3 filter was simulated. The function of an averaging attack using a 3×3 filter is to place average value of the 8 adjacent pixel at the central pixel if the grid.

Fig 5 Watermarked image

Fig 6 Tampered image by filtering attack on the watermarked image using a 3 × 3-averaging filter

The resultant image is shown in Fig 6.Wavelet based watermark detection scheme was applied on this filtered image for the detection of tampering in the images and TAF(w,w) was found to be higher than the threshold . Different size of the filter was chosen. The choice of threshold τ is very important and if it is set to be very low then it will detect the distortion by compression as well, however, a higher threshold will lower the sensitivity of tamper detection process. Table 1 and 2 shows the value of the TAF for average filtering and JPEG compression.
Except for the averaging filter of 1×1 size that amounts to no change in the image, for all the other values TAF is close to 0.5. Thus a threshold of 0.2 was set for the tamper detection, which successfully detected even the small JPEG compression in the image.