CN102024248A - Digital image watermarking method based on local visual attention - Google Patents
Digital image watermarking method based on local visual attention Download PDFInfo
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Abstract
The invention relates to the technical field of information hiding and digital watermarking in multimedia information security, comprising self-adaptive division of an elliptic local feature region as well as embedding and extraction of a digital image watermarking based on local visual attention. The method is as follows: firstly, by means of the feature of an image local region, extracting an image feature point by utilizing a scale invariant feature transform (SIFT) operator with stable performance, and acquiring a group of stable elliptic affine covariant feature regions independent from one another through a selecting strategy based on a minimal spanning tree clustering algorithm; then based on the local feature region, acquiring a round region with scaling and rotational invariance by utilizing elliptic normalization, and carrying out discrete Fourier transformation (DFT) on the round region; and finally embedding the watermarking into a transformed medium frequency region. In the method, an original carrier is unnecessary when the digital watermarking is detected. Simulation experiment results show that the digital image watermarking algorithm can be used for effectively resisting desynchronization attack of a watermarking-containing image, and has excellent robustness for common attacks simultaneously.
Description
Technical field
The digital image watermarking method of paying close attention to based on local visual of the present invention belongs to Information hiding and digital watermark technology field in the multi-media information security, is specifically related to a kind of robustness image watermark new method.
Background technology
The network of accelerated development at present and the digitizing of multi-medium data have greatly improved the efficient and the accuracy of information representation, universal day by day along with the Internet, and the interchange of multimedia messages has reached the unprecedented degree of depth and range.Yet the problem of Chu Xianing is also serious further thereupon, not only makes the digital product safe mass obtain querying, and grievous injury the copyright and the economic interests of Digital Media author, society is produced harmful effect.Therefore, the digital watermark technology of robust seems particularly important.The watermarking algorithm that proposes generally can be resisted the image conventional processing preferably at present, as low-pass filtering, and JPEG compression etc.; However, most of algorithms still can't well be resisted geometric attack, as rotation, convergent-divergent, translation etc.Geometric attack has destroyed the synchronism between carrier and the watermark, though still contain watermark in the carrier, consequent synchronous error makes detecting device can't correctly extract watermark.Therefore, the image watermark algorithm of research opposing geometric attack is one and has challenging problem.
By the end of at present, people mainly adopt three kinds of measure design resist geometric attacks New Scheme of Image Watermarking, are respectively the constructive geometry invariant, hide masterplate or identifiable structures, utilize raw data key character etc.Wherein, preceding two kinds of schemes can be resisted conventional signal Processing and global affine transformation, but can't effectively resist localized distortion, random shearing, geometric transformation combination etc. than complex attack.The 3rd class is based on the method for image content features, its basic thought is, utilize metastable unique point sign watermark embedded location in the image, and with the corresponding local feature of each unique point zone in embed digital watermark independently, utilize unique point to locate and detect digital watermarking simultaneously, thereby effectively resist the attack of desynchronizing.However, this class methods ubiquity local feature zone does not have covariance, though or the zone have a covariance because the instability of operator itself, so geometric attacks such as aspect ratio change, shearing are still lacked robustness.At existing problem in the above-mentioned prior art, a kind of novel digital image watermarking method of research and design based on the local visual concern, existing problem is very necessary in the prior art thereby overcome.
Summary of the invention
In view of existing problem in the above-mentioned prior art, the objective of the invention is a kind of novel digital image watermarking method of research and design based on the local visual concern, thereby solve current digital image water mark method ubiquity local feature zone and do not have covariance, though or the zone has covariance, because the instability of operator itself is so still lack problems such as robustness to geometric attacks such as aspect ratio change, shearings.The digital image watermarking method of paying close attention to based on local visual of the present invention mainly comprises following two aspects: the embedding and the extraction of the digital figure watermark that the self-adaptation in oval local feature zone is divided and paid close attention to based on local visual.
The self-adaptation partiting step in oval local feature of the present invention zone is as follows:
Determining of the first step, elliptical center position:
Utilize minimum spanning tree (MST) clustering algorithm that unique point is classified, the unique point that satisfies the distance restraint condition is classified as a class, for same category feature point, select the bigger unique point of characteristic strength. determine the center in oval local feature zone with the position of these unique points, be designated as O
t(x, y).
Asking for of second step, oval length semiaxis:
With the unique point O that determines in the first step
t(x, y) pairing characteristic dimension is constructed polynomial expression as known conditions, thereby tries to achieve oval length semiaxis, determines that specifically method is as follows:
Here, A
tRepresent current regional area major axis; B
tRepresent current regional area minor axis; s
tThe characteristic dimension of expression present image unique point;
Round in the expression; K, τ are self-adaptation constant (positive integer), are respectively applied for to regulate A
t, B
tSize; A
t, B
tThe upper bound be carrier image size half (suppose that current unique point is positioned at the center of image, this upper bound only is theoretic, generally get less than), A
tLower bound be 1, B
tLower bound be
(when τ=1), therefore, A
t, B
tTheoretical span be:
Wherein, M and N represent the length of initial carrier image and wide respectively;
Asking for of the 3rd step, oval deflection:
Get the deflection of the angle of the determined straight line of barycenter of elliptical center and its a slice neighborhood and x axle, be designated as θ as ellipse
t
Represent the current radius of neighbourhood, A
t, B
tIn 1.2, asked parameter. because geometric moment m
Pq(p, q=1,2 ...) be defined as:
Point p
t(i
c, j
c) be center-of-mass coordinate;
Obtain current barycenter P
tCan try to achieve the current deflection θ in oval local feature zone behind the point coordinate as stated above
t
Determining of the 4th step, covariance elliptic region;
Obtain parameter A
t, B
tAnd θ
tAfter just can from carrier image, be partitioned into oval local feature zone adaptively.
The embedding and the extraction step of the digital figure watermark of paying close attention to based on local visual of the present invention are as follows:
Adopt the redundant strategy that embeds, be about to same digital watermarking and repeatedly be embedded in all local feature zones, the telescopiny step of digital figure watermark is as follows:
The first step, produce the bipolar sequence W={w that size is L by key K ey
i, i=1 ..., L} and as digital watermarking;
Second the step, utilize the SIFT operator from initial carrier, to extract image characteristic point, to obtain characteristics of image point set P={p
i, i=1 ..., n};
The 3rd step, be the center, from carrier, mark off a series of oval local features zone O={o adaptively with the image characteristic point
k, k=1 ..., m};
The 4th step, to each oval local feature zone O={o
k, k=1 ..., m} carries out normalization, embeds and extracts with convenient, realizes the robustness of watermark, is designated as O '={ o
d, d=1 ..., m};
The 5th the step, to each o
d∈ O ' does " mending 0 " operation, to obtain the sub-piece T={t of series of rectangular
d, d=1 ..., m}; To each t
d∈ T does centralization DFT conversion (the conversion initial point is the subimage center);
The 6th goes on foot, digital watermarking is embedded in the DFT territory;
The 7th step, the sub-piece of rectangle that will be embedded with digital watermarking by the IDFT conversion return to spatial domain, obtain
After " going 0 " operation, obtain again
At last with
Replace o
d
The 8th step, with the part-circular of each embed watermark of gained zone o
dAnti-normalization obtains containing the oval local feature of watermark zone o
cAs all local feature zone o
cReplace corresponding o
k, promptly obtain the required watermarking images that contains, finished the embedding of watermark;
The extraction step of digital figure watermark is as follows:
The first step, the use key K ey identical with telescopiny produce original watermark sequence W={w
i, i=1 ..., L};
Second the step, utilize the SIFT operator from image to be detected, to extract image characteristic point, obtain feature point set
The 3rd step, be the center, from image to be detected, mark off a series of oval local features zone adaptively with the image characteristic point
The 4th the step, to each oval local feature zone
Carry out normalization. embed and extract with convenient, realize the robustness of watermark. be designated as
The 5th the step, to each
Do " mending 0 " operation, to obtain the sub-piece of series of rectangular
Again to each
Do centralization DFT conversion;
The 6th goes on foot, is known by DFT character, and after image experience conventional attack or the geometric transformation, the embedding area size on its frequency domain remains unchanged substantially; Can be according to the relative position relation of initial some points at annular region [r
1, r
L] in select an identical fan section, big or small position when embedding, and reselect L point by radius order from small to large therein
For each concentric circles C (r
i), extract watermark according to the following rules:
The digital image watermarking method of paying close attention to based on local visual of the present invention, the affine covariance feature in conjunction with the oval feature zone has proposed a kind of novel method of digital watermarking based on the local visual feature.The simulation experiment result shows that this method not only has preferably not sentience, and normal image processing and rotation, convergent-divergent, shearing, other geometric attacks and combination attacks are all had robustness preferably.
The present invention is a combining image regional area unique characteristics; the image digital watermark embedding grammar that proposes. at first utilize the SIFT operator extraction image characteristic point of stable performance; and obtain one group of stable and affine covariant characteristic area of ellipse independent of each other by selection strategy based on the minimum spanning tree clustering algorithm; then based on the local feature zone; utilize oval normalization to obtain having the border circular areas of convergent-divergent and rotational invariance. border circular areas is carried out the DFT conversion; at last watermark being embedded after the conversion in the intermediate frequency zone. this method is when detecting digital watermarking; do not need initial carrier. reached blind Detecting. The simulation experiment result shows; this digital figure watermark algorithm not only can effectively be resisted and contain watermarking images suffered attack of desynchronizing under various states; simultaneously good robustness is also arranged for conventional attack; it is simple that this method also has calculating in addition; characteristics such as easy realization, this has strengthened it greatly and has been used for the practicality of digital watermarking Works copyright protection.
The digital image watermarking method of paying close attention to based on local visual of the present invention, basic functional principle is: the SIFT operator extraction image characteristic point that utilizes stable performance, and obtain one group of stable and affine covariant characteristic area of ellipse independent of each other by selection strategy based on the minimum spanning tree clustering algorithm, then based on the local feature zone, utilize oval normalization to obtain having the border circular areas of convergent-divergent and rotational invariance. border circular areas is carried out the DFT conversion, at last watermark being embedded after the conversion in the intermediate frequency zone. this method does not need initial carrier when detecting digital watermarking. reached blind Detecting.
The present invention is a combining image regional area unique characteristics; the image digital watermark embedding grammar that proposes. can effectively resist and contain watermarking images suffered attack of desynchronizing under various states; simultaneously good robustness is also arranged for conventional attack; this algorithm also has characteristics such as need not the initial carrier image when calculating simple, easy realization, extraction watermark in addition, and this has strengthened it greatly and has been used for the practicality of digital watermarking Works copyright protection.
Description of drawings
The present invention has six groups of accompanying drawings, wherein:
Fig. 1: the self-adaptation in oval local feature zone is determined figure (covariant characteristic)
Fig. 2: oval normalization process synoptic diagram.
Fig. 3: initial carrier image.
Fig. 4: contain watermarking images behind the embed watermark.
Fig. 5: do not attack the image detection design sketch.
Fig. 6: image detection design sketch under fire.
Embodiment
Specific embodiments of the invention as shown in drawings, digital image watermarking method based on local visual is paid close attention to mainly comprises following two aspects: the embedding and the extraction of the digital figure watermark that the self-adaptation in oval local feature zone is divided and paid close attention to based on local visual.
1, the self-adaptation in oval local feature zone is divided
Local feature zone (LFRs), be meant with the image characteristic point to be sign, the a part of subimage that from carrier image, is partitioned into. because these subimages have reflected the most important semantic information of carrier image, so with embedding and surveyed area as digital watermarking, promptly be equivalent to the content characteristic of digital watermarking and carrier image is bundled, can obtain robustness preferably. this paper adopts has the oval local feature zone of good directivity, and utilizes characteristic dimension and adaptive definite local feature area size of picture material and direction. and concrete grammar is as follows:
1.1 determining of elliptical center position
Because characteristic dimension only depends on the image local characteristic, and its size changes with the image local characteristic changing. but the little unique point of characteristic dimension, its stability is lower; And the characteristic area that the big unique point of characteristic dimension forms overlaps serious, therefore we can choose the unique point in a part of medium scale scope fully. for the characteristic area of mutual overlapping, adopt distance restraint to adjust the distribution of unique point, utilize minimum spanning tree (MST) clustering algorithm that unique point is classified, the unique point that satisfies the distance restraint condition is classified as a class, for same category feature point, select the bigger unique point of characteristic strength. determine the center in oval local feature zone with the position of these unique points, be designated as O
t(x, y).
1.2 asking for of oval length semiaxis
With the unique point O that determines in 1.1
t(x, y) pairing characteristic dimension is constructed polynomial expression as known conditions, thereby tries to achieve oval length semiaxis, determines that specifically method is as follows:
Here, A
tRepresent current regional area major axis; B
tRepresent current regional area minor axis; s
tThe characteristic dimension of expression present image unique point;
Round in the expression; K, τ are self-adaptation constant (positive integer), are respectively applied for to regulate A
t, B
tBig or small .A
t, B
tThe upper bound be carrier image size half (suppose that current unique point is positioned at the center of image, this upper bound only is theoretic, generally get less than), A
tLower bound be 1, B
tLower bound be
(when τ=1). therefore, A
t, B
tTheoretical span be:
Wherein, M and N represent the length of initial carrier image and wide respectively.
1.3 asking for of oval deflection
Compare with the circular feature zone, oval advantage is that there is deflection in it, this also makes it have affine covariance, so determining of deflection is particularly important. consider the demand of robustness, the method that this paper selects for use picture material to determine as deflection, promptly get the deflection of the angle of the determined straight line of barycenter of elliptical center and its a slice neighborhood and x axle, be designated as θ as ellipse
t. step is as follows:
Represent the current radius of neighbourhood, A
t, B
tIn 1.2, asked parameter. because geometric moment m
Pq(p, q=1,2 ...) be defined as:
Point p
t(i
c, j
c) be center-of-mass coordinate.
Obtain current barycenter P
tCan try to achieve the current deflection θ in oval local feature zone behind the point coordinate as stated above
t.
1.4 determining of covariance elliptic region
Obtain parameter A
t, B
tAnd θ
tAfter just can from carrier image, be partitioned into oval local feature zone adaptively. in order to keep the independence in local feature zone, if must make that all elliptical pieces can not be overlapping.,
A unique point is in the local feature zone of another fixed unique point, then this unique point is with disallowable. for this reason, we select to contain the more elliptical piece of unique point number as the local feature zone, because the zone belongs to texture area like this, can satisfy the transparency of digital watermarking better. the oval local feature zone covariant of extraction is in all kinds of attacks, make this zone comprise identical picture material, effect as shown in Figure 1, characteristic area after Gaussian noise processing feature zone, JPEG30% compressive features zone, medium filtering processing feature zone, attack signature zone (c) (d) (e) (f) rotation 30 degree characteristic areas (g) rotations 45 degree characteristic areas (h) amplify 1.5 times comprising (a) original image (b). therefore, on local covariant zone, carry out watermark and embed and extract and can effectively resist normal image and handle and geometric attack.
The embedding of 2 digital watermarkings
The present invention will adopt the redundant strategy that embeds, and be about to same digital watermarking and repeatedly be embedded in all local feature zones. and the telescopiny of whole digital watermarking (committed step) can be described below:
1) produces the bipolar sequence W=(w that size is L by key K ey
i, i=1 ..., L} and as digital watermarking.
2) utilize the SIFT operator from initial carrier, to extract image characteristic point, to obtain characteristics of image point set P={p
i, i=1 ..., n}. wherein initial carrier image comprises (a) Baboon, (b) Lena, (c) Peppers, (d) Plane. as shown in Figure 3
3) be the center with the image characteristic point, from carrier, mark off a series of oval local feature zone O={o adaptively
k, k=1 ..., m} (seeing the 1st joint).
4) to each oval local feature zone O={o
k, k=1 ..., m} carries out normalization, as shown in Figure 2. embed and extract with convenient, realize the robustness of watermark. be designated as O '={ o
d, d=1 ..., m}.
5) to each o
d∈ O ' does " mending 0 " operation, to obtain the sub-piece T={t of series of rectangular
d, d=1 ..., m}. is to each t
d∈ T does centralization DFT conversion (the conversion initial point is the subimage center).
6) digital watermarking is embedded in the DFT territory.
7) the sub-piece of rectangle that will be embedded with digital watermarking by the IDFT conversion returns to spatial domain, obtains
Warp again
8) with the regional o of the part-circular of each embed watermark of gained
dAnti-normalization obtains containing the oval local feature of watermark zone o
c. as all local feature zone o
cReplace corresponding o
kPromptly obtain the required watermarking images that contains, finished the embedding of watermark. (the PSNR value is respectively: 41.32 as shown in Figure 4 wherein to contain watermarking images, 47.85,49.55,49.59). comprise that (a) contains watermarking images Baboon, (b) contains watermarking images Lena, (c) contain watermarking images Peppers, (d) contain watermarking images Plane.
The detection of 3 digital watermarkings
Because watermark information repeatedly is embedded in each independently oval local feature zone. therefore, can adopt method identical when embedding that image division to be detected is become several local feature zones. the testing process of whole digital watermarking is as follows:
1) use the key K ey identical to produce original watermark sequence W={w with telescopiny
i, i=1 ..., L}.
2) utilize the SIFT operator from image to be detected, to extract image characteristic point, obtain feature point set
3) with the image characteristic point be the center, from image to be detected, mark off a series of oval local features zone adaptively
4) to each oval local feature zone
Carry out normalization. embed and extract with convenient, realize the robustness of watermark. be designated as
5) to each
Do " mending 0 " operation, to obtain the sub-piece of series of rectangular
Again to each
Do centralization DFT conversion.
6) know by DFT character that after image experience conventional attack or the geometric transformation, the embedding area size on its frequency domain remains unchanged substantially. still can be according to the relative position relation of initial some points at annular region [r
1, r
L] in select an identical fan section, big or small position when embedding, and reselect L point by radius order from small to large therein
For each concentric circles C (r
i), extract watermark according to the following rules:
Wherein,
With
Be respectively a little
And the point
Amplitude. extracting the result and can be found out that wherein (a) is the testing result of Fig. 4 (a) by Fig. 5, (b) is the testing result of Fig. 4 (b), (c) is the testing result of Fig. 4 (c), (d) is the testing result of Fig. 4 (d).
4, emulation experiment
In order to verify high efficiency of the present invention, below provided the detection performance test respectively, the experimental result of anti-attack ability test, and contrast with document [2] method, comprising: the JPEG compression, additive noise, medium filtering+JPEG, rotation, X, the Y-axis cutting, translation and removal ranks+compression, rotation+shearing+compression etc. in the experiment, selected initial carrier is 512 * 512 * 8bit standard grayscale image B aboon, Lena, the binary random sequence of 16bits has been adopted in Peppers and Plane. digital watermarking. in addition, the parameter assignment k=55 that uses, τ=5.
(1) JPEG compression. treat detected image and carry out 70% JPEG compression.
(2) additive noise. treating detected image, to add intensity be 0.20 additive noise.
(3) medium filtering+JPEG. carries out image to be detected the medium filtering processing and compresses 70%.
(4) X, Y-axis cutting respectively. with the X of image to be detected, Y-axis cutting 0%, 5%. respectively
(5) rotation. image to be detected is rotated counterclockwise 30 degree.
(6) central-line shear angle. picture centre to be detected is sheared 10%.
(7) remove ranks+compression. at first image to be detected is removed 5 row, 17 row, again the gained image is carried out 70% JPEG compression.
(8) rotation+shearing+compression. image to be detected is at first rotated 5 degree, and central-line shear angle 5% again, carries out 70% JPEG compression at last.
Under fire the image detection effect as shown in Figure 6, with the Lena image is example, be respectively through JPEG (70) compression, additive noise (0.20), medium filtering+JPEG (90), rotation 30 degree, X, Y-axis cutting (50%) respectively, central-line shear angle 10%, remove the figure as a result that contains in the watermarking images to be detected that 5 row, 17 row+JPEG (70) compress and rotate 5 degree+central-line shear angle 5%+JPEG (70) compression attack. reconstruct rate difference=7/9,8/9,6/9,9/9,7/9,8/9,5/9,6/9.
Table 1 and table 2 have provided the contrast and experiment of two kinds of image watermark methods.
Table 1 contains the Y-PSNR (dR) between watermarking images and initial carrier
Image | The present invention | Document [2] method |
Baboon | 41.32 | 39.1 |
Lena | 47.85 | 47 |
Peppers | 49.55 | 40.9 |
Plane | 49.59 | 44.8 |
Claims (3)
1. digital image watermarking method of paying close attention to based on local visual is characterized in that mainly comprising following two aspects: the embedding and the extraction of the digital figure watermark that the self-adaptation in oval local feature zone is divided and paid close attention to based on local visual.
2. according to what is claimed is the 1 described digital image watermarking method of paying close attention to based on local visual, it is characterized in that the self-adaptation partiting step in described oval local feature zone is as follows:
Determining of the first step, elliptical center position:
Utilize minimum spanning tree (MST) clustering algorithm that unique point is classified, the unique point that satisfies the distance restraint condition is classified as a class,, select the bigger unique point of characteristic strength for same category feature point; Determine the center in oval local feature zone with the position of these unique points, be designated as O
t(x, y);
Asking for of second step, oval length semiaxis:
With the unique point O that determines in the first step
t(x, y) pairing characteristic dimension is constructed polynomial expression as known conditions, thereby tries to achieve oval length semiaxis, determines that specifically method is as follows:
Here, A
tRepresent current regional area major axis; B
tRepresent current regional area minor axis; s
tThe characteristic dimension of expression present image unique point;
Round in the expression; K, τ are self-adaptation constant (positive integer), are respectively applied for to regulate A
t, B
tSize; A
t, B
tThe upper bound be carrier image size half (suppose that current unique point is positioned at the center of image, this upper bound only is theoretic, generally get less than), A
tLower bound be 1, B
tLower bound be
(when τ=1), therefore, A
t, B
tTheoretical span be:
Wherein, M and N represent the length of initial carrier image and wide respectively;
Asking for of the 3rd step, oval deflection:
Get the deflection of the angle of the determined straight line of barycenter of elliptical center and its a slice neighborhood and x axle, be designated as θ as ellipse
t
Represent the current radius of neighbourhood, A
t, B
tIn 1.2, asked parameter; Because geometric moment m
Pq(p, q=1,2, Λ) be defined as:
Point p
t(i
c, j
c) be center-of-mass coordinate;
Obtain current barycenter P
tCan try to achieve the current deflection θ in oval local feature zone behind the point coordinate as stated above
t
Determining of the 4th step, covariance elliptic region;
Obtain parameter A
t, B
tAnd θ
tAfter just can from carrier image, be partitioned into oval local feature zone adaptively.
3. according to what is claimed is the 1 described digital image watermarking method of paying close attention to based on local visual, it is characterized in that the embedding and the extraction step of the described digital figure watermark of paying close attention to based on local visual is as follows:
Adopt the redundant strategy that embeds, be about to same digital watermarking and repeatedly be embedded in all local feature zones, the telescopiny step of digital figure watermark is as follows:
The first step, produce the bipolar sequence W={w that size is L by key K ey
i, i=1, Λ, L} and as digital watermarking;
Second the step, utilize the SIFT operator from initial carrier, to extract image characteristic point, to obtain characteristics of image point set P={p
i, i=1, Λ, n};
The 3rd step, be the center, from carrier, mark off a series of oval local features zone O={o adaptively with the image characteristic point
k, k=1, Λ, m};
The 4th step, to each oval local feature zone O={o
k, k=1, Λ, m} carries out normalization, embeds and extracts with convenient, realizes the robustness of watermark, is designated as O '={ o
d, d=1, Λ, m};
The 5th the step, to each o
d∈ O ' does " mending 0 " operation, to obtain the sub-piece T={t of series of rectangular
d, d=1, Λ, m}; To each t
d∈ T does centralization DFT conversion (the conversion initial point is the subimage center);
The 6th goes on foot, digital watermarking is embedded in the DFT territory;
The 7th step, the sub-piece of rectangle that will be embedded with digital watermarking by the IDFT conversion return to spatial domain, obtain
After " going 0 " operation, obtain again
At last with
Replace od;
The 8th step, with the part-circular of each embed watermark of gained zone o
dAnti-normalization obtains containing the oval local feature of watermark zone o
cAs all local feature zone o
cReplace corresponding o
k, promptly obtain the required watermarking images that contains, finished the embedding of watermark;
The extraction step of digital figure watermark is as follows:
The first step, the use key K ey identical with telescopiny produce original watermark sequence W={w
i, i=1, Λ, L};
Second the step, utilize the SIFT operator from image to be detected, to extract image characteristic point, obtain feature point set
The 3rd step, be the center, from image to be detected, mark off a series of oval local features zone adaptively with the image characteristic point
The 4th the step, to each oval local feature zone
Carry out normalization; Embed and extract with convenient, realize the robustness of watermark; Be designated as
The 5th the step, to each
Do " mending 0 " operation, to obtain the sub-piece of series of rectangular
Again to each
Do centralization DFT conversion;
The 6th goes on foot, is known by DFT character, and after image experience conventional attack or the geometric transformation, the embedding area size on its frequency domain remains unchanged substantially; Can be according to the relative position relation of initial some points at annular region [r
1, r
L] in select an identical fan section, big or small position when embedding, and reselect L point by radius order from small to large therein
For each concentric circles C (r
i), extract watermark according to the following rules:
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