A robust high-quality three-dimensional model digital watermark embedding and extraction method

Abstract

The application discloses a robust high-quality three-dimensional model digital watermark embedding and extracting method, the watermark embedding method comprises the following steps: filtering a vertex order initial point by using a three-dimensional grid model vertex in-degree; calculating a robust starting point and a vertex order which are not influenced by three-dimensional coordinate values of the vertex by using a sum of geodesic distances of the vertex; dividing the vertex into embeddable watermark points and reference points by using a specific algorithm; and embedding a watermark in a local space of the embeddable watermark points by using a principal component analysis and a quantization method. The application also proposes a watermark extracting method corresponding to the watermark embedding method. Compared with a traditional space domain three-dimensional grid model watermark method, the watermark embedding method has smaller distortion caused to a model surface, stronger anti-noise attack capability and more robust vertex order corresponding to the model.

Description

Technical Field

[0001] This invention relates to the field of digital watermarking technology, and in particular to a robust method for embedding and extracting digital watermarks from high-quality three-dimensional models. Background Technology

[0002] The background of 3D model watermarking embedding technology involves digital rights management and the secure management of multimedia content. 3D models are a new type of media data, widely used in computer-aided design, medical visualization, film and games, smart education, and many other fields. With the development of the internet, streaming media, and games, copying, sharing, and distributing multimedia content containing 3D models has become extremely easy, making copyright protection a critical issue. To prevent illegal copying and distribution, 3D model digital watermarking technology has emerged. This technology aims to identify and protect ownership or copyright by embedding information into 3D models.

[0003] 3D model watermarking technology can be categorized into vulnerable and robust types. Vulnerable watermarks are used for content verification and can detect minor modifications, while robust watermarks maintain model quality while ensuring that the embedded information can still be extracted in the face of various attacks. Watermarks can be embedded in different domains of 3D models, such as the spatial or spectral domains, and are classified according to different application scenarios, including private and public watermarks, blind detection and non-blind detection watermarks, etc. Developing blind detection watermarking technology that is robust to various attacks is currently a key research focus.

[0004] The common attack techniques for 3D model watermarking can be categorized as follows:

[0005] 1. Affine transformation attacks: These mainly include attacks involving rotation, translation, and scaling. Although these operations do not change the shape of the 3D model, they do change the position of the vertices, causing the embedded watermark information to be lost.

[0006] 2. Topology attacks: These mainly include two types of attacks: mesh simplification and mesh encryption. These operations do not change the general shape of the 3D model, but they can add or reduce the number of watermarks or change the order of the watermarks.

[0007] 3. Clipping Attacks: Clipping attacks remove some vertices and faces. This type of attack causes a large amount of watermark information attached to the model to disappear, making the watermark difficult to recover.

[0008] 4. Noise attack: Noise attack changes the shape of the model by adding noise to the original vertices and faces.

[0009] 5. Connectivity attacks: such as vertex rearrangement.

[0010] Under the aforementioned attacks, traditional 3D model watermarking techniques have certain limitations in protecting 3D models. They cannot effectively resist third-party attacks while maintaining invisibility and low distortion, and cannot achieve blind watermark extraction (i.e., without the original model). At the same time, the watermark embedding capacity needs to be as large as possible, and the computational complexity as low as possible. Summary of the Invention

[0011] The purpose of this invention is to address the shortcomings of existing technologies by providing a robust method for embedding and extracting digital watermarks from 3D models.

[0012] This invention is achieved through the following technical solution:

[0013] A robust, high-quality 3D model digital watermark embedding method includes the following steps:

[0014] S1: Preprocess the 3D model to normalize the coordinates of each vertex in the 3D model;

[0015] S2: Determine the arrangement order of the vertices of the 3D model based on its topological structure;

[0016] S3: Classify all vertices into reference points and watermarkable points, ensuring that each watermarkable point is not adjacent to the others.

[0017] S4: Obtain the watermark sequence to be embedded. The watermark sequence consists of multiple watermark information arranged in an ordered manner; preset the watermark parameter x to be embedded. elem y elem z elem and loop num The quantization step size for embedding the watermark is determined based on the watermark parameters.

[0018] S5: Traverse the embeddable watermark points in the order of the vertices. For each embeddable watermark point, select a portion of reference points as the reference points corresponding to the current embeddable watermark point. Establish a local coordinate system based on the reference points corresponding to the current embeddable watermark point, and transform the current embeddable watermark point into the local coordinate system to obtain the local coordinates of the current embeddable watermark point.

[0019] S6: According to the order of the vertices, each embeddable watermark point corresponds to the watermark information in the watermark sequence in turn. The corresponding watermark information is embedded into each embeddable watermark point according to the quantization step size of the watermark.

[0020] S7: Transform the local coordinates of the watermarkable points back to the original coordinate system after watermarking.

[0021] Further, in step S1, the preprocessing specifically involves: calculating the centroid of the 3D model, subtracting the centroid coordinates from the coordinates of all vertices to achieve translation of the 3D model; performing principal component analysis on the translated 3D model to obtain three linearly independent 3D vectors, establishing a global coordinate system based on these three 3D vectors, and transforming each vertex of the 3D model to this coordinate axis; uniformly scaling the coordinates of all vertices of the 3D model so that the x, y, and z components of all vertex coordinates are between [-1, 1].

[0022] Furthermore, in step S2, determining the arrangement order of the vertices of the 3D model based on its topological structure specifically includes the following steps:

[0023] S2.1: Calculate the in-degree of all vertices in the 3D model and group vertices with the same in-degree into a vertex set;

[0024] S2.2: Select the vertex set with the fewest vertices. If there are multiple vertex sets with the fewest vertices, select the vertex set with the largest in-degree.

[0025] S2.3: For the selected set of vertices, calculate the sum of the geodesic distances of each vertex in the set; select the vertex with the largest sum of geodesic distances in the current set as the starting point and add the starting point to the vertex queue;

[0026] S2.4: Calculate the sum of the geodesic distances of each adjacent point of the starting point, and select the adjacent point with the largest sum of geodesic distances to add to the vertex queue;

[0027] S2.5: Based on the two vertices added to the vertex queue in S2.3 and S2.4, use the counterclockwise breadth-first search algorithm to traverse all vertices and add the traversed vertices to the vertex queue in turn. The final arrangement order of the vertices in the vertex queue is the determined arrangement order.

[0028] Furthermore, in step S3, classifying all vertices into reference points and watermarkable points specifically includes the following steps:

[0029] S3.1: Set all vertices to be embeddable watermark points;

[0030] S3.2: Extract the vertices of the 3D model in the order of their arrangement;

[0031] S3.3: If the currently extracted vertex is a watermark-embedd vertex, then set all vertices directly adjacent to the currently extracted vertex as reference points, and continue to extract the next vertex according to the order of the vertices.

[0032] S3.4: If the currently extracted vertex is the reference point, then continue to extract the next vertex according to the order of the vertices;

[0033] S3.5: Repeat S3.2-S3.4 until the last vertex.

[0034] Furthermore, the step of determining the quantization step size for embedding the watermark based on the watermark parameters specifically involves:

[0035] δx = Length average *x elem

[0036] δy = Length average *y elem

[0037] δz=Length average *z elem

[0038] Where δx, δy, and δz are the three components of the watermark quantization step size, Length average This represents the average side length of the 3D model.

[0039] Furthermore, the step of selecting a subset of reference points as reference points corresponding to the current embeddable watermark points, and establishing a local coordinate system based on the reference points corresponding to the current embeddable watermark points, specifically involves selecting reference points with a step size no greater than loop size relative to the current embeddable watermark points. num All reference points are combined to form a reference point set, and all reference points in the reference point set are the reference points corresponding to the currently embeddable watermark points; principal component analysis is performed on the reference points in the reference point set to obtain the local coordinate system.

[0040] Further, in step S6, embedding the corresponding watermark information into each embeddable watermark point according to the quantization step size of the watermark specifically involves:

[0041]

[0042] Where Q(point) locx Q (point) locy ) and Q (point) locz () represents the x, y, and z components of the local coordinates of the currently embeddable watermark point after watermarking. locx point locy and point locz Let x, y, and z be the local coordinates of the currently embeddable watermark point, and q be the watermark information corresponding to the currently embeddable watermark point.

[0043] This invention also proposes a robust, high-quality method for extracting digital watermarks from 3D models. The 3D model is embedded with a digital watermark using the aforementioned watermark embedding method. The watermark extraction method includes:

[0044] 1) Preprocess the 3D model to normalize the coordinates of each vertex; determine the arrangement order of each vertex in the 3D model, and classify all vertices into reference points and points that can be embedded with watermarks;

[0045] 2) Traverse the embeddable watermark points in the order of the vertices. For each embeddable watermark point, establish a local coordinate system based on the reference point corresponding to the current embeddable watermark point, and transform the current embeddable watermark point into the local coordinate system to obtain the local coordinates of the current embeddable watermark point.

[0046] 3) Extract the x, y, and z components of the watermark information corresponding to each embeddable watermark point;

[0047] 4) Sum the three components of the watermark information. If the sum is greater than 1, the watermark information corresponding to the current embeddable watermark point is 1; otherwise, it is 0. Combine all the watermark information in sequence to obtain the watermark sequence embedded in the 3D model.

[0048] The beneficial effects of this invention are as follows:

[0049] This invention enables high-capacity, low-distortion watermark embedding, while the vertex order required for watermark extraction remains unaffected by attacks such as watermark quantization granularity, noise, consistency changes, and vertex rearrangement. Furthermore, the invention allows for adjustments to configuration parameters to enhance noise immunity. Traditional spatial watermarking methods suffer from disrupted vertex order under conditions of high noise and coarse-grained watermark embedding, whereas the pure topology-based vertex ordering method presented in this invention does not, resulting in high robustness of the watermarking technology. Attached Figure Description

[0050] Figure 1 This is a flowchart of the watermark embedding process of the present invention;

[0051] Figure 2 This is a flowchart of the watermark extraction process of the present invention;

[0052] Figure 3 This is a three-dimensional mesh model used for testing in one embodiment of the present invention;

[0053] Figure 4 This is a rendering of the three-dimensional mesh model used in testing according to one embodiment of the present invention after embedding a watermark. Detailed Implementation

[0054] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not limit it in any way.

[0055] In one embodiment of the present invention, a robust, high-quality digital watermarking embedding method for 3D models is provided, aiming to improve the anti-attack and concealment properties of 3D models during the information embedding process, while reducing the impact on the original 3D model structure. It has broad practical value in applications such as copyright protection, data verification, and model authentication. Figure 1 As shown, the watermark embedding method includes the following steps:

[0056] (1) A starting point finding method based on the sum of vertex in-degree and geodesic distance, and a vertex rearrangement method for the 3D model, which includes the following steps:

[0057] (1-1) Read in the 3D model that needs to be embedded with the watermark. This 3D model is generally in .obj format by default. Import it into the program and convert it into a half-sided model. This invention uses a triangular mesh model, in which each face is composed of three vertices, forming a triangle.

[0058] (1-2) The three-dimensional model is preprocessed. The specific steps are as follows: calculate the centroid of the three-dimensional model and translate the model so that the centroid coordinates of the model coincide with the origin of the coordinate system. Perform principal component analysis on the vertex coordinates of the current translated three-dimensional mesh model to calculate three new linearly uncorrelated three-dimensional vectors. Re-establish the coordinate axis based on these three three-dimensional vectors and transform the vertex coordinates of the three-dimensional model into the coordinate axis. In the coordinate axis, each component of the vertex coordinates is uniformly scaled in a space between [-1,1]. Specifically, this means that the x, y and z components of the vertex coordinates are all between [-1,1].

[0059] (1-3) Calculate the in-degree of all vertices in the model and count them. Group vertices with the same in-degree together into a set.

[0060] (1-4) Count the number of vertices in all sets and select the set with the fewest vertices. If there are multiple sets with the fewest vertices, select the set with the largest in-degree.

[0061] (1-5) Calculate the sum of geodesic distances for each vertex in the selected set. The method for calculating the sum of geodesic distances is as follows: the distance between two directly connected vertices is one. Based on this condition, Dijkstra's algorithm is used on the vertices to calculate the shortest distance from the current vertex to any other vertex. After the calculation is completed, the shortest distances from the current vertex to all vertices in the 3D model are summed to complete the calculation of the sum of geodesic distances for each vertex.

[0062] (1-6) Select the vertex with the largest geodesic distance in the current set as the starting point, and add the starting point to the vertex queue. The vertex of the starting point is the first in order. Using the starting point as the initial center point, continue with the following steps.

[0063] (1-7) In a 3D mesh model, two directly connected vertices are each other's neighbors. Find all the neighbors of the center point and select one of them to add to the vertex queue. The calculation method is to calculate the sum of the geodesic distances of all neighbors and select the vertex with the largest sum of geodesic distances to add to the vertex queue.

[0064] (1-8) Based on the vertices whose order is already determined as first and second, use the breadth-first search algorithm to traverse all vertices and add the traversed vertices to the vertex queue in turn to generate the vertex order. The vertex order generation method for the adjacent points of a single vertex is as follows: the half-edge structure can be used to traverse and store all adjacent points of the vertex in a counterclockwise direction. All adjacent points are actually a ring arranged in a counterclockwise order. Determine the last vertex in the ring whose order has been determined in a counterclockwise order. Starting from the next vertex in the ring whose order has not yet been determined after the determined vertex, traverse the ring one by one and add the traversed vertices to the vertex queue in turn.

[0065] (1-9) Use the breadth-first search algorithm to traverse all vertices, and use the order of each vertex in the vertex queue as the order of the vertices.

[0066] (2) The low-distortion 3D watermark embedding method based on local plane is as follows:

[0067] (2-1) Based on the current vertex order of the 3D model, vertices are classified into reference points and watermarkable points. The method is as follows: 1. Set all vertices as watermarkable points. 2. Extract vertices sequentially according to their order. 3. If the currently extracted vertex is a watermarkable point, set all vertices directly adjacent to the currently extracted vertex as reference points, and continue executing step 2. 4. If the currently extracted vertex is a reference point, continue executing step 2. 5. Execute until the last vertex, then end.

[0068] (2 - 2) Calculate the average side length of the 3D model. average And determine the four parameters required for embedding the watermark, namely x elem (X-axis quantization granularity), y elem (Y-axis quantization granularity), z elem (Z-axis quantization granularity), loop num (Reference step size). The quantization step size of the watermark is determined by the parameters above, and the specific formula is as follows:

[0069] δx = Length average *x elem

[0070] δy = Length average *yelem

[0071] δz=Length average *z elem

[0072] δx, δy, and δz are the three components of the watermark quantization step size.

[0073] (2-3) Extract the vertices in the order determined in step one. If a vertex is a point that can be embedded with a watermark, first extract it according to the loop. num The surrounding reference points are determined by traversing the vertices other than the watermark embedding point and selecting those vertices whose step size between them and the watermark embedding point is less than or equal to the loop. num All vertices are grouped into a set. All points in this set that can be embedded with watermarks are removed. The remaining vertices in the set are the reference points corresponding to those vertices, forming a reference point set. The step size is the length of the shortest path between two vertices; the length of the shortest path between two directly connected vertices is 1.

[0074] (2-4) By applying principal component analysis to the reference points in the reference point set, a local centroid coordinate can be obtained. loc and three local coordinate axes Axis locx Axis locy Axis locz Subtract the center value from the coordinates of all reference points in the reference point set and the current watermark embedding point. loc The coordinates of the watermark point are then transformed to the local coordinate axis to obtain the local coordinates of the point that can be embedded. loc .

[0075] (2-5) Obtain the watermark sequence to be embedded. The watermark sequence consists of multiple watermark information (0 or 1). Each embeddable vertex corresponds to the watermark information in the watermark sequence in the order of vertex arrangement. Since the number of vertices in the model is generally much larger than the number of bits in the watermark sequence, the watermark sequence is first repeatedly arranged to form a long sequence. The watermark information in the long sequence is then mapped one-to-one with each vertex in the order of arrangement. The watermark information q corresponding to the embeddable watermark point is extracted, and it is repeatedly embedded into point using a quantization method. loc The three coordinate components are as follows, where the quantization formula for the x component is as follows, and the quantization methods for the y and z components are the same as those for the x component.

[0076]

[0077] Where Q(point) locx () represents the x-component of the local coordinates after the watermark is embedded, point locx reference point locThe x-component of the coordinates, This represents the floor operation.

[0078] (2-6) Perform the inverse transformation corresponding to (2-4) on the local coordinates after embedding the watermark to convert them into global coordinates.

[0079] like Figure 2 As shown, in another embodiment of the present invention, a matching three-dimensional model digital watermark extraction method is also provided. After obtaining a model with an embedded watermark according to the above watermark embedding method, the watermark is extracted according to the following steps.

[0080] (3-1) Same as step (1) in the previous embodiment, preprocess the watermarked model and obtain the vertex arrangement order of the three-dimensional model.

[0081] (3-2) Same as step (2-1) in the previous embodiment, classify the vertices of the watermarked model into reference points and watermark-embedd points.

[0082] (3-3) is the same as steps (2-2) to (2-5) in the previous embodiment. Each vertex is taken out in the order of vertex arrangement. For the watermark embedding point, its reference point set is obtained. The local coordinate system is calculated through the reference points and the coordinates of the watermark embedding point are transformed into the local coordinate system.

[0083] (3-4) Extract the watermark. The operation in the x component is as follows, and the operation in the y and z components is the same as the operation in the x component.

[0084]

[0085] Where, point x For the x-component of the coordinates of the watermarkable point in the local coordinate system, point' x q is the x-component of the coordinates of the watermarked points after extraction. x Let x be the x-component of the watermark information corresponding to the currently embeddable watermark point. Repeat the above operation on the y and z components to obtain the y-component and z-component of the watermark information.

[0086] (3-5) Sum the watermarks of the three components. If the sum is greater than 1, the watermark information embedded in that vertex is determined to be 1; otherwise, it is determined to be 0. After traversing all possible watermark points in the order of vertex arrangement, arrange the watermark information corresponding to each possible watermark point in order to obtain the watermark sequence.

[0087] (3-6) Figure 3The image shows four different common 3D mesh models: a human figure (top left), a rabbit (top right), a horse (bottom left), and an armadillo (bottom right). Table 1 shows the accuracy of the model watermark under vertex rearrangement attacks, affine transformation attacks, and different levels of noise attacks for these four 3D mesh models under corresponding configuration parameters.

[0088] Table 1

[0089]

[0090]

[0091] The experimental results show that the watermarking method is completely robust to affine transformation and vertex rearrangement attacks, and also performs well against noise attacks, especially on models with a small number of vertices. Figure 4 The rendering images after watermarking are shown under the configuration parameters in Table 1. It can be seen that this watermarking embedding method has little impact on the quality of the 3D mesh model itself.

[0092] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robust high-quality 3D model digital watermark embedding method, characterized by, The method comprises the following steps: S1: preprocessing the three-dimensional model to normalize the coordinates of each vertex in the three-dimensional model; S2: determining the arrangement order of each vertex of the three-dimensional model according to the topological structure of the three-dimensional model; S3: classifying all the vertices into reference points and watermark-embeddable points, so that each watermark-embeddable point is not adjacent to each other; S4: obtaining a watermark sequence to be embedded, the watermark sequence being composed of a plurality of watermark information arranged in order; presetting watermark parameters to be embedded, the watermark parameters including an X-axis quantization granularity, a Y-axis quantization granularity, a Z-axis quantization granularity and a reference step length, and determining a quantization step length to be embedded according to the watermark parameters; S5: traversing the watermark-embeddable points in order according to the arrangement order of each vertex, for each traversed watermark-embeddable point, selecting a part of the reference points as the reference points corresponding to the current watermark-embeddable point, establishing a local coordinate system based on the reference points corresponding to the current watermark-embeddable point, and transforming the current watermark-embeddable point into the local coordinate system to obtain the local coordinates of the current watermark-embeddable point; S6: according to the arrangement order of the vertices, each watermark-embeddable point corresponds to the watermark information in the watermark sequence in order, and the corresponding watermark information is embedded into each watermark-embeddable point according to the quantization step length of the watermark; S7: transforming the local coordinates of the watermark-embeddable points after the watermark is embedded back to the original coordinate system; In step S2, the arrangement order of each vertex of the three-dimensional model is determined according to the topological structure of the three-dimensional model, and the step specifically comprises the following steps: S2.1: counting the in-degree of all vertices of the three-dimensional model, and combining the vertices with the same in-degree into a vertex set; S2.2: selecting the vertex set with the least number of vertices, if there are multiple vertex sets with the least number of vertices, selecting the vertex set with the largest in-degree; S2.3: calculating the sum of geodesic distances of each vertex in the selected vertex set, and selecting the vertex with the largest sum of geodesic distances in the current set as the starting point and adding the starting point to the vertex queue; S2.4: calculating the sum of geodesic distances of each adjacent point of the starting point, and selecting the adjacent point with the largest sum of geodesic distances to add to the vertex queue; S2.5: based on the two vertices added to the vertex queue in S2.3 and S2.4, using the counterclockwise breadth-first algorithm to traverse all the vertices and adding the traversed vertices to the vertex queue in order, and the arrangement order of the vertices in the final vertex queue is the determined arrangement order; In step S3, all the vertices are classified into reference points and watermark-embeddable points, and the step specifically comprises the following steps: S3.1: setting all the vertices as watermark-embeddable points; S3.2: taking out the vertices of the three-dimensional model in order according to the arrangement order of each vertex; S3.3: if the current taken vertex is a watermark-embeddable point, setting all the vertices directly adjacent to the current taken vertex as reference points, and continuing to take the next vertex according to the arrangement order of each vertex; S3.4: if the current taken vertex is a reference point, continue to take the next vertex according to the arrangement order of each vertex; S3.5: repeating S3.2-S3.4 until the last vertex.

2. The robust high-quality 3D model digital watermark embedding method as claimed in claim 1, characterized in that, In step S1, the preprocessing is specifically: The center of gravity of the three-dimensional model is calculated, and coordinates of all vertices are subtracted by the center of gravity to realize translation of the three-dimensional model; principal component analysis is performed on the three-dimensional model after the current translation to obtain three linearly independent three-dimensional vectors, and a global coordinate system is established based on the three three-dimensional vectors, and each vertex of the three-dimensional model is converted into the coordinate system; all vertex coordinates of the three-dimensional model are uniformly scaled so that x, y and z components of all vertex coordinates are within [-1, 1].

3. The robust high-quality 3D model digital watermark embedding method as claimed in claim 1, characterized by, The specific calculation method of the sum of geodesic distances of the vertices is that the distance between two directly connected vertices is defined as one, the shortest distance from the vertex to other vertices is calculated by Dijkstra algorithm, and the sum of the shortest distances from the current vertex to each vertex is summed up, that is, the sum of geodesic distances of the vertex is obtained.

4. The robust high-quality 3D model digital watermark embedding method as claimed in claim 1, characterized by, In step S4, the quantization step length to be embedded with the watermark is determined according to the watermark parameter, and the specific method is as follows: δx = Lenth average *x elem δy = Length average *y elem δz = Length average *z elem where δx, δy and δz are three components of the watermark quantization step size, Length average is the average edge length of the three-dimensional model, x elem is the X-axis quantization granularity, y elem is the Y-axis quantization granularity, z elem is the Z-axis quantization granularity.

5. The robust high-quality 3D model digital watermark embedding method as claimed in claim 1, characterized by, In step S5, a part of the reference points are selected as the reference points corresponding to the current embeddable watermark point, and a local coordinate system is established based on the reference points corresponding to the current embeddable watermark point, and the specific method is as follows: All reference points with a step length less than or equal to the reference step length from the current embeddable watermark point are selected to form a reference point set, and all reference points in the reference point set are reference points corresponding to the current embeddable watermark point; principal component analysis is performed on the reference points in the reference point set to obtain a local coordinate system.

6. The robust high-quality 3D model digital watermark embedding method as claimed in claim 4, characterized by, In step S6, the corresponding watermark information is embedded into each embeddable watermark point according to the quantization step length of the watermark, and the specific method is as follows: Q(point locx ) = Q(point locy ) - Q(point locz ) Q(point locy ) = Q(point locz ) - Q(point locx ) Q(point locz ) = Q(point locx ) - Q(point locy ) wherein Q(point locx ), Q(point locy ) and Q(point locz ) are x component, y component and z component of local coordinates of the current watermark-embeddable point after embedding the watermark, point locx , point locy and point locz are x component, y component and z component of local coordinates of the current watermark-embeddable point, and q is watermark information corresponding to the current watermark-embeddable point.

7. The robust high-quality 3D model digital watermark embedding method as claimed in claim 1, characterized by, The transformation in step S7 is the inverse transformation of the transformation in step S5.

8. A robust high-quality 3D model digital watermark extraction method, characterized by, The three-dimensional model is embedded with a digital watermark by using the watermark embedding method in claim 1, and the watermark extraction method comprises: 1) Preprocessing the three-dimensional model to normalize the coordinates of each vertex in the three-dimensional model; determining the arrangement order of each vertex in the three-dimensional model, and classifying all vertices into reference points and embeddable watermark points; 2) Traversing the embeddable watermark points in sequence according to the arrangement order of each vertex, for the embeddable watermark point traversed, establishing a local coordinate system based on the reference points corresponding to the current embeddable watermark point, and transforming the current embeddable watermark point into the local coordinate system to obtain the local coordinates of the current embeddable watermark point; 3) Extracting the x component, y component and z component of the watermark information corresponding to each embeddable watermark point, wherein the extraction method of the x component is as follows, and the extraction methods of the y component and the z component are the same as that of the x component: wherein point x is an x component of the local coordinate of the watermark-embeddable point, point x is an x component of the local coordinate of the watermark-embeddable point after the watermark is extracted, q x is an x component of the watermark information corresponding to the current watermark-embeddable point; 4) Summing up the three components of the watermark information, if greater than 1, the watermark information corresponding to the current embeddable watermark point is 1, otherwise 0; sequentially combining all watermark information to obtain the watermark sequence embedded in the three-dimensional model.

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