7.1-5
BLIND WATERMARKING BASED ON WAVELET
SINGULARITY DETECTION
Jing-Wein Wang
National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan 807, R.O.C.
ABSTRACT
We present a novel blind watermarking method for copyright protection. Two distance measures are devised to genetically select the significant wavelet singularities for lossless and robust embedding. Then, forward and backward pair checksum generated from the embedded singularities is adopted to alternately correct the attacked image errors for blind retrieval.
INTRODUCTION
Watermarking has widely emerged for copyright protection. However, as the watermark modifies pixel values, the fidelity of the original image can be severely degraded. To circumvent the problem, the embedding process has to be lossless. Moreover, the scheme that can detect without the original images is more practical for a huge image database or when we do not know which copy is the original one [1]. Computer simulations demonstrate that the proposed method can effectively resist seven common image-processing attacks, and that it has a comparable performance to that of the related work [2].
THE ALGORITHMS
Singularity Detection:
We propose two filtering conditions, which are the minimum neighboring distance ratio and the 8-adjacency distance ratio, for searching the isolated wavelet singularity as follows.
1. Use a 3×3 template to locate wavelet extrema [3]
ce as a candidate of the singularity [3] cs.
2. Calculate the distances among ce and
8-adjacency pixels and then find out the minimum and maximum neighboring distances, respectively.
arg min
j e nb jp
=
c
−
c
,arg max
j e nb jq
=
c
−
c
,(1)where cnbj is the adjacency pixel around ce, j = 1,..,8.
We can obtain the minimum neighboring distance
ratio drmin, which is set to 0.1, by
e p nb c c
drmin = / . (2)
3. Normalize the sum of the ratio among the neighboring distance and the maximum neighboring distance.
∑
= − − = N j nb e nb e nb c c c c N dr j q 1 ) ( 1 , N = 8. (3) It is chosen that drnb ∈ (0.4, 0.6).Watermark Embedding (Fig. 1):
Step 1. An input image with size 512 × 512 is uniformly 4-level decomposed into subbands through D4 wavelet transformation [3].
Step 2. These subbands are sorted according to their energy importance.
Step 3. Set the sign value to each singularity according
to their polarity,
1,
( , ) 0
0,
( , ) 0
s s sc i j
p
c i j
>
⎧
= ⎨
<
⎩
. (4)Step 4. Divide the subband into subblocks with size 8 × 8.
Step 5. To search the adaptive subblocks which are robust to various attacks, we can select the significant ones by using the genetic algorithm for maximizing the fitness function via,
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
⋅
+
=
Total Selectedblock
block
FA
AA
AA
f
1
, (5)where AA is the accurate acceptance rate classying
both 1 → 1 and 0 → 0 signs, FA is the false acceptance rate classifying both 1 → 0 and 0 → 1
signs.
block
Selected is the selected subblock number andTotal
block
is the number of all subblocks. Generate theretrieval key key1 by cascading the watermarked
subblock number, the forward pair checksum (from left to right) string, and the backward pair checksum (from right to left) string as
j j j
ck
=
p
⊕
p
′,j
′ = +
(
j
1) mod
n
s, (6)where
ck
j is the singularity pair checksum of indexj
,j
=
1, 2,...,
n
s, andn
s is the singularity number of the subblock.Step 6. Generate the retrieval key key2 of mapping sign values to watermark symbols.
Step 7. Perform the inverse wavelet transform to get watermarked image.
Fig. 1. Watermark embedding.
Fig. 2. Blind watermark retrieval. Watermark Retrieval (Fig. 2):
Step 1. Repeat the same steps as embedding and locate
watermarked subblocks with the help of key1.
Step 2. Check the number of singularity for each subblock. Perform one of the following actions for integrity control: (a) Remove the redundant singularity with distance value nearest the filtering conditions (2) and (3); (b) Insert the sign into the suitable place according to the saved forward pair checksum while there is a short number on the retrieved singularities; (c) Examine the forward and backward pair checksums, respectively. Correct the attacked image
errors pixel-by-pixel by referring to key1 (Fig. 3) via
1
,
,
,
j j j j-1 j j jp if s
ck or s
ck
p
p otherwise
−≠
≠
⎧
′ = ⎨
⎩
(7),
j
=
1, 2,...,
n
s, wheres
j is the checksum beforemaking a correction, p′ is the sign value after j
correction, and pj is the inverse operation of the
original sign value pj.
Fig. 3. Sign value correction by using pair checksums. Step 3. Take only the examined values having the same sign both in the forward and backward correction processes and then perform exclusive OR operation
with key2 to retrieve the partial watermark symbols.
Step 4. Follow the neighboring sign values of the undetermined singularity to retrieve the residual watermark symbols cast in the subblock.
EXPERIMENTAL RESULTS
A stamp binary image as in [2] is taken to be the owner information. Genetic algorithms run with population size 20, generations 200, probability of crossover 0.5 and mutation probability 0.01. Fig. 4 shows the comparison results with and without (energy block sorting) genetic block selection using the image Lena. The results demonstrate that the proposed framework can effectively resist common image-processing attacks, and that it has a comparable performance with the related method [2].
Fig. 4. Stirmark 4.0 benchmark for the robust tests.
ACKNOWLEDGEMENT
This work was partially supported by NSC grant no. 95-2221-E-151-024.
REFERENCES
[1] B. Furht and D. Kirovski, Multimedia
watermarking techniques and applications,
Auerbach Publications, 2006.
[2] C.-S. Shieh, H.-C. Huang, F.-H. Wang, and J.-S. Pan, “Genetic watermarking based on
transform-domain techniques,” Pattern Recognition, vol. 37,
pp. 555-565, 2004.
[3] S. G. Mallat, A wavelet tour of signal processing,
2nd Ed., Academic Press, 1999.
Watermarke d Image DWT Singularity Detection Sign
Assignment Divided into Subblocks Singularity Integrity Retrieved Watermark Checksum and Correction XOR key2 key1 1 p p2 p3 p4 pns + + + + + + 1 s s2 s3 s4 sns−1 sns .... Forward Backward Original Image DWT Subband Sorting Singularity
Detection Assignment Sign Divided into Subblocks Checksum Generator IDWT Watermarked Image Secrete Key (key1, key2) Watermark XOR 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
LPF MF JPEG(QF=80) Bright Sharpen Blur Cropping(25%) Attacks N o rm al iz ed C or re la tio n With Selection Without Selection