Local distortion resistant image watermarking relying on salient feature extraction
 Athanasios Nikolaidis^{1}Email author
https://doi.org/10.1186/16876180201297
© Nikolaidis; licensee Springer. 2012
Received: 19 October 2011
Accepted: 2 May 2012
Published: 2 May 2012
Abstract
The purpose of this article is to present a novel method for region based image watermarking that can tolerate local image distortions to a substantially greater extent than existing methods. The first stage of the method relies on computing a normalized version of the original image using image moments. The next step is to extract a set of feature points that will act as centers of the watermark embedding areas. Four different existing feature extraction techniques are tested: Radial Symmetry Transform (RST), scaleinvariant feature transform (SIFT), speeded up robust features (SURF) and features from accelerated segment test (FAST). Instead of embedding the watermark in the DCT domain of the normalized image, we follow the equivalent procedure of first performing the inverse DCT of the original watermark, inversely normalizing it and finally embedding it in the original image. This is done in order to minimize image distortion imposed by inversely normalizing the normalized image to obtain the original. The detection process consists of normalizing the input image and extracting the feature points of the normalized image, after which a correlation detector is employed to detect the possibly inserted watermark in the normalized image. Experimental results demonstrate the relative performance of the four different feature extraction techniques under both geometrical and signal processing operations, as well as the overall superiority of the method against two stateoftheart techniques that are quite robust as far as local image distortions are concerned.
Keywords
digital image watermarking local image distortions image moments radial symmetry transform discrete cosine transform feature extraction SIFT SURF FAST1 Introduction
During the last two decades there has been a great increase in the amount of multimedia information exchanged through the Internet. This resulted in the need for an efficient way to protect copyright on this information. The most sophisticated method to accomplish this in present years is digital watermarking [1–3]. It is interesting to note that it has since been also used in the context of other applications such as integrity checking [4, 5], broadcast monitoring [6, 7] and fingerprinting [8, 9]. When referring to the design of a watermarking algorithm for copyright protection of digital images, there are certain requirements that we would like it to meet [10]:

Robustness: The watermark should be resistant against intentional or unintentional attacks. That means, it should not be easy to render it undetectable or to remove it.

Imperceptibility: The watermark should be invisible. Specifically, it should not affect the overall quality of the original image.

Security: There should exist a large set of different possible keys producing independent watermarks. One should not be able to decide which the embedding key was.

Capacity: It should be possible to embed and, subsequently, detect multiple watermarks in the same image.

Payload: The number of watermark bits that could be embedded should be high.
As one can imagine, it is difficult to fulfill all requirements to the greatest extent simultaneously. A tradeoff should rather be established. In our article, we choose to focus on the robustness requirement having in mind that it is difficult to ensure a high degree of robustness without increasing watermark energy to a level that renders the watermark visible. On the other hand, if watermark energy remains low to ensure invisibility, it is unlikely that the watermark will survive any possible attack. The proposed technique, as will be shown, achieves to balance between these two requirements. Payload is kept at a moderate level, although rather small embedding areas are used for our multibit method and the adapted watermark pattern is duplicated across all of them. Finally, security and capacity remain high.
Possible watermark attacks can be categorized as follows:

Geometrical attacks: these include scaling, shearing, rotation, combinations of them and local distortions such as Stirmark attack or line removal.

Signal processing attacks: examples are lowpass filtering, lossy compression and noise addition.
Most of the proposed methods to date focus on either of these attack categories. The choice of embedding domain and the watermark's shape are two factors that determine which attack category the watermark is more resistant to. In general, watermarks embedded in the spatial domain can be designed in such a way that synchronization after geometric attacks can be achieved, whereas embedding in a transform domain usually provides greater robustness against filtering and compression. Additionally, watermarks having a certain symmetry (usually circular, as in [11, 12]) are employed to cope with geometrical attacks. Certain methods proposed in the recent years tend to be robust against both attack categories. In [13], a scheme is described that involves image segmentation, Gaussian scale model and moment normalization of selected circular regions. The problem encountered in this method is that the inverse normalization of the embedding regions may result in boundary artifacts. Apart from that, the homogeneity criterion of the employed segmentation method cannot provide a stable representation of the image after watermark embedding and/or some attack. In [14], a drawback is the fact that the strongest corner points detected are not necessarily the mostly repeated, i.e., corner strength does not change proportionally for all points after some attack. Another problem is the increased complexity due to both circular convolution needed to ensure rotational invariance and local search needed to overcome instability of feature point position and scale. The methods proposed in [15, 16] also suffer from quantization error due to inverse normalization of the embedding disks although some remedies are proposed in [15] to overcome this. These remedies, however, may affect detector performance. Besides, in [15] the number of correctly detected feature points after watermarking and possible attacks affects the detection threshold used to decide on the existence of the watermark. The watermark embedded using the technique described in [17] cannot withstand shearing attacks and, consequently, any affine geometrical attack involving shearing. That is because of the fact that the watermark is only rotationally invariant due to its structure of homocentric cirques and scaling invariant due to prior scale normalization of the whole image. Finally, in [18], a method is proposed that utilizes the scaleinvariant feature transform (SIFT) to extract circular patches that are scale and translation invariant, and the prototype rectangular watermark is subsequently inversely polarmapped prior to embedding. However, a computational overhead is introduced, again, due to circular convolution needed during detection to compensate for image rotation and, eventually, decide on the existence of the watermark.
In the following sections we describe a watermarking technique that deals successfully with all of the problems stated above and, additionally, provides substantially greater robustness than existing methods against local distortions, while keeping robustness against other usual attacks at an acceptable level. In Section 2, the initial stage of preprocessing which precedes both watermark embedding and detection is first described. In Section 3, the main watermarking procedure is explained and Section 4 presents examples of experimental results that prove the efficiency of the technique. Finally, conclusions about this study are drawn in Section 5.
2 Image preprocessing
Both watermark embedding and detection procedures require that a proper preprocessing of the original image has taken place, so that the watermark embedding or detection areas can be located. Section 2.1 describes the first preprocessing step where the original image is transformed geometrically to a standard form. Section 2.2 briefly overviews the four different feature extraction methods that will alternatively act upon the normalized image to produce the reference points both for watermark embedding and detection.
2.1 Image normalization
and $T=\left(\begin{array}{ccc}1& \phantom{\rule{0.5em}{0ex}}0& \phantom{\rule{0.5em}{0ex}}d1\\ 0& \phantom{\rule{0.5em}{0ex}}1& \phantom{\rule{0.5em}{0ex}}d2\\ 0& \phantom{\rule{0.5em}{0ex}}0& \phantom{\rule{0.5em}{0ex}}1\end{array}\right)$ is a translation matrix, $X=\left(\begin{array}{ccc}1& \phantom{\rule{0.5em}{0ex}}\beta & \phantom{\rule{0.5em}{0ex}}0\\ 0& \phantom{\rule{0.5em}{0ex}}1& \phantom{\rule{0.5em}{0ex}}0\\ 0& \phantom{\rule{0.5em}{0ex}}0& \phantom{\rule{0.5em}{0ex}}1\end{array}\right)$ is a xshearing matrix, $Y=\left(\begin{array}{ccc}1& \phantom{\rule{0.5em}{0ex}}0& \phantom{\rule{0.5em}{0ex}}0\\ \gamma & \phantom{\rule{0.5em}{0ex}}1& \phantom{\rule{0.5em}{0ex}}0\\ 0& \phantom{\rule{0.5em}{0ex}}0& \phantom{\rule{0.5em}{0ex}}1\end{array}\right)$ is a yshearing matrix, and $S=\left(\begin{array}{ccc}\alpha & \phantom{\rule{0.5em}{0ex}}0& \phantom{\rule{0.5em}{0ex}}0\\ 0& \phantom{\rule{0.5em}{0ex}}\delta & \phantom{\rule{0.5em}{0ex}}0\\ 0& \phantom{\rule{0.5em}{0ex}}0& \phantom{\rule{0.5em}{0ex}}1\end{array}\right)$ is a scaling matrix.
This normalized representation of the original image is the input for the next step of preprocessing that is necessary for both watermark embedding and detection.
2.2 Feature extraction
The second step of the preprocessing stage is the feature extraction step. A great variety of feature extraction methods has been proposed in the literature. Lately, there is a tendency of using the socalled scalespace methods such as SIFT [20] for watermarking purposes [18, 21–23]. In our study, we employed this as well as other feature detectors proposed in the literature, but not in the context of image watermarking, during the past few years. These detectors are, more specifically, the radial symmetry transform (RST) introduced in [24], the speeded up robust features (SURF) [25, 26] and the features from accelerated segment test (FAST) [27, 28]. As we will show in the experimental results section, all of them perform adequately well for our application, although their relative performance varies.
2.2.1 Radial symmetry transform
2.2.2 Scaleinvariant feature transform
that is, a convolution of the image with a difference of Gaussians. k is a factor that determines the difference between consecutive scales. An octave of scale space is a series of D(x, y, σ) functions spanning a doubling of σ. Each octave is divided in s intervals and, thus, k = 2^{1/s}. For each new octave, the Gaussian image produced with the doubled value of σ at the previous octave is first downsampled by a factor of 2 at each dimension. The local minima and maxima are found by 3D search in the 8 neighbors of the current scale and the respective 9 neighbors in each of the previous and the next scale.
If the offset $\widehat{\mathbf{x}}$ is larger than 0.5 in any dimension, then the extremum should be closer to another candidate feature point. If so, the interpolation is again performed around a different point. Otherwise the offset is added to the candidate point to produce the interpolated estimate of the extremum.
To discard feature points of low contrast, the value of the secondorder Taylor expansion is computed at the offset $\widehat{\mathbf{x}}$. If this value is less than 0.03 then the candidate point is discarded. Otherwise it is kept, and its final location and scale are, respectively, y + $\widehat{\mathbf{x}}$ and σ, where y is the original location of the candidate point at scale σ.
where r = α/β, Tr(H) = D_{ xx } + D_{ yy } = α + β is the trace of H and Det(H) = D_{ xx }D_{ yy } (D_{ xy } )^{2} = αβ is the determinant of H. If the ratio R for a certain candidate feature point is larger than (r_{ th } + 1)^{2}/r_{ th } , then the feature point is rejected. The method sets the threshold eigenvalue ratio to r_{ th } = 10.
2.2.3 Speeded up robust features
This method was introduced as an alternative to SIFT focusing on computational cost reduction. A fast way of computing the Hessian matrix using integral images is proposed. This approach approximates the second order Gaussian derivatives by box filters. These, in turn, are used to compute the approximate determinant of the Hessian matrix. Instead of subsampling the filtered image of a previous layer, the scale space is constructed by increasing the filter size. For each new octave, the filter size increase per layer is doubled, and so is the sampling interval for the extracted feature points.
2.2.4 Features from accelerated segment test
3 Watermarking scheme
The preprocessing stage described in the previous section is, as already stated, common for both watermark embedding and detection procedures. The extracted feature points are to be used as centers of the areas where the watermark is to be embedded.
3.1 Watermark embedding
where i = 1, . . . , M, w_{ i } (x, y) is the image with same size as f(x, y) and nonzero only in the i th embedding area (where w_{ o } is located), and ${f}_{0}^{w}\left(x,y\right)=f\left(x,y\right)$.
3.2 Watermark detection
4 Experimental results
To test the efficiency of the proposed watermarking technique against local distortions as well as other image processing attacks, we have conducted extensive watermarking experiments on ten well known images of different content, specifically "Airplane", "Boat", "House", "Peppers", "Splash", "Baboon", "Couple", "Lena", "Elaine", and "Lake". Each experiment consisted of embedding a 50 bit watermark message in each of the images and subsequently trying to extract it from the watermarked and attacked version of the image. For all techniques compared and for all images, PSNR is tuned to 40 dB. The bit error rate (BER), that is, the percentage of message bits that have not been detected correctly, is finally calculated. The proposed technique was tested for all four feature detectors under concern and compared to the stateoftheart techniques described in [19, 33]. These methods were selected as two of the recent bibliography that are multibit, permit finetuning of PSNR and are built to resist geometric attacks. It is worth mentioning that these methods act globally, thus distorting the whole of the image. In contrast, our method affects only local regions, thus producing zero distortion in part of the image. This, in turn, results in improved imperceptibility. The parameter values for the feature detectors were those used in the examples of Section 2.2. The range of DCT coefficients used for watermarking with the technique by Dong et al. [19] was chosen to be [28681, 215478], that is 186798 coefficients. The respective range of DCT coefficients for the technique by Tian et al. [33] was [7170, 53870], that is 46701 coefficients. These ranges were chosen as equivalent to the one used in our method. In the following sections, we present results for local geometric attacks, global geometric attacks and signal processing attacks. Some of the attacks were implemented using the Checkmark benchmarking software [34].
4.1 Local geometric attacks
4.2 Global geometric attacks
4.3 Signal processing attacks
In summary, the proposed technique, as expected due to its design, is more robust than the stateoftheart techniques in terms of local geometric distortions. It is also better in terms of shearing attacks and downsampling followed by upsampling. It is only inferior compared to the method by Dong et al., yet with significant performance, under rotation, scaling, general affine transform and signal processing attacks, such as JPEG compression, H.264 intraframe compression, lowpass filtering and noise addition. It is even better, in its SIFTbased and SURFbased versions, than the method by Tian et al. for all these attacks except compression attacks. The most competitive version of our method appears to be the SIFTbased one, followed by the SURFbased, the RSTbased, and the FASTbased.
5 Conclusions
In the current article, a new image watermarking technique is proposed, which is robust against the usual local distortion attacks that are not efficiently coped with by the stateoftheart techniques. According to our technique, a multibit watermark is formed in the DCT domain, inversely transformed and, eventually, geometrically normalized to the spatial domain of the original image. This prevents image interpolation errors in contrast to other techniques in the literature which embed the watermark in a normalized version of the image and afterwards apply inverse normalization. Furthermore, no local search is needed to achieve synchronization during detection. The use of a visibility rule during embedding prevents image deterioration due to overlapping of watermarked areas. Four different feature detection techniques are alternatively used in our study, namely SIFT, SURF, RST, and FAST, in order to produce the regions in which to embed the watermark. Our technique, especially in its SIFTbased version, proves to be more robust against local geometric attacks than certain stateoftheart techniques and has remarkable performance in terms of global geometric distortions and signal processing attacks.
Declarations
Acknowledgements
A. Nikolaidis wishes to acknowledge financial support provided by the Research Committee of the Technological Educational Institute of Serres, Greece, under grant SAT/IC/2331125/1.
Authors’ Affiliations
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