KR100940451B1 - Apparatus for watermarking 3d mesh model using spherical surface parameter technique and method thereof - Google Patents

Abstract

The watermarking method of the 3D mesh model using the spherical parameter technique is to set the coordinates of the 3D mesh model to the Cartesian coordinate system, convert the coordinates of the 3D mesh model set to the Cartesian coordinate system into the spherical coordinate system, and convert the coordinates into the spherical coordinate system. Applying a spherical parameter technique to the three-dimensional mesh model, and inserting a watermark into the three-dimensional mesh model to which the spherical parameter technique is applied. Spherical parameter technique is widely applied in 3D data processing and can effectively analyze and process the vertex coordinates of 3D mesh model that cannot be determined in Cartesian coordinate system after applying spherical parameter technique. In other words, by using the spherical parameter technique, the geometric and phase information characteristics of the 3D mesh model are analyzed in the spherical model, and the watermark is inserted through the addition of vertices and the correction of the phase information. This algorithm can be used as a watermarking algorithm for copyright protection, and can also be used as a mesh segmentation algorithm that is robust against smoothing attacks.

3D mesh model, spherical coordinate system, Cartesian coordinate system, spherical parameterization, watermarking

Description

APPARATUS FOR WATERMARKING 3D MESH MODEL USING SPHERICAL SURFACE PARAMETER TECHNIQUE AND METHOD THEREOF}

The present invention relates to an apparatus and method for inserting / extracting watermarks for three-dimensional images. More particularly, the present invention analyzes the characteristics of a three-dimensional mesh model that cannot be determined in a Cartesian coordinate system by applying spherical parameter techniques to insert a watermark. Device and method for extracting.

Recently, various forms of digital works have appeared in accordance with the provision and distribution of information using the Internet. However, digital works have many problems in copyright protection due to their characteristics. It is easy to store or convert information, so that a large amount of copying is possible without any limitation in open spaces such as the Internet, and after copying, it not only maintains the same data information as the original, but also distributes without the author's consent. The reality is that it is difficult to protect.

This problem of copyright infringement is increasing in seriousness, and many legal, institutional and technical solutions have been devised. To this end, a digital watermarking technology for encrypting data to allow a specific user to access the information and a digital watermarking technology to conceal copyright information on the data and transmit the copyright information to the user so that the data is not externally modified. It is a technical solution to solve the problems mentioned in.

In other words, watermarking is a copyright protection technology for digital data and may be referred to as a copyright display and verification technology for digital content. More specifically, watermarking is a method of concealing copyright information to data and re-detecting the concealed copyright information to detect tampering and forgery of the data and to claim ownership of the author.

In the early stage of the development of watermarking technology, watermark embedding / extraction device for 2D image was mainly used, but recently 3D image is widely used in CAD, animation, virtual reality, etc. Research into inserting this decipherable information and using it as a basis for copyright has been actively conducted.

One of the widely used expression apparatus for 3D images is a mesh structure. The mesh structure basically consists of vertices and information connecting them. In order to insert information into the mesh structure, some modifications are made to the vertices and the connection information. However, even in the same model, the three-dimensional image has an infinite combination of expression methods, that is, coordinates of vertices and connection information. In addition, conversion of rotation, translation, etc. is possible. It is a big challenge to ensure that hidden information (watermarks) inserted in such a high degree of freedom 3D image survives the transformations and intentional attacks that are routinely applied.

As one of the watermark insertion / extraction apparatuses for the 3D mesh model, there is a device that inserts / extracts the watermark from the Cartesian coordinate system based on the coordinate point with respect to the 3D image. There is a need for a watermark insertion / extraction device, which will be described below.

It is an object of the present invention to provide an apparatus and method for inserting a watermart into a three-dimensional mesh model.

Another object of the present invention is to provide an apparatus and method for embedding a watermark in a three-dimensional mesh model that cannot be determined in a rectangular coordinate system.

It is still another object of the present invention to provide an apparatus and method for inserting a watermark into a 3D image using a spherical coordinate system that is robust to transformation such as rotation or translation of the 3D image.

Still another object of the present invention is to provide a watermark embedding apparatus and method for extracting a watermark without an original.

It is still another object of the present invention to provide a mesh refinement method and apparatus for preventing the tendency of the volume of the model to be excessively deformed during the smoothing process of the mesh model.

One embodiment of the present invention, the step of setting the coordinates of the three-dimensional mesh model in the Cartesian coordinate system, converting the coordinates of the three-dimensional mesh model set in the Cartesian coordinate system to the spherical coordinate system, spherical parameters in the mesh model converted to the spherical coordinate system And applying a watermark to the three-dimensional mesh model to which the spherical parameter technique is applied.

In addition, another embodiment of the present invention, the step of setting the coordinates of the three-dimensional mesh model to the Cartesian coordinate system, the reference vertex is set as the center point of the spherical coordinate system, and based on the center point of the set spherical coordinate system, the three-dimensional mesh Converting model coordinates into spherical coordinate system, and applying spherical parameter technique to mesh model converted to spherical coordinate system using latitude (θ) and longitude (Ψ) among the variables of spherical coordinate system (r, θ, Ψ) And generating watermark information, dividing the mesh model, and inserting the watermark into the divided mesh model.

을 계산한 후, 삽입하려는 정보가 1 이면,

을 계산하고, 삽입하려는 정보가 0 이면,

을 계산한 후, 꼭지점 (l) 을 메쉬 모델에 추가하고 면 정보를 수정한 후, 메쉬 모델의 부분 집합 전체에 대해 상기 과정들을 반복한 후, 분할된 부분 집합들을 재구성하여 워터마킹된 메쉬 모델을 획득하는, 워터마크 삽입 단계를 포함하는 워터마크 삽입 방법이다. (여기서,

는 각각 원래의 3 차원 메쉬 모델의 세 꼭지점 (i,j,k) 의 구면좌표임.)Further, another embodiment of the present invention, the step of setting the coordinates of the three-dimensional mesh model in the Cartesian coordinate system, the step of converting the coordinates of the three-dimensional mesh model set in the Cartesian coordinate system to the spherical coordinate system, the mesh model converted to the spherical coordinate system Applying a spherical parameter technique to the, and

After calculating, if the information you want to insert is 1,

If the information you want to insert is 0,

After calculating, add the vertex ( l ) to the mesh model, modify the face information, repeat the above steps for the entire subset of the mesh model, and then reconstruct the divided subsets to form a watermarked mesh model. A watermark embedding method comprising the step of obtaining a watermark. (here,

Are the spherical coordinates of the three vertices (i, j, k) of the original three-dimensional mesh model.)

인 꼭지점들을 선택하는 단계, 선택한 꼭지점들의 질량 중심을 구하고, 질량 중심을 구면 좌표계의 중심점으로 설정하는 단계, 메쉬 모델을 질량 중심으로 이동하여, 구면 파라미터기법을 적용하는 단계, 꼭지점 l 과 꼭지점 i 및 j 가 이루는 삼각면의 면적, 꼭지점 l 과 꼭지점 j 및 k 가 이루는 삼각면의 면적, 및 꼭지점 l 과 꼭지점 k 및 i 가 이루는 삼각면의 면적을 구하고, 삼각면의 면적들이 같으면 워터마크가 삽입되었다고 판단하는 단계, 및 메쉬 모델의 꼭지점

에 대해,

를 구하여,

이면

=1 로,

이면

=0 으로 판정함으로써 워터마크를 추출하는 단계를 포함하는, 워터마크 추출 방법이다. (다만, 꼭지점

={i} 와 인접한 꼭지점의 집합을

={i} 의 1-링 이라 하며

로 표시하고,

의 인접 꼭지점의 개수를 1-링 값이라고 하며

로 표시함. 또한,

는 메쉬 모델의 내부 꼭지점에서 1-링 값이

=12,

=6 인 꼭지점을 제거한 집합을 의미하며,

는 메쉬 모델의 경계 꼭지점에서

=7 인 꼭지점을 제거한 집합을 의미함.)Further, another embodiment of the present invention is to obtain a 1-ring value of each vertex in the three-dimensional mesh model, based on the 1-ring value of the vertices,

Selecting vertices, obtaining the center of mass of the selected vertices, setting the center of mass to the center of the spherical coordinate system, moving the mesh model to the center of mass, applying spherical parametric techniques, vertices l and vertices i, and Find the area of the triangle formed by j, the area of the triangle formed by vertices l and vertices j and k, and the area of the triangle formed by vertices l and vertices k and i. Determining, and the vertices of the mesh model

About,

To obtain

Back side

= 1,

Back side

And extracting the watermark by judging = 0. (But vertex

sets a set of vertices adjacent to = {i}

is called the 1-ring of = {i}

, And

The number of adjacent vertices in is called the 1-ring value.

Marked as. Also,

Is a 1-ring value at the inner vertices of the mesh model.

= 12,

Means a set with no vertices = 6,

At the boundary vertex of the mesh model

Means a set with no vertices = 7)

The present invention provides a method of effectively inserting a watermark into a three-dimensional mesh model that cannot be determined in a rectangular coordinate system by effectively using the characteristics of vertex coordinates using spherical parameter techniques. In addition, when the watermark is inserted in the above-described manner, the present invention can extract the watermark information of the 3D image without the need for the original. In addition, the present invention provides a watermark method and apparatus that is robust to typical geometric transformations such as movement, scaling, and rotation, maintains robustness in mesh ordering, file format conversion, and shows good performance in attacks such as smoothing.

The present invention relates to a method of embedding a watermark in a 3D mesh model using a spherical parameter technique and a method of extracting a watermark from a model having a watermark embedded therein. Take a look.

I. 3d Mesh  Model concept

1 illustrates components of vertices, edges, and triangular faces that form a triangular mesh model. Here, the vertex is usually expressed in the coordinates of the vertex, the edge (side) is represented by the connection of the two vertices, the triangle face is represented by the connection of the three vertices, but in some cases the vertex may be represented by the corner table or polygonal table , The corner may be represented by two triangular surfaces meet, and the triangular surface may be represented by three corners.

2 shows a mesh model represented by vertices, edges, and triangles according to a process. FIG. 2 (a) shows a mesh model of a "man" model represented only by vertices, and FIG. 2 (b) shows a mesh model of a "man" model expressed using vertices and the sides formed following these vertices. 2 (c) shows a mesh model of a “man” model expressed using vertices, the sides formed by the vertices, and the faces formed by the sides, and FIG. 2 (d) shows the completed model. .

은 식 (1) 과 같이 표시할 수 있다. Hereinafter, the mathematical expression of the mesh model will be described based on the basic concept of the mesh model as described above. Triangular mesh model

Can be expressed as in Equation (1).

=(

,

,

) 식 (1)

= (

,

,

) Equation (1)

={1,2,,|M|} 은 꼭지점의 집합 (|M|은 꼭지점의 개수) 을 나타내며,

은 위상정보, 즉, 각 꼭지점들의 연결 상태 정보를 나타내고,

은

상의 n 차원 벡터를 나타내며 식 (2) 와 같이 표시할 수 있다. here

= {1,2 ,, | M |} represents a set of vertices (| M | is the number of vertices),

Represents phase information, that is, connection state information of each vertex,

silver

It represents the n-dimensional vector of the phase and can be expressed as Equation (2).

={

|

} 식 (2)

= {

|

} Expression (2)

={

,

,...,

}는 꼭지점 {

}와 관련된 위치 좌표, 법선 벡터, 칼라정보, Texture Map 정보 등의 속성을 나타내는 벡터이다. 즉,

은 삼각 메쉬 모델

의 모든 기하학적 정보를 담고 있다.here

= {

,

, ...,

} Is the vertex {

} This is a vector representing properties such as position coordinates, normal vector, color information, and texture map information. In other words,

Silver triangular mesh model

Contains all of the geometric information.

에는 꼭지점

={

}

, 변

={

,

}

, 면

={

,

,

}

등 세 개의 기본 정보가 포함되어 있다. 만약 {

,}

이면 {

}와 {

}는 인접한 꼭지점이다.

There is a vertex

= {

}

, Side

= {

,

}

, Cotton

= {

,

,

}

And three basic pieces of information. if {

, }

If {

}Wow {

} Is an adjacent vertex.

={

}와 인접한 꼭지점의 집합을

={

}의 1-링 (ring) 이라 하며

={

{

,

}

} 로 표시하고, 꼭지점

의 인접 꼭지점의 개수를 1-링 값이라고 하며

로 표시한다.At this point

= {

} A set of vertices adjacent to

= {

} Is called the 1-ring

= {

{

,

}

}, Vertex

The number of adjacent vertices in is called the 1-ring value.

To be displayed.

Although only the triangular mesh model is referred to here, the present invention is not limited to the triangular mesh model because the polygon mesh model and the like are all convertible to the triangular mesh model.

Hereinafter, a method of inserting a watermark using a spherical parameter technique to a 3D mesh model defined by these concepts will be described in detail.

II. Watermarking Using Spherical Parameter Techniques

에서 선택한 기준 꼭지점의 질량중심을 구하고 모델을 질량중심으로 옮기는 단계, 구면 파라미터기법 적용 단계, 구면 변환 후 변수 (θ, Ψ) 에 근거한 부분집합으로의 분할 단계, 워터마크 정보의 생성 및 워터마크 삽입 단계를 포함할 수 있는바, 이하에서는 이들 단계에 대해 순차적으로 살펴보도록 한다. Here, we will see how the spherical parameter technique is used for watermarking. Spherical parameter technique is widely used in 3D data processing technology. In particular, this technique can be especially useful for the vertex coordinate characteristics of three-dimensional mesh models that cannot be determined in Cartesian coordinate systems. The present invention applies a spherical parameter technique to be described below after converting from the Cartesian coordinate system to the spherical coordinate system by setting the center of mass of the three-dimensional model as the origin of the spherical coordinate. The watermark analyzes the characteristics of geometric and topological information of the 3D model in the spherical model and inserts them through the addition / change of vertices. The present invention is a reference vertex setting step by the 1-ring search of the vertex, mesh model

Finding the center of mass of the reference vertices selected from and moving the model to the center of mass, applying the spherical parameter technique, splitting into subsets based on the variables (θ, Ψ) after spherical transformation, generating watermark information, and inserting watermarks Bars may include steps, which will be described below with respect to these steps.

1. Reference vertex and center of mass

Criteria vertex selection aims to find the center point of a sphere that is not affected by a general attack. This paper focuses on finding a center point that does not change in mesh segmentation attacks that are commonly used in 3D mesh models.

The mesh segmentation algorithm can be divided into segmentation by approximation and segmentation by interpolation. In mesh segmentation, iterative segmentation creates new surfaces. In general, segmentation can be divided into segmentation process and positioning process. The segmentation process is the process of adding new points to the mesh model. The positioning process is a process of newly constructing the topological information of each vertex based on the added vertex and the existing vertex after segmentation.

= 4 이고 내부 꼭지점 (이하에서 정의됨.) 일 경우

= 6 이다. 일 회의 적용으로 삼각면의 수는 네 배가 된다. 즉, 도 3 에서 꼭지점 삽입 전에 삼각면의 수는 9 개이고, 1 회의 꼭지점 삽입 후에 삼각면의 수는 36 개임을 확인할 수 있다.3 shows an example of a loop subdivision surface method as a method of subdivision by representative approximation. The quad split method is applied to the loop split plane method. Insert the vertices on all sides, split the sides into two, and connect them newly to divide the original triangle into four smaller triangles. The 1-ring value of the inserted vertex (black) is the boundary vertex (defined below).

= 4 and inner vertices (defined below)

= 6 In one application, the number of triangles is quadrupled. That is, in FIG. 3, the number of the triangular surfaces before the insertion of the vertices is nine, and the number of the triangular surfaces after the insertion of one vertex is 36.

= 4 이고 내부 꼭지점일 경우

= 6 이다.4 illustrates an example of a butterfly subdivision surface method as a method of mesh subdivision by representative interpolation. As with the loop split method, the butterfly split method is applied to the 4 division method and the additional vertex is set by applying the interpolation method from the surrounding vertex coordinates. The insertion method of a vertex is a butterfly scheme using eight surrounding vertices. The butterfly dividing plane inserts a new point into the symmetrical edge. If you find a new insertion point for the four surrounding edges, one triangle is replaced by four new triangles, and the generated surface becomes a surface capable of first derivative (C ¹ Surface). However, the non-division algorithm, like the loop dividing surface, is a boundary vertex if the 1-ring value of the inserted vertex is the boundary vertex.

= 4 and inside vertices

= 6

Considering the mesh refinement, we select the reference vertices in the following way.

개의 꼭지점을 두 개의 집합으로 분류한다. 1) mesh model

Classify vertices into two sets.

,

,

={

,

}

일 때, 적어도 두 개의 꼭지점

,

가 존재하여 {

,

,

}

, {

,

,

}

이면 이와 같은 꼭지점

,

의 집합을 내부 꼭지점이라고 하며

로 표시한다.

,

,

= {

,

}

At least two vertices

,

Is present {

,

,

}

, {

,

,

}

Vertices like this

,

Is a set of internal vertices,

To be displayed.

,

,

={

,

}

일 때,

이 존재하여 {

,

,

}

이 성립되며,

에서

과 같은 다른 꼭지점이 존재하지 않으면 이런 꼭지점의 집합을 경계 꼭지점 집합이라고 하며

로 표시한다. 따라서 메쉬 모델의 꼭지점은

=

와 같이 표시할 수 있다.

,

,

= {

,

}

when,

Is present {

,

,

}

Is established,

in

If no other vertices exist, such a set of vertices is called a boundary vertex set.

To be displayed. So the vertex of the mesh model

=

Can be displayed as:

에서 1-링 값이

=6,

=3 인 꼭지점을 제거하고 그 집합을

라 하며

에서 1-링 값이

=4 인 꼭지점을 제거하고 그 집합을

라고 한다. 집합

의 원소 개수(꼭지점 의 개수)를

라고 한다. 2) assembly of vertices

1-ring value in

= 6,

Remove the vertex with = 3 and set that set

And

1-ring value in

Remove the vertex that = 4 and set that set

It is called. set

The number of elements in (number of vertices)

It is called.

에 속하는 꼭지점들의 질량 중심을 구면좌표계의 원점으로 설정한다. 설정된 구면좌표계의 중심점을 (

,

,

)라고 하면,

,

,

는 식 (3) 과 같이 표현된다. 여기서, (

,

,

) 는 꼭지점

={

} 의 좌표이다.3)

Set the center of mass of the vertices belonging to the origin of the spherical coordinate system. The center point of the set spherical coordinate system

,

,

),

,

,

Is expressed as equation (3). here, (

,

,

) Is a vertex

= {

} The coordinates of.

=

,

=

,

=

식 (3)

=

,

=

,

=

Formula (3)

2. Spherical Parameter Technique

(위도),

(경도) 만 처리하면 된다. 여기서는 직교좌표계에서 구면좌표계로의 변환을 "cart2sph" 로, 구면좌표계에서 직교좌표계로의 변환을 “sph2cart" 라고 표시한다. 구면좌표계는 보통 (

,

,

) 로 나타낸다. 도 5 에는 이러한 구면좌표계의 좌표 (r,

,

) 를 도시하고 있다. 여기서

은 원점에서부터의 거리로서,

범위의 값을 갖고,

축에서의 각도

는

,

축을 축으로 하여

축에서부터 돌아간 각

는

의 값을 갖는다. 아래의 식 (4) 및 식 (5) 에 의해 직교좌표계로부터 구면좌표계를, 구면좌표계로부터 직교좌표계를 얻을 수 있다. Spherical parameter technique is to find 1: 1 mapping from model to sphere. In 2003, Gotsman applied spherical parameterization to a model with Genus = 0 in Cartesian coordinates. (Genus is a term that mathematically expresses the number of handles or rings on a quadratic surface.) The center vertex of the 1-ring, the convex combination point of the boundary of the 1-ring, and the center of the sphere are on a straight line. Using the property of laying, some vertices on the sphere were fixed and then a system of equations for other vertices was established and solutions were used. This method is simple and intuitive, but it has a disadvantage of being difficult to solve because of the nonlinear system of equations and a large amount of calculation. There is also a phenomenon in which a partial point is degenerated into a circle rather than a sphere. A sphere is a special two-dimensional surface that exists in three-dimensional space. If you apply spherical coordinate system, the distance from spherical center is replaced by constants

(Latitude),

(Hardness) only need to be processed. Here, the transformation from Cartesian coordinate system to spherical coordinate system is called "cart2sph", and the transformation from spherical coordinate system to Cartesian coordinate system is called "sph2cart".

,

,

). 5 shows coordinates of this spherical coordinate system (r,

,

) Is shown. here

Is the distance from the origin,

Has a range of values,

Angle from axis

Is

,

On the axis

Angle from the axis

Is

Has the value of. According to the following equations (4) and (5), a spherical coordinate system can be obtained from a rectangular coordinate system and a rectangular coordinate system can be obtained from a spherical coordinate system.

식 (4)

Formula (4)

식 (5)

Equation (5)

=1 로 설정하고, 식 (5) 를 이용하여 구면좌표계 상의 구면좌표를 직교좌표계 상의 직교 좌표로 변환함으로써 구면파라미터 기법을 적용한다. Referring to the step of applying the spherical parameter technique, first, the mesh model is moved to the center point set by Equation (3), and the vertex coordinate values of the moved mesh model are converted into spherical coordinates in the spherical coordinate system. In the spherical coordinate system

Spherical parameter technique is applied by setting = 1 and converting spherical coordinates in the spherical coordinate system to rectangular coordinates in the rectangular coordinate system using equation (5).

6 (a) and 6 (b) show an example in which the "man" model before the application of the spherical parameter technique is compared with the "man" model after the application. (1) to (7) of FIG. 6 (a) show the mesh structure and vertex distribution of the "man" model before applying the spherical parameter technique, and (1 ') to (7') of FIG. We show the mesh structure and vertex distribution of the "man" model after applying parametric techniques. (A) of FIG. 6 (a) and (1 ') of FIG. 6 (b) show the completed models before and after application of the spherical parameter technique, respectively, (2) to (4) and FIG. (2 ') to (4') of 6 (b) show the mesh models of vertices and sides before and after applying the spherical parameter technique, respectively, (5) to (7) and 6 ( (5 ') ~ (7') of b) show each mesh model consisting of vertices before and after applying spherical parameter technique.

3. Insert watermark

After applying the spherical parameter technique, the model to which the spherical parameter technique is applied is divided into several sets based on the amount of watermark information, and then watermark information is inserted into the divided sets.

3.1 Create Watermark Information

이라고 하면

은 식 (8) 과 같다. 삽입강도를 위하여 삽입 정보의 최대 길이는 64bit 로 한정한다.According to an embodiment of the present invention, a random bit string having a multiple length of 2 is generated and used as watermark information. FIG. 7 illustrates an embodiment (when n = 3) in which watermark information is oversampled and inserted into each part of the divided mesh model. Watermark information

Speaking of

Is the same as (8). For the insertion strength, the maximum length of the insertion information is limited to 64 bits.

, 여기서

{0, 1},

=2ⁿ 식 (8)

, here

{0, 1},

= 2 ⁿ expressions (8)

=2³, w₁= 1, w₂=1, w₃=0, w₄=0, w₅=1, w₆=0, w₇=0, w₈=1 이며, 따라서 W₃={1,1,0,0,1,0,0,1} 임을 확인할 수 있다. In the embodiment of FIG. 7, n = 3,

= 2 ³ , w ₁ = 1, w ₂ = 1, w ₃ = 0, w ₄ = 0, w ₅ = 1, w ₆ = 0, w ₇ = 0, w ₈ = 1, so W ₃ = { 1,1,0,0,1,0,0,1}.

3.2 Splitting a Mesh Model

(위도)와

(경도)의 값에 따라 부분집합으로 분할한다. 부분집합의 인덱스는

의 분할개수와

의 분할개수를 인덱스로 사용하여

으로 표시한다. 분할 방법은 표 1 과 같다.Parameterized mesh model

(Latitude) and

Divide into subsets according to the value of (hardness). The index of the subset is

The number of divisions

Using the number of partitions as an index

Indicated by. The division method is shown in Table 1.

Division unit

) Division unit

)       Division number         n = 1

          -         2         n = 2

/2           -         4         n = 3

/4           -         8         n = 4

/4

/2         16         n = 5

/4

/4         32         n = 6

/8

/4         64

이며, 이들 워터마크 정보는 각각 분할된 메쉬모델의 부분집합

,

,

,

,

,

,

,

에 삽입된다. 각 부분집합에는 오버 샘플링된 후의 워터마크 정보가 삽입된다.FIG. 8 shows, as one embodiment, a vertex distribution in the case where the “man” model is parameterized and then divided into eight subsets (when n = 3). If n = 3, the watermark information to insert is

The watermark information is a subset of each divided mesh model.

,

,

,

,

,

,

,

Is inserted into Watermark information after oversampling is inserted into each subset.

3.3 Watermark embedding algorithm

(도 9 (b)) 이고, 삽입되는 꼭지점을

이라고 하면, 꼭지점

삽입 후에는, 새로운 세 개의 면

이 구성된다 (도 9 (c)). 즉, 꼭지점 삽입 전과 후의 삼각면은 식 (9) 과 같다. 9 illustrates a method of adding a vertex in a method of inserting a watermark in a model to which a spherical parameter technique is applied. 9 (a) shows that a triangular plane consisting of vertices i, j, k exists as part of the mesh model. 9 (b) shows that only a triangular plane consisting of vertices i, j, and k is selected in the divided mesh model. The original triangle

(Fig. 9 (b)), the vertex to be inserted

Speaking of vertices

After insertion, three new sides

This is constituted (Fig. 9 (c)). In other words, the triangular plane before and after insertion of the vertex is as shown in Equation (9).

식 (9)

Formula (9)

은 공유하는 면이 적어도 두 개 존재하기 때문에, 추가되는 점은 메쉬 모델의 내부 꼭지점임을 알 수 있다. 세 개의 삼각면 (

) 이 추가된 후,

는 메쉬 모델에서 사용되지 않는다. 삼각 면

에 추가되는 꼭지점

은 세 꼭지점

의 질량 중심으로 설정하며 좌표값은 다음과 같다.Fig. 9 (d) shows again the triangular plane consisting of vertices i, j, k with new vertices inserted in this way as part of the original mesh model. Newly added side

Since there are at least two faces that share the silver, it can be seen that the added point is the inner vertex of the mesh model. Three triangular planes (

) Is added,

Is not used in the mesh model. Triangle

Vertex added to

Silver three vertices

Set to the center of mass of. The coordinates are as follows.

의 구면파라미터기법 적용 후 값을 각각

라고 할 경우, 추가되는 꼭지점의 좌표

는 식 (10) 과 같다.1) triangular

After applying the spherical parameter technique of,

Is the coordinate of the added vertex.

Is the same as (10).

식 (10)

Formula (10)

를 다음과 같이 변경하여 워터마크를 삽입한다. 삽입강도는

값에 의하여 결정된다. 2) Coordinates of added vertices

Change as follows to insert a watermark. Insertion strength

Determined by the value.

의 구면좌표

에서

로 구한다. Step 1: Three Vertices of the Circle Mesh Model

Spherical coordinates

in

Obtain as

Step 2: If the information you want to insert is "1"

이고,

ego,

If the information to insert is "0"

이다.

to be.

Step 3: After adding the vertices to the mesh model, modify the information on the face as follows:

Step 4: Repeat steps 1 through 3 for all subsets of the mesh model.

Step 5: Reconstruct the partitioned subset to obtain a watermarked mesh model.

3.4 Watermark Extraction Algorithm

Watermark extraction is a reverse process of the watermark embedding algorithm. Since the present invention uses the center of mass, the watermark can be detected by various methods.

In the watermark extraction method, first, predetermined vertices are selected from a mesh model, the center of mass of the selected vertices is obtained, the mesh model is moved to the center of mass, and then spherical parameter techniques are applied. Thereafter, it is determined whether the watermark is inserted in each vertex, and when it is determined that the watermark is inserted, the watermark is extracted. When it is determined that the watermark is not inserted, it is determined whether the watermark is embedded in the other vertices. In addition, by repeating the above process for the remaining subsets of the mesh model to configure Wn, watermark extraction is completed.

4. Algorithm Evaluation

Various experiments were performed to evaluate the performance of the present invention. Hereinafter, the experimental results will be analyzed. 10 shows three mesh models used in the experiment. 10 (a) is a "man" model, FIG. 10 (b) is a "bunny" model, and FIG. 10 (c) is a "horse" model. Among them, the "man" model is an open model, the "bunny" model and "horse" are closed models. Table 2 shows the model information used in the experiment.

를 0.002 로 설정하여 워터마크를 삽입한 "man" 모델이고, 도 11 (b) 는 삽입강도

를 0.002 로 설정하여 워터마크를 삽입한 "bunny" 모델이고, 도 11 (c) 는 삽입강도

를 0.003 으로 설정하여 워터마크를 삽입한 "horse" 모델이다. 표 3 에서는 삽입 전 후 메쉬 모델의 파라미터 값들을 비교하여 나타내었다.11 shows a mesh model in which a watermark is inserted. Figure 11 (a) is the insertion strength

Is a "man" model with a watermark set to 0.002, and FIG. 11 (b) shows the insertion strength.

Is a "bunny" model with the watermark set to 0.002, Figure 11 (c) is the insertion strength

Is a "horse" model with a watermark set to 0.003. Table 3 compares the parameter values of the mesh model before and after insertion.

12 is an image showing the spherical parameterization process of the "bunny" model. (a) shows the original "bunny" model as a mesh structure consisting of vertices, sides and faces, (b) shows the spherical parameterization results for the "bunny" model, and (c) shows the The vertex distribution is shown in three dimensions, and (d) is a "bunny" model with a watermark embedded. The watermark bit string used in the proposed algorithm is limited to a maximum of 64 bits and generated using a random number generator with a seed value. The watermark information was inserted independently in the divided mesh model and a large amount of overlapping was possible.

13 schematically illustrates a process of embedding a watermark by applying a spherical parameter technique. As a premise before applying the spherical parameter technique, first, a rectangular coordinate of a 3D mesh model is set in a rectangular coordinate system (110). A detailed method of setting the rectangular coordinates of the three-dimensional mesh model in the rectangular coordinate system will be described later with reference to FIG. 14. After setting the rectangular coordinates of the 3D mesh model, the rectangular coordinates on the rectangular coordinate system are converted into spherical coordinates on the spherical coordinate system (120). A spherical parameter technique is applied to the mesh model converted into spherical coordinates (130). At this time, fix r = k (k is a constant) in spherical coordinates. A specific application method of the spherical parameter technique will be described later with reference to FIG. 15. If the spherical parameter technique is applied to the mesh model, a watermark is inserted (140).

) 과 내부 꼭지점 (

) 으로 분류한다.

에 속하는 꼭지점들을 기준 꼭지점으로 설정한다. (여기서,

는 꼭지점들의 집합

에서 1-링 값이

= 6,

= 3 인 꼭지점을 제거한 집합이고,

는 꼭지점들의 집합

에서 1-링 값이

= 4 인 꼭지점을 제거한 집합이다.) FIG. 14 illustrates in more detail a process of embedding a watermark by applying a spherical parameter technique as an embodiment of the present invention. Steps 210 to 230 are prerequisites before applying the spherical parameter technique. The step of setting the rectangular coordinates of the three-dimensional mesh model of FIG. 13 in the rectangular coordinate system and converting the rectangular coordinates in the rectangular coordinate system into spherical coordinates in the spherical coordinate system is performed. do. First, a reference vertex is selected to find a center point of a sphere which is not affected by a general mesh model attack (210). Boundary vertices for vertex selection

) And internal vertex (

).

Set vertices belonging to as reference vertices. (here,

Is a set of vertices

1-ring value in

= 6,

Is a set with no vertices = 3,

Is a set of vertices

1-ring value in

Is a set with no vertices = 4)

,

,

)라고 하면,

,

,

는 상기 식 (3) 과 같이 표현된다. 즉, (

,

,

) 이 기준 꼭지점들의 질량 중심으로 탐색되면서 구면좌표계의 중심점이 되는 것이다. 탐색된 질량 중심을 이용하여 메쉬 모델을 (

,

,

) 로 이동한다(230). 이러한 과정을 통해 질량 중심으로 이동된 새로운 꼭지점들의 좌표값들을 구할 수 있다. 단계 240 에서는 구면 파라미터 기법을 적용한다. 구면 파라미터 기법을 적용하는 구체적인 방법에 대해서는 이하 도 15 와 관련하여 설명한다. The center of mass of the reference vertices set as described above is searched (220). The center of mass of the reference vertices is set as the origin of the spherical coordinate system. The center point of the set spherical coordinate system

,

,

),

,

,

Is expressed as in the formula (3). In other words, (

,

,

This is the center point of the spherical coordinate system as it is searched by the center of mass of these vertices. Use the searched center of mass to build a mesh model (

,

,

Move to (230). Through this process, the coordinate values of the new vertices moved to the center of mass can be obtained. In step 240, a spherical parameter technique is applied. A detailed method of applying the spherical parameter technique will be described below with reference to FIG. 15.

15 specifically illustrates the steps of applying spherical parameter technique.

,

,

) 으로 이동한다.(310) 단계 1 (310) 은 도 14 의 단계 230 에 대응한다. 새로운 꼭지점들의 좌표 값 (

,

, )은 다음과 같다.Step 1: The center point of the mesh model set by Eq. (3)

,

,

(Step 310) corresponds to step 230 of FIG. The coordinates of the new vertices (

,

, )Is as follows.

,

,

)=(

-

,

-

,

-

) 식(6)(

,

,

) = (

-

,

-

,

-

) (6)

의 꼭지점 좌표 값을 구면좌표계로 변환시킨다. (320)Step 2: Mesh Model Obtained by Equation (4)

Convert the vertex coordinate value of to spherical coordinate system. (320)

,

,

)=cart2sph(

,

,

),

식(7)(

,

,

) = cart2sph (

,

,

),

Formula (7)

=k (k 는 상수) 로 설정 (330) 하고, 식 (5) 를 이용하여 구면좌표계를 직교좌표계로 변환 (340) 한다. 메쉬 모델

의

={

|

} 은 그대로 적용한다. 구면 파라미터 기법이 적용된 메쉬 모델을 분할 (250) 하고, 워터마크 정보를 생성하여(260), 생성된 워터마크 정보를 분할된 메쉬 모델에 삽입한다(270). Step 3: From the Spherical Coordinate System From the Result of Equation (7)

= k (k is a constant) is set (330), and the spherical coordinate system is converted to the rectangular coordinate system (340) using Equation (5). Mesh model

of

= {

|

} Is applied as is. The mesh model to which the spherical parameter technique is applied is divided (250), watermark information is generated (260), and the generated watermark information is inserted into the divided mesh model (270).

16 specifically illustrates a watermark extraction method.

인 꼭지점들을 선택한다.(410)Step 1: Find the 1-ring values of each vertex in the mesh model and based on that value

Select vertices (410).

Step 2: Find the center of mass of the selected vertices and set them as the center points of the spherical coordinate system (420).

Step 3: After moving the mesh model to the center of mass (430), the spherical parameter technique is applied (440).

=3 인 꼭지점을 선택하고(450), 다음과 같은 방법으로 워터마크 삽입여부를 판단한다.(460)Step 4:

A vertex of = 3 is selected (450), and it is determined whether a watermark is inserted in the following manner.

=3 인 꼭지점을

이라 하면, 삼각 면

의 면적을 구하고, 구한 면적들이 같으면 워터마크가 삽입되었다고 판단하고 단계 5 로 넘어간다. 면적들이 다르면

=3 인 다른 꼭지점을 선택하여 단계 4 를 반복한다.

Vertices = 3

Speaking of triangular faces

If the obtained area is the same, it is determined that the watermark has been inserted, and the process proceeds to step 5. If the areas are different

Repeat step 4 with other vertices = 3.

에서

를 구한다.Step 5 (470): Three Vertices

in

Obtain

이면

=1 이고,if

Back side

= 1

이면

=0 이다. if

Back side

= 0

, 여기서

를 구성하면 워터마크 추출이 완료된다.Repeating the process for the remaining subsets of the mesh model (480),

, here

After the configuration, the watermark extraction is completed.

4.1 Robustness to Form Conservation Attacks

Shape preservation attacks include geometric transformations such as movement, scaling, and rotation, changing the order of storage of vertices, and file format transformations. Geometric transformations only change the coordinate values of the vertices, and the 1-ring values of the vertices, the center of the selected spherical coordinate system, and the connection information of the vertices are not affected. As a result of the experiment, the proposed algorithm obtains the same spherical parameterization result even after the transformation such as movement, rotation, and scaling, and it is possible to extract the inserted watermark information.

There are attacks in the mesh model that change the storage order of vertices. The proposed algorithm could extract the watermark information because the 1-ring value of the vertex and the selected spherical coordinate center did not change even if the storage order of the vertices was changed. The "Invert faces" attack is a transformation that only transforms the orientation of the faces, and the "close holes" attack is an attack technique that adds a triangle mesh. The proposed algorithm is not affected.

Table 4 shows the format used in the file format conversion experiment. The PLY file format and STL file format include ASCII and binary formats. In this case, all experiments were converted to ASCII format. Collada version 1.4.1 was used for DAE files, and OBJ and OFF files were tested using the meshlab program distributed in March 2007. Watermark information could be extracted from all models used in the experiment.

 4.2 Robustness to Morphological Attacks

 There are a variety of attacks on shape transformation. This paper focuses on attacks such as mesh segmentation, mesh simplification, and mesh smoothing.

4.2.1 Mesh Segmentation Attack Experiment

Popular mesh segmentation techniques include loop segmentation, butterfly segmentation, and midpoint subdivision surface. In the experiment, the vertices of the model to be subdivided were selected in the whole model and the experimental results are shown in Table 5. In “Watermark (%)” of Table 5, the number of vertices added when watermark is inserted and the number of vertices extracted after attack are expressed as a percentage. "Insert / Extract" represents the number of bits extracted after the tertiary segmentation. The present invention has shown particularly high robustness against central point split attack.

4.2.2 Mesh Smoothing Attack Experiment

In smoothing, Laplacian smoothing is used a lot. According to the present invention, watermark information could be extracted even after six times of Laplacian smoothing.

HC Laplacian smoothing is also a popular attack technique in mesh models. All of the models used in the experiments were able to extract watermarks even after the sixth HC Laplacian smoothing.

4.2.3 Mesh Simplified Attack Experiment

Simplification of the mesh model includes techniques such as Clustering Decimation and Quadric Edge Collapse Decimation (QECD). Here, we experimented with the QECD technique and the results can be found in Table 6.

In both models, watermark extraction was possible even after the second QECD.

As described above, the present invention effectively utilizes the characteristics of the vertex coordinates using spherical parameter techniques, thereby effectively inserting the watermark into the three-dimensional mesh model that cannot be determined in the rectangular coordinate system. In addition, the present invention is robust to typical geometric transformations such as movement, scaling, and rotation, and maintains robustness in mesh ordering and file format conversion, and shows good performance in attacks such as smoothing.

FIG. 1 illustrates components of vertices, edges, and triangular faces of a triangular mesh model.

2 illustrates a mesh model represented by vertices, edges, and triangles.

3 illustrates one embodiment of a loop split surface method.

Figure 4 shows a butterfly splitting mask and the added vertices.

5 shows the coordinates (r, θ, Ψ) of the spherical coordinate system.

6 (a) shows the “man” model before applying the spherical parameter technique.

6 (b) shows the “man” model after applying the spherical parameter technique.

FIG. 7 shows an embodiment (n = 3) of oversampling watermark information.

8 illustrates one embodiment of a vertex distribution of a segmented mesh model.

Fig. 9 shows an embodiment of a vertex adding method in embedding watermarks.

10 is an embodiment of an experimental mesh model (man model, bunny model, horse model).

FIG. 11 illustrates a result of inserting a watermark into the mesh model of FIG. 10.

12 illustrates one embodiment of a spherical parameterization process of a bunny model.

13 is a watermark embedding flowchart according to an embodiment of the present invention.

14 is a watermark embedding flowchart according to another embodiment of the present invention.

15 is a flowchart of application of a spherical parameter technique according to an embodiment of the present invention.

16 is a watermark extraction flowchart according to an embodiment of the present invention.

Claims (23)

As a method of inserting a watermark into a three-dimensional mesh model using spherical parametric techniques, Setting the coordinates of the three-dimensional mesh model in a Cartesian coordinate system, Converting coordinates of the 3D mesh model set as the rectangular coordinate system to a spherical coordinate system; Applying a spherical parameter technique to the mesh model converted into the spherical coordinate system, and And embedding a watermark in the three-dimensional mesh model to which the spherical parameter technique is applied. The method of claim 1, Converting the coordinates of the three-dimensional mesh model to the spherical coordinate system, Setting base vertices, Setting the reference vertex as the center point of the spherical coordinate system, and And converting the 3D mesh model coordinates into a spherical coordinate system based on the center point of the set spherical coordinate system. The method of claim 1, Inserting the watermark, Generating watermark information, Dividing the mesh model to which the spherical parameter technique is applied; and Embedding a watermark in the divided mesh model. The method of claim 2, The setting of the reference vertex comprises: dividing the vertices of the three-dimensional mesh model into a boundary vertex set and an inner vertex set, and And setting the center of mass as a reference vertex by obtaining the center of mass of the vertices of the three-dimensional mesh model using the set of boundary vertices and the set of inner vertices. The method of claim 3, wherein The watermark information is over sampled and inserted into the divided mesh model. The watermark information is a random bit string having a multiple length of two.

ego, (

) Dividing the mesh model includes dividing the mesh model into subsets using latitude (θ) and longitude (Ψ) values. The method of claim 3, wherein And inserting the watermark using a vertex ( l ) addition method. The method of claim 6, The added vertex ( l ) is added to a triangular plane of the three-dimensional mesh model, and is set to the center of mass of three vertices (i, j, k) forming the triangular plane. The method of claim 7, wherein Inserting the watermark,

Step to calculate (here,

Are the spherical coordinates of the three vertices (i, j, k) of the original three-dimensional mesh model.), If the information you want to insert is 1,

If the information you want to insert is 0,

Calculating the Modifying face information after adding the vertex l to the mesh model, Repeating the calculating and modifying the entire subset of the mesh model, and Reconstructing the partitioned subset to obtain a watermarked mesh model. A method of extracting a watermark of a 3D mesh model using spherical parameter technique, Obtaining the 1-ring values of each vertex in the three-dimensional mesh model, Based on the 1-ring value of the vertices,

Selecting vertices, Obtaining a center of mass of the selected vertices and setting the center of mass as a center point of a spherical coordinate system; Moving the mesh model to the center of mass, applying spherical parametric techniques, and

And judging whether or not the watermark is to be inserted based on a vertex (hereinafter, referred to as vertex l ) of = 3. (Only the vertex

sets a set of vertices adjacent to = {i}

is called the 1-ring of = {i}

, And

The number of adjacent vertices in is called the 1-ring value.

Marked as. Also,

Is a 1-ring value at the inner vertices of the mesh model.

= 12, Means a set with no vertices = 6,

At the boundary vertex of the mesh model

Means a set with no vertices = 7) The method of claim 9, Determining whether to insert the watermark, Obtaining an area of a triangular plane formed by the vertices l and vertices i and j, an area of a triangular plane formed by the vertices l and vertices j and k, and an area of a triangular plane formed by the vertices l and vertices k and i , Vertices i, j, k are adjacent vertices of vertex l ), and If the areas of the triangular planes are the same, it is determined that a watermark has been inserted.

Repeating obtaining the area of the triangular plane for another vertex that satisfies = 3. The method of claim 10, If you determine that a watermark has been inserted, Vertex of the mesh model

About,

Step of obtaining

Back side

= 1,

Back side

Determining = 0, and For the remaining subset of the three-dimensional mesh model, the steps (step 1-ring values of the respective vertices,

Selecting the vertices, setting the center point of the spherical coordinate system, applying the spherical parameter technique, determining whether to insert the watermark, and if it is determined that the watermark has been inserted.

Obtaining

Determining a; and repeating the method). An apparatus for inserting a watermark into a three-dimensional mesh model using spherical parametric techniques, Means for setting the coordinates of a three-dimensional mesh model in a Cartesian coordinate system, Means for converting coordinates of the three-dimensional mesh model set in the rectangular coordinate system into a spherical coordinate system; Means for applying a spherical parameter technique to the mesh model converted into the spherical coordinate system, and And means for embedding a watermark in the three-dimensional mesh model to which the spherical parameter technique is applied. The method of claim 12, Means for converting the coordinates of the three-dimensional mesh model to the spherical coordinate system, Set the base vertex, Set the reference vertex as the center point of the spherical coordinate system, And converting the 3D mesh model coordinates into a spherical coordinate system on the basis of the center point of the set spherical coordinate system. The method of claim 12, Means for embedding the watermark, Means for generating watermark information, and Means for dividing the mesh model to which the spherical parameter technique is applied; And inserting the watermark information into the divided mesh model. The method of claim 13, Divide the vertices of the three-dimensional mesh model into a boundary vertex set and an inner vertex set, And calculating the center of mass of the vertices of the three-dimensional mesh model using the set of boundary vertices and the set of inner vertices, thereby setting the center of mass as the reference vertex. The method of claim 14, The watermark information is over sampled and inserted into the divided mesh model. The watermark information is a random bit string having a multiple length of two.

ego, (

, here

{0, 1},

= 2 ⁿ ) The means for dividing the mesh model divides the mesh model into subsets using latitude (θ) and longitude (Ψ) values. The method of claim 14, And means for embedding the watermark inserts a watermark using a vertex ( l ) addition method. The method of claim 17, The added vertex ( l ) is added to a triangular plane of the three-dimensional mesh model, and is set to the center of mass of three vertices (i, j, k) forming the triangular plane. The method of claim 16, Means for dividing the mesh model, After deriving the parameter value based on one or more of the vertex distribution, the topological information, the presence or absence of the hole, and the Genus value (the number of rings on the quadratic surface), And dividing the mesh model by using the parameter value, or dividing the mesh model by applying the parameter value to the longitude and latitude values. The method of claim 18, Means for embedding the watermark,

, And (here,

Are the spherical coordinates of the three vertices (i, j, k) of the original three-dimensional mesh model.), If the information you want to insert is 1,

If the information you want to insert is 0,

, And After adding the vertex l to the mesh model, modify the face information, Repeating the operations for the entire subset of the mesh model, And reconstructing the divided subset to obtain a watermarked mesh model. An apparatus for extracting watermarks of three-dimensional mesh models using spherical parametric techniques, Means for obtaining the 1-ring values of each vertex in the three-dimensional mesh model, Based on the 1-ring value of the vertices,

Means for selecting vertices, Means for obtaining a center of mass of the selected vertices and setting the center of mass to a center point of a spherical coordinate system; Means for moving the mesh model to the center of mass to apply spherical parametric techniques, and

And means for determining whether to insert a watermark based on a vertex (= vertex l ) of = 3. (Only the vertex

sets a set of vertices adjacent to = {i}

is called the 1-ring of = {i}

, And

The number of adjacent vertices in is called the 1-ring value.

Marked as. Also,

Is a 1-ring value at the inner vertices of the mesh model.

= 12,

Means a set with no vertices = 6,

At the boundary vertex of the mesh model

Means a set with no vertices = 7) The method of claim 21, Means for determining whether to insert the watermark, Calculating the area of the triangular plane formed by the vertices l and the vertices i and j, the area of the triangular plane formed by the vertices l and the vertices j and k, and the area of the triangular plane formed by the vertices l and vertices k and i Vertices i, j, k are adjacent vertices of vertex l ), If the areas of the triangular planes are the same, it is determined that a watermark has been inserted.

And calculating the area of the triangular plane for another vertex satisfying = 3. The method of claim 22, If you determine that a watermark has been inserted, Vertex of the mesh model

About,

Obtaining,

Back side

= 1,

Back side

And a watermark extracting means for determining to be = 0.

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