CN105761314B - A kind of Model Simplification Method kept based on notable color attribute feature - Google Patents

Abstract

The present invention relates to a kind of Model Simplification Methods kept based on notable color attribute feature, belong to computer graphics, technical field of virtual reality.The technology specifically comprises the steps of：Original mesh model data is read in, Regularization is carried out to grid model, includes the Regularization of the geometric position on vertex and color attribute；Calculate the quadric error matrix on all vertex；The conspicuousness that attribute is executed to model calculates, and obtains the attribute significance on all vertex；The geometric attribute error and color attribute error for calculating side to be folded, then obtain the collapse cost on side to be folded；All sides are ranked up from small to large according to collapse cost；Therefrom the side of selection Least-cost carries out folding operation, and updates relevant information, including global characteristics importance, and the side being associated collapse cost；Edge contraction operation is repeated, simplifies requirement or heap until reaching as sky.The present invention can be not only realized well to the lattice simplified of property grid, while can effectively keep the notable attributive character of the color of model, and the color notable feature of model can be still kept when the rate of simplification reaches 90%.

Description

A Model Simplification Method Based on Feature Preservation of Salient Color Attributes

technical field

The invention relates to a three-dimensional model simplification method based on salient color attribute feature preservation, and belongs to the technical fields of computer graphics and virtual reality.

Background technique

In the fields of computer graphics and computer vision, objects can often be represented by triangular meshes. Due to the increasing progress in data acquisition technology and modeling technology, it is easy for people to obtain large-scale grid model representations of objects in computers, and 3D models are becoming more and more complex. Although complex models can contain the closest object descriptions, they require more storage space and more time to render. However, in many applications, highly complex models with excessive detail are usually not required. A simplified grid model can not only reduce the physical storage space of the model, save the drawing time of the model, but also greatly reduce the network transmission time of the model. In addition, the simplified model can also accelerate a series of calculations related to shape information in graphics, including finite element analysis, collision detection, visibility testing, shape recognition, etc. Therefore, it is of great significance to appropriately simplify the complex multi-detail model to a certain extent.

With the development of computer technology, mesh simplification technology has been widely used in many computer graphics and virtual reality. These models usually contain not only complex geometric details, but also various surface properties, such as color, texture, and surface normal vectors, etc. Mesh acquisition techniques such as scanning usually produce some complex mesh models with attributes. The geometric and attribute details of these models can negatively affect the performance of some applications. For example, computer games and distributed virtual environments often run in environments with limited rendering and network transmission capabilities, so models with too high a level of detail cannot be used. The research on mesh simplification algorithm with attributes has also become a very meaningful work.

Therefore, according to the grid type, it can be divided into two categories, namely the triangular mesh simplification algorithm and the quadrilateral mesh simplification algorithm. Quadrilateral grid is a new grid representation method in recent years, and the most widely used is the triangular grid model. The present invention is mainly aimed at the triangular grid.

Triangular mesh simplification algorithms can also be classified according to different methods. According to whether the mesh model is manifold, it can be divided into manifold mesh simplification algorithm and non-manifold mesh simplification algorithm. According to whether it is related to the viewpoint, it can be divided into viewpoint-related simplification and viewpoint-independent simplification; according to whether it interacts with users during the simplification process, it can be divided into interactive simplification algorithm and automatic simplification algorithm. There are many classification methods, some of which have cross-mixing in their algorithms. The current research results can be divided into three categories. The first category is local geometric operation simplification algorithm. This type of algorithm realizes the gradual simplification of the original model by continuously using local simplification operations such as vertex removal, edge folding, point pair shrinkage and triangle removal in the simplification process. The main advantage of this type of algorithm lies in the efficient execution of the algorithm and its ease of implementation. At the same time, the multi-resolution model of the original grid model can be obtained in the process of realization. The most representative of this type of algorithm is the quadratic error metric grid simplification algorithm proposed by Garland. In the algorithm, multiple point pair folding is used to achieve efficient simplification of the model while keeping the simplification error within a controllable range. . The second type is the surface clustering algorithm. This type of algorithm first divides the surface of the original model into several pieces according to certain clustering rules, and then replaces each small piece with some simple geometric surfaces such as planes, spheres, or cylinders. block models, and then re-triangulate each block model. In the replacement process, the simple geometric surface with the smallest error is selected to replace each piece of the original model. The simpler one is to use only a plane instead, and the model obtained in this way is also relatively simple. The third type of algorithm is the direct sampling method, which can also be called the mesh re-division method. In this type of algorithm, a certain number of points are first distributed on the surface of the mesh model according to certain rules, and then a new model is obtained by using the Delaunay triangulation rule on the point cloud of these points. One of the more representative algorithms is based on the isotropic and anisotropic central Venn diagram subdivision method. The main advantage of this type of algorithm is that it can make the grid distribution more uniform and regular.

Compared with the mesh model simplification algorithm without attributes, the current research on mesh simplification algorithms with attributes is still relatively small. For a limited number of surface models, such as height field models, a very simple simplification algorithm can be adopted. However, more general models require more advanced simplification techniques. When Hoppe simplifies the mesh, attributes are explicitly included when measuring the error. Certain methods for adding color to a wavelet-based multiresolution model were explored by Certain et al. The algorithm proposed by Cohen first simplifies the mesh model, and then reparameterizes the texture to correspond to the simplified mesh. Garland et al. extended the three-dimensional vector representing the vertex to a high-dimensional vector. The vector not only contains the position information of the vertex, but also contains other attribute information such as the color or texture of the grid, and then uses the extended quadratic error measurement algorithm for the band attribute. The grid is simplified. Fahn et al. proposed a simplification algorithm to keep the color of the model patch. This algorithm can only simplify the model of the associated attribute of the patch, but cannot simplify the model of the associated attribute of the vertex. For mesh models with texture attributes, Liu Xiuwen et al. considered the importance of geometry and texture attributes comprehensively, and used them as the folding cost of each half edge to determine the folding order of all edges in the model. The texture cost is introduced from the inconsistency of geometric space and texture space after folding, so that the cost of edge folding is the weighted sum of geometric cost and texture cost. In the processing of strong feature edges, the policy of prohibiting folding is adopted. In the processing of the boundary edge, the simplification quality of the boundary is well controlled by turning from the weak feature point to the strong feature point. The algorithm effectively weakens the texture pulling phenomenon in the simplification process. The visual effect of the simplified model is guaranteed.

The current simplification algorithms for mesh models with attributes can be divided into two types. The first method is to process the geometric information and attribute information of the model at the same time, that is, to extend the original algorithm that only considers the geometric information of the grid, so that the processing of the two information is carried out simultaneously. Such as extending the three-dimensional grid to a high-dimensional grid, and then simplifying the high-dimensional grid. Among them, how to coordinate geometric information and attribute information, and how to define high-dimensional grids are the difficulties of this type of algorithm. The second approach divides the mesh simplification algorithm with attributes into two steps. The first step does not consider the attribute information of the grid, but only simplifies the grid without attributes, and then maps the attribute information of the original grid model to the simplified grid. This method is carried out step by step, and how to remap the attribute information of the original grid to the simplified model is the difficulty of the algorithm.

Contents of the invention

The object of the present invention is to solve the mesh simplification problem of the three-dimensional model with color attributes, and propose a method for model simplification based on the preservation of salient color attribute features.

The purpose of the present invention is achieved through the following technical solutions.

A kind of model simplification method based on the preservation of salient color attribute feature of the present invention, its specific implementation steps are:

Step 1: Normalize the original mesh 3D model. The original mesh 3D model includes color attributes of vertices. Specifically:

Step 1.1: Process the color attributes of vertices of the original mesh 3D model.

Express the color attribute of the vertex of the original mesh 3D model as a 3D vector composed of red, green and blue (RGB) color components, and obtain the color attribute coordinates of the vertex. Then, the weighted color component method is adopted to calculate the color difference between any two vertices of the original mesh 3D model through formula (1). Use the symbols c _i and c _j to represent any two vertices of the original mesh 3D model, and use the symbols c _i (r _i , g _i , b _i ) and c _j (r _j , g _j , b _j ) to represent the original mesh The color 3D vectors of any two vertices c _i and c _j of the lattice 3D model.

Among them, D( _ci ,c _j ) represents the color difference between any two vertices c _i and c _j of the original mesh 3D model; w _r , w _g , w _b represent the weighting coefficients corresponding to red, green and blue respectively , w _r > w _b , w _g > w _b .

Preferably, w _r =3, w _g =4, and w _b =2.

The color difference D( _ci ,c _j ) between any two vertices c _i and c _j of the original mesh 3D model can be the Euclidean distance between vertices c _i and c _j , but the prerequisite is that the RGB space is a Uniform color space: that is, the equal color difference of each color should form a sphere in RGB space; and the colors at different positions on the sphere and the color at the center of the sphere should show the same difference. The RGB space obviously does not meet this condition, and using the Euclidean distance to measure the color difference in the RGB space does not conform to the human visual sense. Studies have shown that the human eye has different sensitivities to the three primary colors of red, green, and blue, and is more sensitive to red and green. Therefore, when calculating the color difference, it is necessary to treat the three primary colors differently to make the calculation more accurate. In order to compensate the non-uniformity of RGB space, the weighted color component method is adopted for the calculation of color difference: that is, three weighting coefficients w _r , w _g , and w _b are added.

Step 1.2: Standardize the geometric coordinates and color attribute coordinates of each vertex of the original mesh 3D model to the same range.

Based on the operation in step 1.1, the coordinate ranges of the geometric coordinates and color attribute coordinates of each vertex of the original mesh 3D model may be different. In order to make the spatial position and color attribute information play an equal role in the calculation of the folding cost, the original mesh The geometric coordinates and color attribute coordinates of each vertex of the 3D model are within the same range, that is, the three components of the vertex color coordinates of the original mesh 3D model are all within the range of [0, m], then the original mesh 3D model vertices The three dimensions of the geometric coordinates need to be standardized to the range [0,m], m∈[1,10].

Set the coordinate ranges of the three dimensions of the bounding box of the original grid 3D model to [x _min , x _max ], [y _min , y _max ], [z _min , z _max ] respectively, then calculate by formula (2) The normalized coordinate value of any vertex in the original mesh 3D model.

Among them, (x _a , y _a , z _a ) represent the geometric coordinates of any vertex in the original mesh 3D model; (x′ _b , y′ _b , z′ _b ) represent the specification of any vertex in the original mesh 3D model The geometric coordinates after transformation; d=max{x _max -x _min , y _max -y _min , z _max -z _min }.

After the operation in step 1, a normalized grid 3D model is obtained.

Step 2: Obtain the saliency of color attributes of all vertices of the normalized three-dimensional grid model.

On the basis of the operation in step 1, the color attribute salience of all vertices of the normalized mesh 3D model is calculated, specifically:

Step 2.1: Calculate the gray value of each vertex in the normalized grid 3D model.

Use symbols (r _a , g _a , b _a ) to represent the color attribute coordinates of any vertex in the normalized mesh 3D model. For the convenience of research, the color vector of the vertex is reduced to a one-dimensional vector. Using grayscale can convert the color model into a high-quality black-and-white model. Different colors in the RGB space correspond to different grayscale values, and different grayscale values also correspond to different RGB vectors. Using the gray value of the vertex to represent the original color information can not only reduce the dimension of the original model, but also represent the original model without distortion. The gray value of each vertex in the normalized grid 3D model is calculated by formula (3), represented by gray(a).

gray(a)＝0.299r _a +0.587g _a +0.114b _a (3)

Through this conversion, a color model can be converted into a high-quality grayscale model.

Step 2.2: Calculate the neighborhood gray value of each vertex in the normalized grid 3D model.

Calculate the neighborhood of vertex a with radius σ by formula (4), where σ is an artificially set value. The neighborhood of vertex a is defined using Euclidean distance.

N(a,σ)={x|||x-a||<σ,x∈U} (4)

Among them, N(a,σ) represents the neighborhood of vertex a whose radius is σ; U represents the normalized three-dimensional mesh model.

Then, the neighborhood gray value of vertex a is calculated by formula (5); the neighborhood gray value of vertex a adopts the Gaussian weighted average gray value of the vertex gray.

Among them, G(gray(a),σ) represents the neighborhood gray value of vertex a; exp( ) represents the power of the natural base e.

Step 2.3: Calculate the saliency of the color attribute of each vertex in the normalized mesh 3D model. The saliency of the color attribute of the vertex is calculated by the difference of the gray values of different radii, as shown in formula (6).

S(a)＝|G(gray(a),2σ)-G(gray(a),σ)| (6)

Among them, S(a) represents the salience of the color attribute of vertex a in the normalized three-dimensional mesh model.

In order to calculate the salience degree of the grid attribute in the neighborhood of different specifications, formula (7) is used to calculate the salience degree of the color attribute of vertex a under a certain specification.

S _t (a)＝|G(gray(a),2σ _t )-G(gray(a),σ _t )| (7)

Among them, S _t (a) represents the color attribute salience of vertex a under specification t; σ _t represents the neighborhood radius of vertex a under specification t; t∈{1,2,3};σ _t ∈{ε, The values of 2ε, 3ε} and ε are 0.3% to 0.8% of the diagonal length of the bounding box of the normalized grid 3D model.

In order to synthesize the results of different specifications, the nonlinear suppression operator is used to synthesize the color attribute saliency S _t (a) of vertex a under different specifications, and formula (6) is further rewritten as formula (8).

Among them, M _t represents the maximum value of S _t (a) calculated by vertex a under specification t; Indicates the average value of vertex a except M _t in S _t (a) calculated under specification t.

By formula (8), the color attribute salience of all vertices of the normalized mesh 3D model can be obtained.

Step 3: Calculate the geometric attribute error and color attribute error of each edge to be folded sequentially, and the folding cost of the edge to be folded; the edge to be folded is represented by the symbol (v _k , v _k′ ).

Step 3.1: Calculate the error of the color attribute of the edge to be folded (indicated by the symbol E _c ).

Step 3.1.1: Calculate the quadratic color error measure of each vertex in the normalized grid 3D model through formula (9).

Q _vc (a) = ΣQ _fc (a) (9)

Among them, Q _vc (a) represents the color quadratic error measure of any vertex a in the normalized mesh 3D model; Q _fc (a) represents a certain neighbor of vertex a in the normalized mesh 3D model The color quadratic error measure of the triangular face; ΣQ _fc (a) represents the sum of the color quadratic error measure of all adjacent triangular faces of vertex a in the normalized mesh 3D model.

When calculating the color quadratic error measure Q _fc (a) of an adjacent triangular face of vertex a in the normalized mesh 3D model, because there are three vertices of the same triangular face with the same color or two of them When the colors of the vertices are the same, the three color vectors of the triangular face cannot form a plane. Therefore, for a triangular surface whose three vertices have the same color or two of the vertices have the same color, the calculation method of the color quadratic error measure Q _fc (a) is:

When the colors of the three vertices of a triangular surface are the same, it is equivalent to a point in the color space, and the color of the point is represented by the symbol v 1, _{v 1 =} (r ₁ ,g ₁ ,b ₁ ), ( r ₁ , g ₁ , b ₁ ) respectively represent the values of the three components in the RGB space; then the color quadratic error measure Q _fc (a) of the triangular surface with the same color of the three vertices is calculated by the formula (10).

where I is the identity matrix.

When the colors of any two vertices in a triangular patch are the same, the color plane where the triangle is located degenerates into a straight line. Use symbols v _c1 , v _c2 and v _c3 to represent the colors of the three vertices respectively, v _c1 = (r ₁ , g ₁ , b ₁ ), v _c2 = v _c3 = (r ₂ , g ₂ , b ₂ ), ( r ₁ , g ₁ , b ₁ ) and (r ₂ , g ₂ , b ₂ ) both represent the values of the three components in the RGB space; then for the color quadratic error measure Q _fc of a triangular surface with two vertices of the same color (a) is calculated by formula (11).

in,

Through the operation of this step, the color quadratic error measure of vertices v _k and v _k ' on the edge to be folded (v _k , v _k' ) is obtained.

Step 3.1.2: Use formula (12) to calculate the vertices obtained after folding the points v _k and v _k′ on the edge to be folded (indicated by symbols (v _k , v _k′ ) (indicated by symbols Indicates the color quadratic error measure (indicated by the symbol Q _c ).

_Qc = _Qvc (k) + _Qvc (k') (12)

Among them, Q _vc (k) and Q _vc (k′) can be calculated by formula (9).

Step 3.1.3: Calculate the color attribute error E _c of the edge to be folded.

The vertices obtained after the points v _k and v _k' on the edge to be folded (v _k , v _k′ ) are folded have geometric properties (with the symbol ) and color feature attributes (with the symbol express), (x,y,z) is the vertex The three-dimensional geometric coordinates of , (r, g, b) is the vertex color 3d vector. The color attribute error E _c of the edge to be folded is calculated by formula (13).

Step 3.2: Calculate the geometric property error of the edge to be folded (expressed by the symbol E _g ).

Step 3.2.1: Calculate the geometric quadratic error measure of each vertex in the normalized grid 3D model through formula (14).

Q _vg (a)＝∑Q _fg (a) (14)

Among them, Q _vg (a) represents the geometric quadratic error measure of any vertex a in the normalized three-dimensional mesh model; Q _fg (a) represents an adjacent Geometric quadratic error measure of triangular faces; ∑Q _fg (a) represents the sum of geometric quadratic error measures of all adjacent triangular faces of vertex a in the normalized mesh 3D model.

Step 3.2.2: Use formula (15) to calculate the point v _k of the edge to be folded (v _k , v _k′ ) and the vertex obtained after v _k′ is folded The geometric quadratic error measure of (denoted by the symbol Q _g ).

The edges in the normalized mesh 3D model are divided into three types: internal edges, simple edges and boundary edges; the points in the normalized mesh 3D model are divided into two types: internal points and boundary points. Both endpoints of an interior edge are interior points; one endpoint of a simple edge is an interior point and the other endpoint is a border point; both endpoints of a border edge are border points. Boundary edges have only one contiguous face and all other edges have two contiguous faces.

If the edge to be folded (v _k , v _k′ ) is a simple edge or an internal edge, the point v _k of the edge to be folded (v _k , v _k′ ) and the vertex obtained after v _k′ are calculated by formula (15) The geometric quadratic error measure Q _g .

_Qg = _Qvg (k) + _Qvg (k') (15)

Among them, Q _vg (k) and Q _vg (k′) can be calculated by formula (14).

If the edge to be folded (v _k , v _k′ ) is a boundary edge, then the vertex v _k and v _k′ of the edge to be folded (v _k , v _k′ ) are folded The calculation method of the geometric quadratic error measure Q _g is:

Make a vertical plane of its associated plane for the edge to be folded (v _k , v _k′ ), and merge the quadratic matrix of the vertical plane (indicated by the symbol Q _p ) to the edge to be folded (v _k , v _k′ ) From the quadratic matrix of the boundary points, the geometric quadratic error measure Q _g of the edge to be folded (v _k , v _k′ ) is obtained, as shown in formula (16).

Among them, Q _t is the quadratic matrix of any border point on the side to be folded (v _k , v _k′ ); t represents the sequence number of the border point on the side to be folded (v _k , v _k′ ), and t is integer; Indicates the sum of quadratic matrices of all boundary points on the edge to be folded (v _k , v _k′ ); w is a constant whose function is to ensure that the boundary edge is moderately simplified, and at the same time make the position of the target point close to Boundary edges; w ∈ [100,1000].

Step 3.2.3: Calculate the geometric attribute error E _g of the edge to be folded by formula (17).

Step 3.3: Calculate the folding cost of the edge to be folded (indicated by the symbol cost) through formula (18).

Among them, S(v _k ) and S(v _k′ ) are calculated by formula (8).

Step 4: Sort all the edges to be folded according to the folding cost from small to large.

Step 5. From the results of step 5, select the edge to be folded with the least cost and perform the folding operation to obtain a new model.

Step 6. Repeat steps 2 to 6 until the simplification requirements are met.

Beneficial effect

Compared with the existing technology, the method of the present invention is mainly to study the simplification method of the model with color, and innovatively transforms the RGB space, so that the algorithm takes into account the color attribute information of the model at the same time during the simplification, so that the model In the process of simplification, not only the global geometric features can be maintained, but also the color attribute information of the grid can be maintained. The results show that the algorithm of the method of the present invention can not only realize the simplification of the model with the attribute grid, but also effectively maintain the salient attribute features of the model, and can still maintain the salient features of the color of the model when the simplification rate reaches 90%.

Description of drawings

Fig. 1 is the front view of the original grid three-dimensional model in the specific embodiment of the present invention;

Fig. 2 is a three-dimensional schematic diagram of an original grid three-dimensional model in a specific embodiment of the present invention;

Fig. 3 is the schematic diagram that the original grid three-dimensional model in the specific embodiment of the present invention is transformed into gray scale model;

Fig. 4 is the schematic diagram of the model corresponding to ε, 2ε, and 3ε obtained respectively for σ _t in the specific embodiment of the present invention and the model schematic diagram obtained after integrating the results of different specifications; wherein, Fig. 4 (a) is that σ _t is ε Figure 4(b) is a schematic diagram of the model obtained when _σt is 2ε; Figure 4(c) is a schematic diagram of the model obtained when _σt is 3ε; Figure 4(d) is the result of combining different specifications, The schematic diagram of the obtained model is shown in;

Fig. 5 is the schematic diagram of the simplified effect comparison of the automobile model of the present invention; Wherein, Fig. 5 (a) is the three-dimensional model of the original grid; Fig. 5 (b) is the simplified result schematic diagram of the QEM method; Fig. 5 (c) adopts the present invention Simplified results schematic of the method.

Detailed ways

According to the above technical solutions, the present invention will be described in detail below in conjunction with the accompanying drawings and implementation examples.

In this embodiment, the car model shown in Figure 1 and Figure 2 is simplified using the model simplification method proposed by the present invention based on the preservation of significant color attribute features. The original model has a total of 10474 patches, and the specific operation process is as follows:

Step 1: Normalize the original mesh 3D model. The original mesh 3D model includes color attributes of vertices. Specifically:

Step 1.1: Process the color attributes of vertices of the original mesh 3D model.

Express the color attribute of the vertex of the original mesh 3D model as a 3D vector composed of red, green and blue (RGB) color components, and obtain the color attribute coordinates of the vertex. Then, the weighted color component method is adopted to calculate the color difference between any two vertices of the original mesh 3D model through formula (1). Use the symbols c _i and c _j to represent any two vertices of the original mesh 3D model, and use the symbols c _i (r _i , g _i , b _i ) and c _j (r _j , g _j , b _j ) to represent the original mesh The color 3D vectors of any two vertices c _i and c _j of the lattice 3D model.

Wherein, D( _ci ,c _j ) represents the color difference between any two vertices c _i and c _j of the original mesh 3D model; w _r =3, w _g =4, w _b =2.

Step 1.2: Standardize the geometric coordinates and color attribute coordinates of each vertex of the original mesh 3D model to the same range.

Based on the operation in step 1.1, the coordinate ranges of the geometric coordinates and color attribute coordinates of each vertex of the original mesh 3D model may be different. In order to make the spatial position and color attribute information play an equal role in the calculation of the folding cost, the original mesh The geometric coordinates and color attribute coordinates of each vertex of the 3D model are within the same range, that is, the three components of the vertex color coordinates of the original mesh 3D model are all within the range of [0, m], then the original mesh 3D model vertices The three dimensions of the geometric coordinates of need to be specified in the range [0,m], where m=2.

Set the coordinate ranges of the three dimensions of the bounding box of the original grid 3D model to [x _min , x _max ], [y _min , y _max ], [z _min , z _max ] respectively, then calculate by formula (2) The normalized coordinate value of any vertex in the original mesh 3D model.

Among them, (x _a , y _a , z _a ) represent the geometric coordinates of any vertex in the original mesh 3D model; (x′ _b , y′ _b , z′ _b ) represent the specification of any vertex in the original mesh 3D model The geometric coordinates after transformation; d=max{x _max -x _min , y _max -y _min , z _max -z _min }.

After the operation in step 1, a normalized grid 3D model is obtained.

Step 2: Obtain the saliency of color attributes of all vertices of the normalized three-dimensional grid model.

On the basis of the operation in step 1, the color attribute salience of all vertices of the normalized mesh 3D model is calculated, specifically:

Step 2.1: Calculate the gray value of each vertex in the normalized grid 3D model.

Use symbols (r _a , g _a , b _a ) to represent the color attribute coordinates of any vertex in the normalized mesh 3D model. For the convenience of research, the color vector of the vertex is reduced to a one-dimensional vector. Using grayscale can convert the color model into a high-quality black-and-white model. Different colors in the RGB space correspond to different grayscale values, and different grayscale values also correspond to different RGB vectors. Using the gray value of the vertex to represent the original color information can not only reduce the dimension of the original model, but also represent the original model without distortion. The gray value of each vertex in the normalized grid 3D model is calculated by formula (3), represented by gray(a).

gray(a)＝0.299r _a +0.587g _a +0.114b _a (3)

Through this conversion, a color model can be transformed into a high-quality grayscale model, as shown in Figure 3.

Step 2.2: Calculate the neighborhood gray value of each vertex in the normalized grid 3D model.

Calculate the neighborhood of vertex a with radius σ by formula (4), where σ is an artificially set value. The neighborhood of vertex a is defined using Euclidean distance.

N(a,σ)={x|||x-a||<σ,x∈U} (4)

Among them, N(a,σ) represents the neighborhood of vertex a whose radius is σ; U represents the normalized three-dimensional mesh model.

Then, the neighborhood gray value of vertex a is calculated by formula (5); the neighborhood gray value of vertex a adopts the Gaussian weighted average gray value of the vertex gray.

Among them, G(gray(a),σ) represents the neighborhood gray value of vertex a; exp( ) represents the power of the natural base e.

Step 2.3: Calculate the saliency of the color attribute of each vertex in the normalized mesh 3D model. The saliency of the color attribute of the vertex is calculated by the difference of the gray values of different radii, as shown in formula (6).

S(a)＝|G(gray(a),2σ)-G(gray(a),σ)| (6)

Among them, S(a) represents the salience of the color attribute of vertex a in the normalized three-dimensional mesh model.

In order to calculate the salience degree of the grid attribute in the neighborhood of different specifications, formula (7) is used to calculate the salience degree of the color attribute of vertex a under a certain specification.

S _t (a)＝|G(gray(a),2σ _t )-G(gray(a),σ _t )| (7)

Among them, S _t (a) represents the color attribute salience of vertex a under specification t; σ _t represents the neighborhood radius of vertex a under specification t; t∈{1,2,3};σ _t ∈{ε, 2ε, 3ε}, the value of ε is 0.3% of the diagonal length of the bounding box of the normalized mesh 3D model.

In order to synthesize the results of different specifications, the nonlinear suppression operator is used to synthesize the color attribute saliency S _t (a) of vertex a under different specifications, and formula (6) is further rewritten as formula (8).

Among them, M _t represents the maximum value of S _t (a) calculated by vertex a under specification t; Indicates the average value of vertex a except M _t in S _t (a) calculated under specification t.

By formula (8), the color attribute salience of all vertices of the normalized mesh 3D model can be obtained.

Step 3: Calculate the geometric attribute error and color attribute error of each edge to be folded in turn, and the folding cost of the edge to be folded.

Step 3.1: Calculate the color attribute error E _c of the edge to be folded.

Step 3.1.1: Calculate the quadratic color error measure of each vertex in the normalized grid 3D model through formula (9).

Q _vc (a) = ΣQ _fc (a) (9)

Among them, Q _vc (a) represents the color quadratic error measure of any vertex a in the normalized mesh 3D model; Q _fc (a) represents a certain neighbor of vertex a in the normalized mesh 3D model The color quadratic error measure of the triangular face; ΣQ _fc (a) represents the sum of the color quadratic error measure of all adjacent triangular faces of vertex a in the normalized mesh 3D model.

When calculating the color quadratic error measure Q _fc (a) of an adjacent triangular face of vertex a in the normalized mesh 3D model, because there are three vertices of the same triangular face with the same color or two of them When the colors of the vertices are the same, the three color vectors of the triangular face cannot form a plane. Therefore, for a triangular surface whose three vertices have the same color or two of the vertices have the same color, the calculation method of the color quadratic error measure Q _fc (a) is:

When the colors of the three vertices of a triangular surface are the same, it is equivalent to a point in the color space, and the color of the point is represented by the symbol v 1, _{v 1 =} (r ₁ ,g ₁ ,b ₁ ), ( r ₁ , g ₁ , b ₁ ) respectively represent the values of the three components in the RGB space; then the color quadratic error measure Q _fc (a) of the triangular surface with the same color of the three vertices is calculated by the formula (10).

where I is the identity matrix.

When the colors of any two vertices in a triangular patch are the same, the color plane where the triangle is located degenerates into a straight line. Use symbols v _c1 , v _c2 and v _c3 to represent the colors of the three vertices respectively, v _c1 = (r ₁ , g ₁ , b ₁ ), v _c2 = v _c3 = (r ₂ , g ₂ , b ₂ ), ( r ₁ , g ₁ , b ₁ ) and (r ₂ , g ₂ , b ₂ ) both represent the values of the three components in the RGB space; then for the color quadratic error measure Q _fc of a triangular surface with two vertices of the same color (a) is calculated by formula (11).

in,

Through the operation of this step, the color quadratic error measure of vertices v _k and v _k ' on the edge to be folded (v _k , v _k' ) is obtained.

Step 3.1.2: Use formula (12) to calculate the point v _k on the edge to be folded (v _k , v _k′ ) and the vertex obtained by folding v _k′ The color quadratic error measure Q _c .

_Qc = _Qvc (k) + _Qvc (k') (12)

Among them, Q _vc (k) and Q _vc (k′) can be calculated by formula (9).

Step 3.1.3: Calculate the color attribute error E _c of the edge to be folded.

The vertices obtained after the points v _k and v _k' on the edge to be folded (v _k , v _k′ ) are folded have geometric properties and the color feature attribute (x,y,z) is the vertex The three-dimensional geometric coordinates of , (r, g, b) is the vertex color 3d vector. The color attribute error E _c of the edge to be folded is calculated by formula (13).

Step 3.2: Calculate the geometric property error E _g of the edge to be folded.

Step 3.2.1: Calculate the geometric quadratic error measure of each vertex in the normalized grid 3D model through formula (14).

Q _vg (a) = ΣQ _fg (a) (14)

Among them, Q _vg (a) represents the geometric quadratic error measure of any vertex a in the normalized three-dimensional mesh model; Q _fg (a) represents an adjacent Geometric quadratic error measure of triangular faces; ∑Q _fg (a) represents the sum of geometric quadratic error measures of all adjacent triangular faces of vertex a in the normalized mesh 3D model.

Step 3.2.2: Use formula (15) to calculate the point v _k of the edge to be folded (v _k , v _k′ ) and the vertex obtained after v _k′ is folded The geometric quadratic error measure Q _g .

The edges in the normalized mesh 3D model are divided into three types: internal edges, simple edges and boundary edges; the points in the normalized mesh 3D model are divided into two types: internal points and boundary points. Both endpoints of an interior edge are interior points; one endpoint of a simple edge is an interior point and the other endpoint is a border point; both endpoints of a border edge are border points. Boundary edges have only one contiguous face and all other edges have two contiguous faces.

If the edge to be folded (v _k , v _k′ ) is a simple edge or an internal edge, the point v _k of the edge to be folded (v _k , v _k′ ) and the vertex obtained after v _k′ are calculated by formula (15) The geometric quadratic error measure Q _g .

_Qg = _Qvg (k) + _Qvg (k') (15)

Among them, Q _vg (k) and Q _vg (k′) can be calculated by formula (14).

If the edge to be folded (v _k , v _k′ ) is a boundary edge, then the vertex v _k and v _k′ of the edge to be folded (v _k , v _k′ ) are folded The calculation method of the geometric quadratic error measure Q _g is:

The side to be folded (v _k , v _k′ ) is made a vertical plane _of its associated plane, and the quadratic matrix Q _p of _the vertical plane is merged into the quadratic In the type matrix, the geometric quadratic error measure Q _g of the edge to be folded (v _k , v _k′ ) is obtained, as shown in formula (16).

Among them, Q _t is the quadratic matrix of any border point on the side to be folded (v _k , v _k′ ); t represents the sequence number of the border point on the side to be folded (v _k , v _k′ ), and t is integer; Indicates the sum of quadratic matrices of all boundary points on the edge to be folded (v _k , v _k′ ); w is a constant whose function is to ensure that the boundary edge is moderately simplified, and at the same time make the position of the target point close to Boundary edges; w=100.

Step 3.2.3: Calculate the geometric attribute error E _g of the edge to be folded by formula (17).

Step 3.3: Calculate the folding cost of the edge to be folded by formula (18).

Among them, S(v _k ) and S(v _k′ ) are calculated by formula (8).

Step 4: Sort all the edges to be folded according to the folding cost from small to large.

Step 5. From the results of step 5, select the edge to be folded with the least cost and perform the folding operation to obtain a new model.

Step 6. Repeat steps 2 to 6 until the simplification requirements are met.

Corresponding to _σt being ε, 2ε, 3ε, the schematic diagrams of the obtained models are shown in Fig. 4(a), Fig. 4(b) and Fig. 4(c) respectively. Combining the results of different specifications, the schematic diagrams of the obtained models are shown in Fig. 4(d).

In order to illustrate the effect of the present invention, the method of QEM (quadratic error measurement, only considering geometric features) and the method of the present invention are used simultaneously to simplify the automobile model as shown in Figure 1 and Figure 2, and the comparison diagram obtained is as shown in Figure 2 5.

Figure 5(a) is the original colored car model. Fig. 5 (b) and Fig. 5 (c) all are the model under 90% of simplification rate; Fig. 5 (b) is the simplified result of QEM method, and it does not consider color attribute feature; Fig. 5 (c) adopts the present invention Simplified result of the method. It is not difficult to see that the method of the present invention realizes the simplification of the color attribute model. Second, guided by the saliency of the model's color attributes, Figure 5(c) preserves the salient features of the grid better than Figure 5(b). The headlight part can be well preserved until the simplification rate is 90%. The car light at the right door has disappeared in Figure 5(b), but it still remains in Figure 5(c). The color boundary of the front mirror part of the car in Fig. 5(c) is also clearer than that in Fig. 5(b). This shows that the algorithm of the method of the present invention can not only realize the grid simplification of the grid with attributes well, but also effectively maintain the remarkable attribute characteristics of the grid.

Although the embodiment of the present invention has been described in conjunction with the accompanying drawings, for those skilled in the art, some improvements can be made without departing from the principle of the present invention, and these should also be considered as belonging to the protection scope of the present invention.

Claims (2)

1. A model simplification method based on salient color attribute feature preservation, is characterized in that: its specific implementation steps are: Step 1. Normalize the original grid 3D model; the original grid 3D model includes the color attributes of vertices; specifically: Step 1.1: process the color attribute of the vertices of the original mesh 3D model; Express the color attribute of the vertices of the original grid 3D model as a 3D vector composed of red, green and blue RGB color components to obtain the color attribute coordinates of the vertices; then, adopt the weighted color component method to calculate the The color difference between any two vertices; use the symbols c _i and c _j to represent any two vertices of the original mesh 3D model, and use the symbols c _i (r _i , g _i , b _i ) and c _j (r _j , g _j , b _j ) respectively represent the color three-dimensional vectors of any two vertices c _i and c _j of the original mesh three-dimensional model; Among them, D( _ci ,c _j ) represents the color difference between any two vertices c _i and c _j of the original mesh 3D model; w _r , w _g , w _b represent the weighting coefficients corresponding to red, green and blue respectively , w _r >w _b , w _g >w _b ; The color difference D( _ci ,c _j ) between any two vertices c _i and c _j of the original mesh 3D model can be the Euclidean distance between vertices c _i and c _j , but the prerequisite is that the RGB space is a Uniform color space: that is, the equal color difference color of each color should form a sphere in RGB space; and the colors at different positions on the sphere and the color at the center of the sphere should show the same difference; RGB space obviously does not meet this condition, Using Euclidean distance to measure color difference in RGB space does not conform to human visual perception; research shows that human eyes have different sensitivities to red, green and blue primary colors, and are more sensitive to red and green, so when calculating color difference The three primary colors need to be treated differently to make the calculation more accurate; in order to compensate the non-uniformity of the RGB space, the weighted color component method is adopted for the calculation of the color difference: that is, three weighting coefficients w _r , w _g , and w _b are added; Step 1.2: Standardize the geometric coordinates and color attribute coordinates of each vertex of the original grid 3D model to the same range; Based on the operation in step 1.1, the coordinate ranges of the geometric coordinates and color attribute coordinates of each vertex of the original mesh 3D model may be different. In order to make the spatial position and color attribute information play an equal role in the calculation of the folding cost, the original mesh The geometric coordinates and color attribute coordinates of each vertex of the 3D model are within the same range, that is, the three components of the vertex color coordinates of the original mesh 3D model are all within the range of [0, m], then the original mesh 3D model vertices The three dimensions of the geometric coordinates need to be specified in the range of [0,m], m∈[1,10]; Set the coordinate ranges of the three dimensions of the bounding box of the original grid 3D model to [x _min , x _max ], [y _min , y _max ], [z _min , z _max ] respectively, then calculate by formula (2) The normalized coordinate value of any vertex in the original mesh 3D model; Among them, (x _b , y _b , z _b ) represents the geometric coordinates of any vertex in the original mesh 3D model; (x′ _b , y′ _b , z′ _b ) represents the specification of any vertex in the original mesh 3D model The geometric coordinates after transformation; d=max{x _max -x _min , y _max -y _min , z _max -z _min }; After the operation of step 1, the normalized grid 3D model is obtained; Step 2, obtaining the color attribute salience of all vertices of the normalized grid three-dimensional model; On the basis of the operation in step 1, the color attribute salience of all vertices of the normalized mesh 3D model is calculated, specifically: Step 2.1: Calculating the gray value of each vertex in the normalized grid 3D model; Use the symbol (r _a , g _a , b _a ) to represent the color attribute coordinates of any vertex in the normalized mesh 3D model; for the convenience of research, the color vector of the vertex is reduced to a one-dimensional vector; using grayscale can Convert the color model to a high-quality black-and-white model. Different colors in the RGB space correspond to different gray values, and different gray values also correspond to different RGB vectors; use the gray value of the vertex to represent the original color information, not only can reduce the dimension of the original model, but also represent the original model without distortion; the gray value of each vertex in the normalized grid 3D model is calculated by formula (3), represented by gray(a) ; gray(a)＝0.299r _a +0.587g _a +0.114b _a (3) Through this conversion, a color model can be converted into a high-quality grayscale model; Step 2.2: Calculate the neighborhood gray value of each vertex in the normalized grid 3D model; Calculate the neighborhood of vertex a with radius σ by formula (4), where σ is an artificially set value; the neighborhood of vertex a is defined by Euclidean distance; N(a,σ)={x|||x-a||<σ,x∈U} (4) Among them, N(a,σ) represents the neighborhood of vertex a whose radius is σ; U represents the normalized three-dimensional mesh model; Then, the neighborhood gray value of vertex a is calculated by formula (5); the neighborhood gray value of vertex a adopts the Gaussian weighted average gray value of the vertex gray; Among them, G(gray(a),σ) represents the neighborhood gray value of vertex a; exp(·) represents the power of the natural base e; Step 2.3: Calculate the salience degree of the color attribute of each vertex in the normalized grid three-dimensional model; calculate the salience degree of the color attribute of the vertex by the difference of the gray levels of different radii, as shown in formula (6); S(a)＝|G(gray(a),2σ)-G(gray(a),σ)| (6) Wherein, S(a) represents the salience degree of the color attribute of vertex a in the normalized grid three-dimensional model; In order to calculate the salience degree of the grid attribute in the neighborhood of different specifications, use the formula (7) to calculate the salience degree of the color attribute of the vertex a under a certain specification; S _t (a)＝|G(gray(a),2σ _t )-G(gray(a),σ _t )| (7) Among them, S _t (a) represents the color attribute salience of vertex a under specification t; σ _t represents the neighborhood radius of vertex a under specification t; t∈{1,2,3};σ _t ∈{ε, 2ε, 3ε}, the value of ε is 0.3% to 0.8% of the diagonal length of the bounding box of the normalized grid 3D model; In order to synthesize the results of different specifications, the nonlinear suppression operator is used to synthesize the color attribute saliency S _t (a) of vertex a under different specifications, and formula (6) is further rewritten as formula (8); Among them, M _t represents the maximum value of S _t (a) calculated by vertex a under specification t; Indicates the average value of vertex a except M _t in S _t (a) calculated under specification t; By formula (8), the color attribute salience of all vertices of the normalized grid three-dimensional model can be obtained; Step 3. Calculate the geometric attribute error and color attribute error of each edge to be folded sequentially, as well as the folding cost of the edge to be folded; the edge to be folded is represented by the symbol (v _k , v _k′ ); Step 3.1: Calculate the color attribute error of the edge to be folded, represented by the symbol _Ec ; Step 3.1.1: Calculate the secondary error measure of the color of each vertex in the normalized grid three-dimensional model by formula (9); Q _vc (a)＝∑Q _fc (a) (9) Among them, Q _vc (a) represents the color quadratic error measure of any vertex a in the normalized mesh 3D model; Q _fc (a) represents a certain neighbor of vertex a in the normalized mesh 3D model The color quadratic error measure of the triangular face; ∑Q _fc (a) represents the sum of the color quadratic error measure of all adjacent triangular faces of vertex a in the normalized mesh three-dimensional model; When calculating the color quadratic error measure Q _fc (a) of an adjacent triangular face of vertex a in the normalized mesh 3D model, because there are three vertices of the same triangular face with the same color or two of them When the colors of the vertices are the same, the three color vectors of the triangular face cannot form a plane; therefore, for a triangular face with the same color of three vertices or the same color of two vertices, the color quadratic error measure Q _fc ( a) The calculation method is: When the colors of the three vertices of a triangular surface are the same, it is equivalent to a point in the color space, and the color of the point is represented by the symbol v 1, _{v 1 =} (r ₁ ,g ₁ ,b ₁ ), ( r ₁ , g ₁ , b ₁ ) respectively represent the values of the three components in the RGB space; then for the color quadratic error measure Q _fc (a) of the triangular surface with the same color of the three vertices is calculated by the formula (10); Wherein, I is the identity matrix; When the colors of any two vertices in a triangular facet are the same, the color plane where the triangle is located degenerates into a straight line; the colors of the three vertices are represented by symbols v _c1 , v _c2 and v _c3 respectively, v _c1 =(r ₁ ,g ₁ ,b ₁ ), v _c2 =v _c3 =(r ₂ ,g ₂ ,b ₂ ), (r ₁ ,g ₁ ,b ₁ ) and (r ₂ ,g ₂ ,b ₂ ) all represent the RGB space The value of the three components in; then for the color quadratic error measure Q _fc (a) of the same triangular surface of the color of two vertices is calculated by formula (11); in, Through the operation of this step, the color quadratic error measure of the vertices v _k and v k' on the side to be folded (v _k , v _{k '} ) is obtained; Step 3.1.2: Calculate the quadratic error measure Q _c of the color represented by the vertex v obtained by folding the point v _k on the edge to be folded (v _k , v _k′ ) and v _k′ through formula (12); _Qc = _Qvc (k) + _Qvc (k') (12) Among them, Q _vc (k) and Q _vc (k′) can be calculated by formula (9); Step 3.1.3: Calculate the color attribute error E _c of the edge to be folded; The vertices obtained after the points v _k and v _k' on the edge to be folded (v _k , v _k′ ) are folded have geometric properties Representation and Color Feature Properties express, (x,y,z) is the vertex The three-dimensional geometric coordinates of , (r, g, b) is the vertex The color three-dimensional vector; the color property error E _c of the edge to be folded is calculated by formula (13); Step 3.2: Calculate the geometric attribute error of the edge to be folded, represented by the symbol _Eg ; Step 3.2.1: Calculate the geometric quadratic error measure of each vertex in the normalized grid three-dimensional model by formula (14); Q _vg (a)＝∑Q _fg (a) (14) Among them, Q _vg (a) represents the geometric quadratic error measure of any vertex a in the normalized three-dimensional mesh model; Q _fg (a) represents an adjacent The geometric quadratic error measure of the triangular surface; ∑ Q _{f g} (a) represents the sum of the geometric quadratic error measures of all adjacent triangular faces of the vertex a in the three-dimensional mesh model after normalization; Step 3.2.2: Calculate the geometric quadratic error measure of the point v _k of the edge to be folded (v _k , v _k′ ) and the vertex v obtained by folding v _k′ through the formula (15), expressed by the symbol Q _g ; Divide the edges in the normalized mesh 3D model into three categories: internal edges, simple edges, and boundary edges; divide the points in the normalized mesh 3D model into two categories: internal points and boundary points; internal Both endpoints of an edge are interior points; one endpoint of a simple edge is an interior point and the other is a border point; both endpoints of a border edge are border points; border edges have only one adjoining face while other edges have two adjacent surface; If the edge to be folded (v _k , v _k′ ) is a simple edge or an internal edge, the point v _k of the edge to be folded (v _k , v _k′ ) and the vertex obtained after v _k′ are calculated by formula (15) The geometric quadratic error measure Q _g of v; _Qg = _Qvg (k) + _Qvg (k') (15) Among them, Q _vg (k) and Q _vg (k′) can be calculated by formula (14); If the edge to be folded (v _k , v _k′ ) is a boundary edge, then the geometric quadratic error measure Q _g of the point v _k of the edge to be folded (v _k , v _k′ ) and the vertex v obtained by folding v _k′ The calculation method is: The side to be folded (v _k , v _k′ ) is made a vertical plane _of its associated plane, and the quadratic matrix Q _p of _the vertical plane is merged into the quadratic In the type matrix, the geometric quadratic error measure Q _g of the edge to be folded (v _k , v _k′ ) is obtained, as shown in formula (16); Among them, Q _t′ is the quadratic matrix of any border point on the side to be folded (v _k , v _k′ ); t′ represents the sequence number of the border point on the side to be folded (v _k , v _k′ ), t 'is a positive integer; Indicates the sum of quadratic matrices of all boundary points on the edge to be folded (v _k , v _k′ ); w is a constant whose function is to ensure that the boundary edge is moderately simplified, and at the same time make the position of the target point close to Boundary edge; w∈[100,1000]; Step 3.2.3: Calculate the geometric attribute error E _g of the edge to be folded by formula (17); Step 3.3: Calculate the folding cost of the edge to be folded by formula (18). Among them, S(v _k ) and S(v _k′ ) are calculated by formula (8); Step 4. Sort all the edges to be folded according to the folding cost from small to large; Step 5. From the results of step 4, select the edge to be folded with the least cost to perform the folding operation to obtain a new model; Step 6. Repeat steps 2 to 6 until the simplification requirements are met. 2. A model simplification method based on preservation of salient color attribute features as claimed in claim 1, characterized in that: w _r =3, w _g =4, w _b =2.