KR100945724B1 - Line watermarking resilient against local deformation - Google Patents

Abstract

The line watermarking method disclosed in the present invention includes: wavelet transforming a polygon line in an image to be inserted using a wavelet descriptor, generating a random sequence of ± 1 values as a bipolar watermark, and wavelet of the wavelet transformed polygon line. And inserting a bipolar watermark into the coefficients, and inversely wavelet transforming the wavelet transformed polygon lines to reflect the watermarked polygon lines in the inserted object image.

The line watermarking method of the present invention has a robust effect on local deformation attacks as well as rotation attacks, scaling attacks, and translation attacks.

Blind Watermarking, Watermark, Bipolar Watermark, Wavelet Technician

Description

Robust line watermarking method for local deformation {LINE WATERMARKING RESILIENT AGAINST LOCAL DEFORMATION}

FIELD OF THE INVENTION The present invention relates to a blind watermarking method, and more particularly, to a line watermarking method that is robust to local deformation attacks as well as RST attacks including rotation, scaling and translation. It is about.

Digital images facilitate efficient distribution, reproduction, and manipulation. However, these advantages also cause copyright problems. As is known, digital watermarking is a technique that can protect the copyright of digital products. Digital watermarks are signals that can be detected or extracted. The signal here is generally copyrighted to prove ownership of the digital product.

In general, there are two types of images. One is a raster image and the other is a vector image. Raster images are data structures that represent a generally rectangular grid of pixels or point of color and are used in many digital devices such as digital cameras. Vector images are based on geometric elements such as points, lines, curves, and polygons, and are widely used in digital maps, geographical information systems (GIS), 2D graphics, and cartoon images.

Currently, various watermarking methods have been developed in relation to the raster image described above, but the number of watermarking methods related to vector images is very limited. Since the representation of the vector image is different from that of the raster image, the watermarking method used in the raster image cannot be directly applied.

Conventionally, a vector graphic image watermarking method using Fourier descriptor of a polygon line has been proposed. Fourier descriptors are a type of shape analysis that transforms the vertex coordinates of a polygon line into Fourier domains. Although the watermarking method using a Fourier descriptor is robust to RST attacks, it is vulnerable to local deformation attacks.

Local deformation is known to be a very effective attack to neutralize vector image watermarking. Manipulating the positions of several vertices significantly degrades the performance of watermarking or the system using Fourier descriptors.

The present invention has been made in view of the above problems, and proposes a line watermarking method that is robust and resilient to RST attacks and local deformation attacks.

The line watermarking method of the present invention, which is presented as a means for solving the problem, is largely divided into a watermark embedding process and a watermark detection process.

The watermark embedding process may include wavelet transforming a polygon line in an image to be inserted using a wavelet descriptor, generating a random number sequence having a value of ± 1 as a bipolar watermark, and performing a wavelet coefficient on the wavelet transformed polygon line. Inserting a bipolar watermark and inverse wavelet transforming the wavelet transformed polygon lines to reflect the watermarked polygon lines in the image to be inserted.

Preferably, the bipolar watermark of the present invention has a zero mean value and unit variance. In addition, a bipolar watermark is inserted into the wavelet coefficient in consideration of the intensity factor (value less than 1).

The watermark detection process includes wavelet transforming a polygon line in a detection target image using a wavelet descriptor, and calculating a correlation value between the bipolar watermark used in the watermark embedding process and the wavelet coefficients of the wavelet transformed polygon line. And calculating a normalized correlation value by dividing the correlation value by an average of the correlation values, and determining that a watermark has been detected when the normalized correlation value is larger than a threshold value. The threshold is an arbitrary value between 0 and 1, and is determined in consideration of the watermark extraction error probability.

The line watermarking method according to the present invention as described above is robust to rotational attack, scaling attack, movement attack and local deformation attack.

Specific features and advantages of the present invention will become more apparent from the following detailed description based on the accompanying drawings. In the meantime, when it is determined that the detailed description of the known functions and configurations related to the present invention may unnecessarily obscure the subject matter of the present invention, it should be noted that the detailed description is omitted.

1. Wavelet Technician

In order to represent and extract features from shapes, various descriptors have been studied in the field of shape recognition and retrieval. Among them, wavelet descriptors are widely used because they have many desirable properties such as multi-resolution representation, invariance, uniqueness, stability, and spatial localization. These wavelet descriptors break the curve into components of various scales. The coarsest scale component carries broad approximation information, while the finer scale component contains local detail.

을 상정한다.Specifically, the clockwise closed curve represented by Equation 1

Assume

[Equation 1]

는 정규화된 호 길이이고,

은 임의의 시작점

로부터 곡선을 따르는 호 길이이고,

은 전체 호 길이이다. 웨이블릿 변환을 매개 변수화된 좌표에 적용함으로써 다음과 같은 수학식을 얻을 수 있다.here,

Is the normalized arc length,

Is a random starting point

Arc length along the curve from

Is the total arc length. By applying the wavelet transform to the parameterized coordinates, the following equations can be obtained.

[Equation 2]

[Equation 3]

에서의 근사 계수로 지칭된다.Equation 3 is the scale

It is referred to as an approximation coefficient at.

[Equation 4]

에서의 상세 신호로 지칭된다. 이때

인 경우 가장 미세한 스케일이 되며,

인 경우 가장 거친 스케일이 된다. 수학식 3, 4는 웨이블릿 도메인 상에서 상기 곡선을 표현하는 웨이블릿 기술자이다.Equation 4 is the scale

It is referred to as the detailed signal in. At this time

Is the finest scale,

Is the roughest scale. Equations 3 and 4 are wavelet descriptors representing the curve on the wavelet domain.

,

,

및

은 웨이블릿 도메인으로 변환된 곡선

의 웨이블릿 계수(wavelet coefficient)이다. 여기서 곡선(curve)은 복수개의 정점(vertices)을 갖는 폴리곤 라인(polygon line)으로 이해해도 좋다.Meanwhile, in Equation 2

,

,

And

Is a curve transformed into a wavelet domain

Is the wavelet coefficient of. Here, the curve may be understood as a polygon line having a plurality of vertices.

The line watermarking method disclosed by the present invention will be described in detail with reference to FIGS. 1 and 2.

2. Watermark embedding process (S100)

Using the wavelet descriptor, the polygon line in the image to be inserted (hereinafter, referred to as an “inserted image”) is wavelet transformed (S101). Here the wavelet descriptor is applied to the vertices that make up the polygon line.

Next, a random number sequence having a value of ± 1 is generated as a bipolar watermark (S103). Bipolar watermarks have a zero mean value and unit variance. The bipolar watermark generated as described above is multiplied in the size of the detailed wavelet coefficient as shown in Equation 5 below to use the constant property of the wavelet descriptor (S105).

[Equation 5]

는 폴리곤 라인

의 원(또는 최초) 웨이블릿 계수의 크기이며,

는 바이폴라 워터마크이고,

은

에 의해 워터마킹된 웨이블릿 계수의 크기이며, k=0, 1, …, N-1이고, 그리고

는 상기 바이폴라 워터마크의 강도(power)를 결정하는 팩터이다(이하, '강도 팩터'). 이때, 워터마킹된 곡선의 웨이블릿 기술자 크기는 음수가 아니어야 하므로(non-negative), 강도 팩터(

)는 1보 다 작아야 한다.here,

The polygon line

The magnitude of the circle (or first) wavelet coefficient of,

Is a bipolar watermark,

silver

Is the magnitude of the wavelet coefficient watermarked by k = 0, 1,. , N-1, and

Is a factor that determines the power of the bipolar watermark (hereinafter, 'intensity factor'). Since the wavelet descriptor size of the watermarked curve should be non-negative, the intensity factor (

) Must be less than 1.

를 삽입한 후, 웨이블릿 계수

를 역 웨이블릿 변환(inverse wavelet transform)하여, 삽입대상 이미지에 워터마킹된 폴리곤 라인

을 반영한다(S107).Bipolar watermark as described above

After inserting the wavelet coefficients

Inverse wavelet transform to polygon lines watermarked in the image to be inserted

Reflect this (S107).

3. Watermark Detection Process (S200)

을 웨이블릿 변환한다(S201). 기지의 값인 바이폴라 워터마크(제S100 과정에서 이용된

와 웨이블릿 계수의 크기

간의 상관값(

, correlation)을 상관값의 평균()로 나누어 정규화된 상관값(

)를 구한다(S203, S205). First, using a wavelet descriptor, a polygon line in an image to be detected (hereinafter referred to as an 'detection target image')

The wavelet transform is performed (S201). Known bipolar watermark (used in step S100)

And the magnitude of the wavelet coefficients

Correlation value between

, correlation) is the mean of the correlation values ( Divided by)

) Is obtained (S203, S205).

)이 임계값보다 큰 경우, 폴리곤 라인

에는 바이폴라 워터마크

가 포함된 것으로 판단한다(S209). It is determined whether this normalized correlation value has a value larger than the threshold value (S207). Here, the threshold value is selected between 0 and 1 in consideration of the error probability obtained by the experiment. Normalized correlation value (

) Is greater than the threshold, the polygon line

The Bipolar Watermark

It is determined that the included (S209).

Looking at this process in more detail as follows.

[Equation 6]

를 정의하고 있다. 만약 폴리곤 라인

이

(여기서,

)으로 워터마킹되었다면, 상기 수학식 6은 다음과 같이 정리된다.Equation 6 is the correlation value mentioned above

It defines. If the polygon line

this

(here,

Equation 6 is summarized as follows.

[Equation 7]

이

로 워터마킹되었다면, 수학식 6은 다음과 같이 표현된다.Conversely, polygon lines

this

Equation 6 is expressed as follows.

[Equation 8]

및

가 독립적임과 아울러 동일하게 분포된 무작위 변수이며, 또한

가 제로 평균값을 가지고 있다고 가정하면, 상관값

의 평균

는 아래와 같다.Also,

And

Are independent and equally distributed random variables,

Is a zero mean value, the correlation

Average of

Is shown below.

[Equation 9]

를 평균

로 나누어, 상관값

를 [0, 1]의 범위 내로 정규화한다. 이러한 경우, 정규화된 상관값

은

가 된다.In the present invention, the correlation value

Average

Divided by

Normalize to within the range of [0, 1]. In this case, the normalized correlation value

silver

Becomes

를 모르는 상태이다. 그러나

가 제로 평균값을 가지고 있다는 가정 하에서는 다음의 수학식이 만족된다.Meanwhile, the present invention is based on blind watermarking. Therefore, wavelet coefficients of the original polygon line during watermark detection

I do not know. But

Assuming that has a mean value of zero, the following equation is satisfied.

[Equation 10]

인 이상적인 경우에 정규화된 상관값

는 1이 된다. 즉, 정규화된 상관값

의 값이 1이라면, 폴리곤 라인

에는 바이폴라 워터마크

가 삽입되어 있는 것이다. 여기서, 정규화된 상관값

는 가해지는 공격에 의해 값이 1보다 작아지는 경우가 발생하게 된다. 따라서 앞서 언급한 임계값이 고려되며, 이는 공격과 그에 해당하는 에러 확률을 실험적으로 계산하여 정하게 된다. 다시 말해,

가 이 임계값보다 큰 경우, 워터마크

가 삽입된 것이고,

가 임계값보다 작은 경우, 워터마크

가 삽입되지 않은 것이다.In other words,

Normalized Correlation Values for Ideal Cases

Becomes 1 That is, the normalized correlation value

If is a value of 1, then the polygon line

The Bipolar Watermark

Is inserted. Where the normalized correlation value

Is a value less than 1 due to the attack. Therefore, the aforementioned threshold is considered, which is determined by experimentally calculating the attack and the corresponding error probability. In other words,

Is greater than this threshold, the watermark

Is inserted,

Is less than the threshold, the watermark

Is not inserted.

Meanwhile, the above-described line watermarking method of the present invention may be implemented through a program for executing the functions of the processes S100 and S200 or a recording medium on which the program is recorded.

4. 'RST attack' and 'local deformation attack'

The RST attack on the polygon line can be made through modification of the wavelet coefficients as described above. Hereinafter, a rotation attack, a scaling attack, a translation attack, and a local deformation attack will be described.

4.1. Scaling attacks

The scaling of the polygon line is represented by the following equation (11).

[Equation 11]

,

,

및

에 동일 스케일링 팩터

가 스케일링된다는 것을 의미한다.Equation 11 above uses the linearity of the wavelet transform, thereby providing a wavelet coefficient given by Equations 3 and 4.

,

,

And

Same scaling factor

Means that is to be scaled.

Meanwhile, the polar coordinates relationship of the wavelet coefficients is expressed by Equations 12 and 13 below.

[Equation 12]

[Equation 13]

에 의해 스케일링되더라도, 위상은 바뀌지 않는다는 것을 알 수 있다.Looking at Equations 12 and 13,

It can be seen that even if scaled by, the phase does not change.

를 원 폴리곤 라인의 웨이블릿 계수라 하면,

로 스케일링된 폴리곤 라인에서 웨이블릿 계수의 크기는

이다. 그리고 스케일링된 폴리곤 라인에 대한 상관값

는 다음과 같다.here,

If is the wavelet coefficient of the original polygon line,

For polygon lines scaled by, the magnitude of the wavelet coefficient

to be. And correlation values for scaled polygon lines

Is as follows.

[Equation 14]

는 다음과 같다.In addition, the normalized correlation value

Is as follows.

[Equation 15]

는 앞서 살펴본

와 동일하다. 왜냐하면, 분자

와 분모가 모두

에 의해 곱해지기 때문이다. 따라서 본 발명의 라인 워터마킹 방법은 스케일링 공격에 강건하다는 것을 알 수 있다.Normalized correlation value in Equation 15 above

As we saw earlier

Is the same as Because, molecule

And the denominator

Is multiplied by. Therefore, it can be seen that the line watermarking method of the present invention is robust to scaling attacks.

4.2. Moving attack

The displacement on the polygon line only affects the approximation coefficient. The movement is summarized by the following equation (16).

[Equation 16]

[Equation 17]

,

에 관한 극좌표 관계는 다음과 같다.And wavelet coefficient of the detail signal.

,

The polar coordinate relationship for is

Equation 18

[Equation 19]

That is, the line watermarking method of the present invention uses the detailed coefficients, and the coefficients are invariant in the movement and thus are robust to the movement attack.

4.3. Spinning attack

만큼 회전한 폴리곤 라인에 관해서는 다음과 같이 표현된다.Counterclockwise angle with center pivot point

Regarding the polygon lines rotated by much, they are expressed as follows.

[Equation 20]

[Equation 21]

Such rotation is expressed in polar coordinates, and it is convenient to derive the wavelet coefficient of the detailed signal by the following equation (22).

[Equation 22]

Looking at Equation 22, even if the rotation is made does not affect the size of the wavelet descriptor. Therefore, it can be seen that the line watermarking method of the present invention is robust against rotational attack.

4.4. Local deformation attack

및 이에 대응하는 웨이블릿 프레임 표현을 고려해 본다. The wavelet descriptor has a stability characteristic, meaning that a small difference in the shape of the polygon line (curve) corresponds to a small difference in its representation or vice versa. Square-integrable functions to generalize this

And a wavelet frame representation corresponding thereto.

[Equation 23]

내의 프레임을 구성하도록

를 선택함으로써,

인 경우에는 아래의 수학식 24를 얻을 수 있다.The function of Equation 23 is

To organize the frames within

By selecting

In the case of the following equation (24) can be obtained.

[Equation 24]

The Euclidean norm (2-norm) of the wavelet expression is defined as

[Equation 25]

If the two representations are close to each other, it is readily understood that the curves (polygon lines) they represent will also be similar. The importance of the stability measure is that slight changes in the shape of the curve will not cause large changes in the wavelet representation, as a result ensuring that the wavelet representation is stable against local deformation. On the other hand, the basic function of a Fourier descriptor is a sine curve that is both periodic and wide (not sufficiently local in space), so that a small perturbation of one coefficient affects the overall contour of the shape. That means that small changes in shape will also affect the overall modulus.

5. Experimental Example

The polygon line in the experimental image shown in FIG. 3 is a polygon line with 1,744 vertices. In FIG. 3, (a) is an image before watermarking, and (b) is an image after watermarking. The difference between the two is difficult to visually identify.

5.1. RST attack

To demonstrate the robustness of the method to geometric distortion, an RST attack was applied to vector graphic images with watermarked polygon lines. The experimental distribution of the normalized correlator of 1,000 watermark detections (left) with incorrect keys and 1000 watermark detections with correct keys was tested using several keys. 4 (a).

The experimental distribution after moving the polygon line by -100 pixels on the x-axis and 200 pixels on the y-axis is shown in FIG. 4B. Experimental distribution after 0.5-fold scaling and 30 degree rotation is shown in FIGS. 4C and 4D, respectively.

For RST attacks, the experimental distribution of the line watermarking method according to the present invention represents a well separated probability-distribution-function (PDF). By carefully selecting the false error probability threshold, the line watermarking method according to the present method will generate extremely low detection error and good detection performance. The results support the robustness against these RST attacks.

5.2. Local deformation attack

In order to prove robustness to local deformation, the local portion of the watermarked polygon line was modified as shown in FIG. 5. In FIG. 5A, approximately 10% of adjacent vertices around (150, 50) were moved by -20 pixels on the x axis and by +20 pixels on the y axis. The modified part is referred to as an arrow in FIG. 5 (b).

The watermarked polygon lines were changed in the same way by using the Fourier descriptor.

Experimental distributions from the method according to the invention using wavelet descriptors and the method using Fourier descriptors are shown in FIGS. 5 (c) and 5 (d), respectively. It can be seen that the correlation PDF of the method according to the invention using wavelet descriptors is well separated.

Normalized mean correlation values for the correct and inaccurate portions were 0.8306 and 0.0016, respectively. However, the detection performance according to the method using the Fourier descriptor was not as good as the present invention. The normalized mean correlation values for the correct and inaccurate portions were 0.1638 and 0.0016, respectively. These distributions of correlation output support the assertion that for localized attack, the watermarking method of the present invention is more efficient than the method using Fourier descriptors.

1 and 2 are schematic flowcharts showing a line watermarking method according to the present invention;

3 is an experimental image before watermarking and an experimental image after watermarking.

4 is an experimental probability distribution plot of normalized correlation output for 1,000 watermarked polygon lines with incorrect keys and correct keys.

5 is an experimental probability distribution plot of normalized correlation output of watermarked lines, locally modified lines, and 1,000 polygon lines watermarked using incorrect and correct keys.

Claims (8)

Wavelet transforming a polygon line in the image to be inserted using the wavelet descriptor; Generating a random number sequence having a value of ± 1 as a bipolar watermark; Inserting the bipolar watermark into a wavelet coefficient of the wavelet transformed polygon line; Performing a fourth wavelet transform on the wavelet transformed polygon line to reflect the watermarked polygon line on the insertion target image; A fifth step of wavelet transforming the polygon lines in the detection target image using the wavelet descriptor; A sixth step of calculating a correlation value between the bipolar watermark of the second step and the wavelet coefficients of the wavelet transformed polygon line according to the fifth step; A seventh step of calculating a normalized correlation value by dividing the correlation value by an average of correlation values; And An eighth step of determining that a watermark is detected when the normalized correlation value is larger than a threshold value; Line watermarking method comprising a. The method according to claim 1, The bipolar watermark is, Line watermarking method characterized in that it has a zero mean value and unit variance. The method according to claim 1, The bipolar watermark of the third step, Line watermarking method, characterized in that inserted into the magnitude of the wavelet coefficient in consideration of the strength factor. The method according to claim 3, And said intensity factor is less than one. delete The method according to claim 1, The threshold value is a value considering an experimental error probability, and is a value between 0 and 1, wherein the line watermarking method. A first function of wavelet transforming the polygon lines in the object to be inserted using the wavelet descriptor; A second function of generating a random number sequence of ± 1 values as a bipolar watermark; A third function of inserting the bipolar watermark into the wavelet coefficients of the wavelet transformed polygon line; And A fourth function of inverse wavelet transforming the wavelet transformed polygon line to reflect the watermarked polygon line in the embedding target image; Consists of a computer with recorded programs, including The program may include a fifth function of wavelet transforming a polygon line in a detection target image using a wavelet descriptor, and a correlation value between the wavelet coefficients of the bipolar watermark of the second function and the wavelet transformed polygon line by the fifth function. A sixth function for calculating, a seventh function for calculating a normalized correlation value by dividing the correlation value by an average of correlation values, and an eighth function for determining that a watermark is detected when the normalized correlation value is greater than a threshold value ; Record medium comprising a. delete

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