CN105761314B - A kind of Model Simplification Method kept based on notable color attribute feature - Google Patents
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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
Technical Field
The invention relates to a three-dimensional model simplification method based on significant color attribute feature preservation, and belongs to the technical field of computer graphics and virtual reality.
Background
In the field of computer graphics and computer vision, objects can be represented by triangular meshes in general. Due to the increasing progress in data acquisition and modeling techniques, it is easy for people to obtain large-scale mesh model representations of objects in computers, and 3D models are becoming more and more complex. Although complex models can contain descriptions of the closest objects, they require more storage space and more time to render. However, in many applications, highly complex models containing too much detail are generally not required. The simplified grid model not only can reduce the physical storage space of the model and save the drawing time of the model, but also can greatly reduce the network transmission time of the model. In addition, the compact model can accelerate a series of calculations related to shape information in graphics, including finite element analysis, collision detection, visibility testing, shape recognition, and the like. Therefore, it is significant to properly simplify the complex multi-detail model to some extent.
With the development of computer technology, grid reduction technology has been widely applied in many computer graphics and virtual reality. These models usually contain not only complex geometric detail information, but also various surface properties such as color, texture, and surface normal vectors, among others. Grid acquisition techniques such as scanning typically produce complex grid models with properties. The geometric details and attribute details of these models can negatively impact the performance of some applications. Such as computer games and distributed virtual environments, are often run in environments with limited rendering and network transmission capabilities, and therefore models with too high a level of detail are not available. The research on the attribute mesh simplification algorithm also becomes a significant work.
So the mesh type can be divided into two categories, namely triangular mesh simplification algorithm and quadrilateral mesh simplification algorithm. Quadrilateral meshes are newly-appeared mesh representation methods in recent years, and are most widely applied to triangular mesh models, and the invention mainly aims at triangular meshes.
The triangular mesh simplification algorithm can also be classified according to different methods, and can be classified into a manifold mesh simplification algorithm and a non-manifold mesh simplification algorithm according to whether the mesh model is manifold or not. A division into view-dependent simplification and view-independent simplification can be made depending on whether or not it is view-dependent; interactive and automatic simplification algorithms can be classified according to whether or not a user is interacted with in the simplification process. The classification method is various, and some algorithms have cross-mixing. The current research results can be divided into three categories, the first category being local geometry operation simplification algorithms. Such algorithms achieve stepwise simplification of the original model in simplification by continually using local simplification operations such as vertex removal, edge folding, point-to-point contraction, and triangle removal. The main advantage of this type of algorithm is the efficient execution of the algorithm and the ease with which it can be implemented. Meanwhile, a multi-resolution model of the original mesh model can be obtained in the implementation process. The most representative of the algorithms is a quadratic error metric grid simplification algorithm proposed by Garland, and the algorithm realizes efficient simplification of a model by performing point pair folding for multiple times, and simultaneously enables the simplification error to be within a controllable range. The second type is a surface clustering algorithm, which divides the surface of the original model into several blocks according to a certain clustering rule, then replaces each small block model with some simple geometric surfaces such as planes, spheres, or cylinders, and then triangulates each block model again. In the replacement process, the simple geometric surface with the minimum error is selected to replace each block of the original model. One of the simpler is to replace the model with a flat surface, and the model obtained in this way is also simpler. The third type of algorithm is a direct sampling method, which may also be referred to as a mesh repartitioning method. In the algorithm, a certain number of points are distributed on the surface of a grid model according to a certain rule, and then a new model is obtained by using a Delaunay triangulation rule on point clouds of the distributed points. A representative algorithm for comparison is a central wien graph subdivision scheme based on isotropy and anisotropy. The main advantage of this type of algorithm is that it enables a more uniform and regular distribution of the grid.
There is still less current research on the attribute mesh simplification algorithm than the non-attribute mesh model simplification algorithm. For a limited number of surface models, such as the height field model, a very simple simplified algorithm can be adopted. However, more general models require more advanced simplification techniques, Hoppe simplified grids, where the measurement error explicitly contains the attribute. Certain et al discusses the addition of color to a wavelet based multi-resolution model. The algorithm proposed by Cohen first simplifies the mesh model, and then re-parameterizes the texture and maps it onto the simplified mesh. Garland et al expands a three-dimensional vector representing a vertex to a high-dimensional vector, and simplifies the band attribute mesh by using an expanded quadratic error metric algorithm after the vector includes not only the position information of the vertex but also other attribute information such as the color or texture of the mesh. Fahn et al propose a simplified algorithm for preserving model patch color, which can only simplify the model of patch associated attributes, but cannot simplify the model of vertex associated attributes. The method comprehensively considers the geometrical importance and the importance of the texture attributes aiming at the grid model with the texture attributes, Liuxiu and the like, and determines the folding sequence of all edges in the model by taking the geometrical importance and the importance of the texture attributes as the folding cost of each half edge. Texture cost is introduced from the inconsistency of the folded geometric space and the texture space, so that the edge folding cost is the weighted sum of the geometric cost and the texture cost, and a folding forbidding strategy is adopted in the aspect of processing the strong characteristic edge. In the aspect of processing the boundary edge, the simplification quality of the boundary is well controlled by turning from the weak characteristic point to the strong characteristic point. The algorithm effectively weakens the texture pulling phenomenon in the simplification process. The visual effect of the simplified model is ensured.
Current simplified algorithms for mesh models with attributes can be divided into two categories. The first method is to process the geometric information and attribute information of the model at the same time, i.e. the original algorithm only considering the geometric information of the grid is expanded, so that the processing of the two kinds of information is synchronously performed. Such as extending the three-dimensional mesh to a high-dimensional mesh and then simplifying the high-dimensional mesh. How to coordinate geometric information and attribute information and how to define a high-dimensional grid are the difficulties of the algorithm. The second approach is to divide the lattice reduction algorithm with attributes into two steps. In the first step, attribute information of the grids is not considered, only the grids without attributes are simplified, and then the attribute information of the original grid model is mapped to the simplified grids. This method is performed in steps, where how to remap the attribute information of the original mesh onto the simplified model is a difficult point of the algorithm.
Disclosure of Invention
The invention aims to solve the problem of grid simplification of a three-dimensional model with color attributes, and provides a model simplification method based on significant color attribute feature preservation.
The purpose of the invention is realized by the following technical scheme.
The invention relates to a model simplification method based on significant color attribute feature preservation, which comprises the following specific implementation steps:
step one, normalizing the original grid three-dimensional model. The original mesh three-dimensional model includes color attributes of the vertices. The method specifically comprises the following steps:
step 1.1: and processing the color attributes of the vertexes of the three-dimensional model of the original mesh.
And expressing the color attribute of the vertex of the three-dimensional model of the original grid as a three-dimensional vector consisting of red, green and blue (RGB) color components to obtain the color attribute coordinate of the vertex. Then, a weighted color component method is adopted to calculate the color difference of any two vertexes of the original mesh three-dimensional model through the formula (1). By the symbol ciAnd cjAny two vertices representing the three-dimensional model of the original mesh, denoted by the symbol ci(ri,gi,bi) And cj(rj,gj,bj) Any two vertexes c of original mesh three-dimensional modeliAnd cjThe color three-dimensional vector of (1).
Wherein D (c)i,cj) Two arbitrary representing three-dimensional models of the original meshA vertex ciAnd cjThe color difference of (a); w is ar、wg、wbRespectively representing the weighting coefficients, w, for red, green and bluer＞wb，wg＞wb。
Preferably, wr＝3、wg＝4、wb＝2。
Any two vertexes c of original mesh three-dimensional modeliAnd cjColor difference D (c) ofi,cj) May adopt a vertex ciAnd cjEuclidean distance between them, but with the proviso that the RGB space is a uniform color space: namely, the color with equal color difference of each color should form a spherical surface in the RGB space; and the colors at different positions on the sphere and at the center of the sphere should show the same difference. The RGB space obviously does not satisfy this condition, and the measurement of chromatic aberration in the RGB space by euclidean distance does not conform to human perception. Research shows that human eyes have different sensitivities to the three primary colors of red, green and blue and are more sensitive to the red and the green, so that the three primary colors need to be treated differently when calculating color difference, and calculation is more accurate. To compensate for the non-uniformity of the RGB space, a weighted color component method is adopted for the calculation of the color difference: i.e. adding wr、wg、wbThree weighting coefficients.
Step 1.2: and (4) standardizing the geometric coordinates and the color attribute coordinates of each vertex of the original mesh three-dimensional model to be in the same range.
On the basis of the operation of step 1.1, the coordinate ranges of the geometric coordinates and the color attribute coordinates of each vertex of the original mesh three-dimensional model may be different, and in order to enable the spatial position and the color attribute information to play an equal role in calculating the folding cost, the geometric coordinates and the color attribute coordinates of each vertex of the original mesh three-dimensional model are normalized to be in the same range, that is: and the three components of the vertex color coordinates of the three-dimensional model of the original grid are all in the range of [0, m ], so that the three dimensions of the geometric coordinates of the vertices of the three-dimensional model of the original grid need to be specified in the range of [0, m ], and m belongs to [1,10 ].
Setting the coordinate ranges of three dimensions of bounding boxes of the original grid three-dimensional model as xmin,xmax]，[ymin,ymax]，[zmin,zmax]And calculating the coordinate value of any vertex in the original mesh three-dimensional model after normalization by using the formula (2).
Wherein (x)a,ya,za) Representing the geometric coordinate of any vertex in the original mesh three-dimensional model; (x'b,y′b,z′b) Representing the geometric coordinate of any vertex in the original mesh three-dimensional model after normalization; d ═ max { xmax-xmin,ymax-ymin,zmax-zmin}。
And (5) obtaining a normalized grid three-dimensional model through the operation of the first step.
And step two, obtaining the color attribute significance of all vertexes of the normalized mesh three-dimensional model.
On the basis of the operation of the first step, calculating the color attribute significance of all the vertexes of the normalized mesh three-dimensional model, specifically:
step 2.1: and calculating the gray value of each vertex in the normalized mesh three-dimensional model.
By the symbol (r)a,ga,ba) And representing the color attribute coordinates of any vertex in the normalized grid three-dimensional model after calculation. For the sake of research, the color vector of the vertex is reduced to a one-dimensional vector. Using gray scale enables converting a color model into a high quality black and white model, with different colors in the RGB space corresponding to different gray scale values, which also correspond to different RGB vectors. The gray value of the vertex is used to represent the original color information, which can not only reduce the original color informationThe dimension of the model can represent the original model without distortion. The gray value of each vertex in the normalized mesh three-dimensional model is calculated by formula (3) and is represented by gray (a).
gray(a)＝0.299ra+0.587ga+0.114ba(3)
By this conversion, a color model can be converted into a high-quality gray model.
Step 2.2: and calculating the neighborhood gray value of each vertex in the normalized grid three-dimensional model.
And (4) calculating the neighborhood of the vertex a with the radius of sigma through formula (4), wherein sigma is an artificial set value. The neighborhood of vertex a is defined using the euclidean distance.
N(a,σ)＝{x|||x-a||＜σ,x∈U} (4)
Wherein N (a, σ) represents a neighborhood of vertex a with radius σ; u represents the normalized mesh three-dimensional model.
Then, calculating the neighborhood gray value of the vertex a through a formula (5); and the neighborhood gray value of the vertex a adopts the Gaussian weighted average gray value of the vertex gray.
Wherein G (gray (a), σ) represents the neighborhood gray value of vertex a; exp (·) represents the power of the natural base e.
Step 2.3: and calculating the color attribute significance of each vertex in the normalized mesh three-dimensional model. The color attribute saliency of the vertex is calculated by the difference of the grays of different radii as shown in equation (6).
S(a)＝|G(gray(a),2σ)-G(gray(a),σ)| (6)
Wherein, s (a) represents the color attribute saliency of the vertex a in the normalized mesh three-dimensional model.
In order to calculate the saliency of the grid attribute in the neighborhood of different specifications, the color attribute saliency of the vertex a in a certain specification is calculated by using formula (7).
St(a)＝|G(gray(a),2σt)-G(gray(a),σt)| (7)
Wherein S ist(a) Representing the color attribute significance of the vertex a under the specification t; sigmatRepresenting the neighborhood radius of the vertex a under the specification t; t belongs to {1,2,3 }; sigmatThe element is epsilon, 2 epsilon and 3 epsilon, and the value of epsilon is 0.3-0.8% of the diagonal length of the bounding box of the normalized grid three-dimensional model.
In order to synthesize results of different specifications, a nonlinear suppression operator is adopted to synthesize the color attribute significance S of the vertex a under different specificationst(a) Equation (6) is further rewritten as equation (8).
Wherein M istRepresents S calculated under the specification tt(a) Maximum value of (1);represents S calculated under the specification tt(a) In, except for MtOther than average values.
And (5) obtaining the color attribute significance of all the vertexes of the normalized mesh three-dimensional model through a formula (8).
Step three, calculating the geometric attribute error and the color attribute error of each edge to be folded and the folding cost of the edge to be folded in sequence; symbol for edge to be folded (v)k,vk′) And (4) showing.
Step 3.1: calculating the color of the edge to be foldedColor attribute error (with notation E)cRepresentation).
Step 3.1.1: and (5) calculating by using a formula (9) to obtain the color quadratic error measure of each vertex in the normalized mesh three-dimensional model.
Qvc(a)＝ΣQfc(a) (9)
Wherein Q isvc(a) Representing the color quadratic error measure of any vertex a in the normalized grid three-dimensional model; qfc(a) Representing the color quadratic error measure of a certain adjacent triangular surface of the vertex a in the normalized mesh three-dimensional model; Sigma-Qfc(a) And representing the sum of the color quadratic error measures of all the adjacent triangular surfaces of the vertex a in the normalized mesh three-dimensional model.
Calculating color quadratic error measure Q of certain adjacent triangular surface of vertex a in normalized mesh three-dimensional modelfc(a) In this case, since there is a case where the three vertexes of the same triangular surface have the same color or two vertexes thereof have the same color, the three color vectors of the triangular surface cannot constitute a plane. Thus, for a triangular surface with three vertices of the same color or two vertices of the same color, the color quadratic error measure Qfc(a) The calculation method comprises the following steps:
when the three vertices of a triangular patch are of the same color, it corresponds to a point in color space, denoted by the symbol v1Color of the point, v1＝(r1,g1,b1)，(r1,g1,b1) Values representing three components in the RGB space, respectively; the color quadratic error measure Q for the three vertices of a triangle of the same colorfc(a) Calculated by equation (10).
Where I is the identity matrix.
When the colors of any two vertexes in a triangular patch are the same, the color plane where the triangle is located is degraded into a straight line. By the symbol vc1、vc2And vc3Respectively representing the colors of three vertices, vc1＝(r1,g1,b1)，vc2＝vc3＝(r2,g2,b2)，(r1,g1,b1) And (r)2,g2,b2) Values that each represent three components in the RGB space; the color quadratic error measure Q of the triangular surface having the same color for the two verticesfc(a) Calculated by equation (11).
Wherein,
by the operation of this step, the edge (v) to be folded is obtainedk,vk′) Vertex v ofkAnd vk′A color quadratic error measure of (2).
Step 3.1.2: calculate the edge to be folded (using the symbol (v)) by equation (12)k,vk′) Representation) of a point vkAnd vk′Vertex obtained after folding (by sign)Expressed) of a color quadratic error measure (in the notation Q)cRepresentation).
Qc＝Qvc(k)+Qvc(k′) (12)
Wherein Q isvc(k) And Qvc(k') can be calculated by the formula (9).
Step 3.1.3:calculating the color attribute error E of the edge to be foldedc。
Edge to be folded (v)k,vk′) Point v onkAnd vk′Vertex obtained after foldingWith geometric properties (by symbols)Representation) and color feature attributes (symbolized)To indicate that),(x, y, z) is the vertex(r, g, b) are the verticesThe color three-dimensional vector of (1). Calculating to obtain the color attribute error E of the edge to be folded by the formula (13)c。
Step 3.2: calculating the geometric attribute error of the edge to be folded (by the symbol E)gRepresentation).
Step 3.2.1: and (4) calculating by using a formula (14) to obtain the geometric quadratic error measure of each vertex in the normalized mesh three-dimensional model.
Qvg(a)＝∑Qfg(a) (14)
Wherein Q isvg(a) Geometric quadratic error measurement representing any vertex a in normalized mesh three-dimensional modelDegree; qfg(a) Representing the geometric quadratic error measure of a certain adjacent triangular surface of a vertex a in the normalized mesh three-dimensional model; sigma Qfg(a) And representing the sum of geometric quadratic error measures of all adjacent triangular surfaces of the vertex a in the normalized mesh three-dimensional model.
Step 3.2.2: calculating the edge (v) to be folded by the formula (15)k,vk′) Point v ofkAnd vk′Vertex obtained after foldingGeometric quadratic error measure of (by the sign Q)gRepresentation).
Dividing edges in the normalized grid three-dimensional model into three types: internal edges, simple edges and boundary edges; points in the normalized grid three-dimensional model are divided into two types: interior points and boundary points. Both end points of the inner edge are inner points; one end point of the simple side is an internal point, and the other end point is a boundary point; both end points of the boundary edge are boundary points. The boundary edge has only one abutment surface and the other edges have two abutment surfaces.
If the edge (v) is to be foldedk,vk′) Is a simple side or an inner side, the side to be folded (v) is calculated by the formula (15)k,vk′) Point v ofkAnd vk′Vertex obtained after foldingGeometric quadratic error measure of (Q)g。
Qg＝Qvg(k)+Qvg(k′) (15)
Wherein Q isvg(k) And Qvg(k') can be calculated by the formula (14).
If the edge (v) is to be foldedk,vk′) Is a boundary edge, the edge (v) to be foldedk,vk′) Point v ofkAnd vk′FoldingThe vertex obtained afterGeometric quadratic error measure of (Q)gThe calculation method comprises the following steps:
edge to be folded (v)k,vk′) Making a vertical plane of its associated plane, and fitting the quadratic matrix of this vertical plane (by the symbol Q)pRepresentation) is incorporated into the edge (v) to be foldedk,vk′) In a quadratic matrix of the upper boundary points, the edge (v) to be folded is obtainedk,vk′) Geometric quadratic error measure of (Q)gAs shown in equation (16).
Wherein Q istTo be folded (v)k,vk′) A quadratic matrix of any one of the upper boundary points; t denotes the edge to be folded (v)k,vk′) The upper boundary points are numbered sequentially, and t is a positive integer;indicating the edge to be folded (v)k,vk′) The sum of quadratic matrixes of all upper boundary points; w is a constant which has the function of ensuring that the boundary edge is properly simplified and simultaneously enabling the position of the target point to be close to the boundary edge when the simple edge is folded; w is equal to 100,1000]。
Step 3.2.3: calculating the geometric attribute error E of the edge to be folded by the formula (17)g。
Step 3.3: the folding cost (denoted by the symbol cost) of the edge to be folded is calculated by equation (18).
Wherein, S (v)k) And S (v)k′) Is calculated by the formula (8).
And step four, sequencing all the edges to be folded according to the folding cost from small to large.
And step five, selecting the edge to be folded with the minimum cost from the results of the step five to perform folding operation, so as to obtain a new model.
And step six, repeating the operations from the step two to the step six until the simplification requirement is met.
Advantageous effects
Compared with the prior art, the method mainly researches a simplification method of a model with colors, innovatively transforms an RGB space, and allows an algorithm to consider color attribute information of the model during simplification, so that the model can maintain global geometric characteristics and color attribute information of a grid during simplification. The result shows that the algorithm of the method not only can well realize model simplification of the grid with the attributes, but also can effectively keep the obvious attribute characteristics of the model, and can still keep the color obvious characteristics of the model when the simplification rate reaches 90 percent.
Drawings
FIG. 1 is a front view of a three-dimensional model of an original mesh in an embodiment of the present invention;
FIG. 2 is a three-dimensional schematic view of a three-dimensional model of an original mesh in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a transformation of an original mesh three-dimensional model into a gray scale model according to an embodiment of the present invention;
FIG. 4 shows a graph corresponding to σ in an embodiment of the present inventiontIs epsilon, 2Respectively obtaining model schematics of epsilon and 3 epsilon and synthesizing results of different specifications to obtain the model schematics; wherein, FIG. 4(a) is σtA model schematic diagram obtained when is epsilon; FIG. 4(b) is atA model schematic diagram obtained when the value is 2 epsilon; FIG. 4(c) is atA model schematic diagram obtained when the value is 3 epsilon; FIG. 4(d) is a schematic diagram of a model obtained by combining the results of different specifications;
FIG. 5 is a simplified effect comparison of the automobile model of the present invention; wherein, fig. 5(a) is an original mesh three-dimensional model; FIG. 5(b) is a simplified result diagram of the QEM method; FIG. 5(c) is a simplified result diagram of the process of the present invention.
Detailed Description
According to the technical scheme, the invention is described in detail by combining the drawings and the implementation examples.
In this embodiment, the model simplification method based on the significant color attribute feature preservation proposed by the present invention is used to simplify the automobile model shown in fig. 1 and 2, where the original model totals 10474 patches, and the specific operation process is as follows:
step one, normalizing the original grid three-dimensional model. The original mesh three-dimensional model includes color attributes of the vertices. The method specifically comprises the following steps:
step 1.1: and processing the color attributes of the vertexes of the three-dimensional model of the original mesh.
And expressing the color attribute of the vertex of the three-dimensional model of the original grid as a three-dimensional vector consisting of red, green and blue (RGB) color components to obtain the color attribute coordinate of the vertex. Then, a weighted color component method is adopted to calculate the color difference of any two vertexes of the original mesh three-dimensional model through the formula (1). By the symbol ciAnd cjAny two vertices representing the three-dimensional model of the original mesh, denoted by the symbol ci(ri,gi,bi) And cj(rj,gj,bj) Any two vertexes c of original mesh three-dimensional modeliAnd cjThe color three-dimensional vector of (1).
Wherein D (c)i,cj) Any two vertices c representing the three-dimensional model of the original meshiAnd cjThe color difference of (a); w is ar＝3、wg＝4、wb＝2。
Step 1.2: and (4) standardizing the geometric coordinates and the color attribute coordinates of each vertex of the original mesh three-dimensional model to be in the same range.
On the basis of the operation of step 1.1, the coordinate ranges of the geometric coordinates and the color attribute coordinates of each vertex of the original mesh three-dimensional model may be different, and in order to enable the spatial position and the color attribute information to play an equal role in calculating the folding cost, the geometric coordinates and the color attribute coordinates of each vertex of the original mesh three-dimensional model are normalized to be in the same range, that is: and the three components of the vertex color coordinates of the original mesh three-dimensional model are all in the range of [0, m ], so that the three dimensions of the geometric coordinates of the vertices of the original mesh three-dimensional model need to be specified in the range of [0, m ], and m is 2.
Setting the coordinate ranges of three dimensions of bounding boxes of the original grid three-dimensional model as xmin,xmax]，[ymin,ymax]，[zmin,zmax]And calculating the coordinate value of any vertex in the original mesh three-dimensional model after normalization by using the formula (2).
Wherein (x)a,ya,za) Representing the geometric coordinate of any vertex in the original mesh three-dimensional model; (x'b,y′b,z′b) Representing the geometric coordinate of any vertex in the original mesh three-dimensional model after normalization; d ═ max { xmax-xmin,ymax-ymin,zmax-zmin}。
And (5) obtaining a normalized grid three-dimensional model through the operation of the first step.
And step two, obtaining the color attribute significance of all vertexes of the normalized mesh three-dimensional model.
On the basis of the operation of the first step, calculating the color attribute significance of all the vertexes of the normalized mesh three-dimensional model, specifically:
step 2.1: and calculating the gray value of each vertex in the normalized mesh three-dimensional model.
By the symbol (r)a,ga,ba) And representing the color attribute coordinates of any vertex in the normalized grid three-dimensional model after calculation. For the sake of research, the color vector of the vertex is reduced to a one-dimensional vector. Using gray scale enables converting a color model into a high quality black and white model, with different colors in the RGB space corresponding to different gray scale values, which also correspond to different RGB vectors. The original color information is represented by the gray value of the vertex, so that the dimensionality of the original model can be reduced, and the original model can be represented without distortion. The gray value of each vertex in the normalized mesh three-dimensional model is calculated by formula (3) and is represented by gray (a).
gray(a)＝0.299ra+0.587ga+0.114ba(3)
By this conversion a color model can be converted into a high quality gray scale model as shown in fig. 3.
Step 2.2: and calculating the neighborhood gray value of each vertex in the normalized grid three-dimensional model.
And (4) calculating the neighborhood of the vertex a with the radius of sigma through formula (4), wherein sigma is an artificial set value. The neighborhood of vertex a is defined using the euclidean distance.
N(a,σ)＝{x|||x-a||＜σ,x∈U} (4)
Wherein N (a, σ) represents a neighborhood of vertex a with radius σ; u represents the normalized mesh three-dimensional model.
Then, calculating the neighborhood gray value of the vertex a through a formula (5); and the neighborhood gray value of the vertex a adopts the Gaussian weighted average gray value of the vertex gray.
Wherein G (gray (a), σ) represents the neighborhood gray value of vertex a; exp (·) represents the power of the natural base e.
Step 2.3: and calculating the color attribute significance of each vertex in the normalized mesh three-dimensional model. The color attribute saliency of the vertex is calculated by the difference of the grays of different radii as shown in equation (6).
S(a)＝|G(gray(a),2σ)-G(gray(a),σ)| (6)
Wherein, s (a) represents the color attribute saliency of the vertex a in the normalized mesh three-dimensional model.
In order to calculate the saliency of the grid attribute in the neighborhood of different specifications, the color attribute saliency of the vertex a in a certain specification is calculated by using formula (7).
St(a)＝|G(gray(a),2σt)-G(gray(a),σt)| (7)
Wherein S ist(a) Representing the color attribute significance of the vertex a under the specification t; sigmatRepresenting the neighborhood radius of the vertex a under the specification t; t belongs to {1,2,3 }; sigmatE is epsilon, 2 epsilon and 3 epsilon, and the value of epsilon is a normalized grid three-dimensional modelThe diagonal length of the form bounding box is 0.3%.
In order to synthesize results of different specifications, a nonlinear suppression operator is adopted to synthesize the color attribute significance S of the vertex a under different specificationst(a) Equation (6) is further rewritten as equation (8).
Wherein M istRepresents S calculated under the specification tt(a) Maximum value of (1);represents S calculated under the specification tt(a) In, except for MtOther than average values.
And (5) obtaining the color attribute significance of all the vertexes of the normalized mesh three-dimensional model through a formula (8).
And step three, calculating the geometric attribute error and the color attribute error of each edge to be folded and the folding cost of the edge to be folded in sequence.
Step 3.1: calculating the color attribute error E of the edge to be foldedc。
Step 3.1.1: and (5) calculating by using a formula (9) to obtain the color quadratic error measure of each vertex in the normalized mesh three-dimensional model.
Qvc(a)＝ΣQfc(a) (9)
Wherein Q isvc(a) Representing the color quadratic error measure of any vertex a in the normalized grid three-dimensional model; qfc(a) Representing the color quadratic error measure of a certain adjacent triangular surface of the vertex a in the normalized mesh three-dimensional model; Sigma-Qfc(a) Color quadratic error measure representing all adjacent triangular faces of vertex a in normalized mesh three-dimensional modelAnd (c).
Calculating color quadratic error measure Q of certain adjacent triangular surface of vertex a in normalized mesh three-dimensional modelfc(a) In this case, since there is a case where the three vertexes of the same triangular surface have the same color or two vertexes thereof have the same color, the three color vectors of the triangular surface cannot constitute a plane. Thus, for a triangular surface with three vertices of the same color or two vertices of the same color, the color quadratic error measure Qfc(a) The calculation method comprises the following steps:
when the three vertices of a triangular patch are of the same color, it corresponds to a point in color space, denoted by the symbol v1Color of the point, v1＝(r1,g1,b1)，(r1,g1,b1) Values representing three components in the RGB space, respectively; the color quadratic error measure Q for the three vertices of a triangle of the same colorfc(a) Calculated by equation (10).
Where I is the identity matrix.
When the colors of any two vertexes in a triangular patch are the same, the color plane where the triangle is located is degraded into a straight line. By the symbol vc1、vc2And vc3Respectively representing the colors of three vertices, vc1＝(r1,g1,b1)，vc2＝vc3＝(r2,g2,b2)，(r1,g1,b1) And (r)2,g2,b2) Values that each represent three components in the RGB space; the color quadratic error measure Q of the triangular surface having the same color for the two verticesfc(a) Calculated by equation (11).
Wherein,
by the operation of this step, the edge (v) to be folded is obtainedk,vk′) Vertex v ofkAnd vk′A color quadratic error measure of (2).
Step 3.1.2: calculating the edge to be folded (v) by the formula (12)k,vk′) Point v onkAnd vk′Vertex obtained after foldingMeasure of color quadratic error Qc。
Qc＝Qvc(k)+Qvc(k′) (12)
Wherein Q isvc(k) And Qvc(k') can be calculated by the formula (9).
Step 3.1.3: calculating the color attribute error E of the edge to be foldedc。
Edge to be folded (v)k,vk′) Point v onkAnd vk′Vertex obtained after foldingHaving geometric propertiesAnd color feature attributes (x, y, z) is the vertex(r, g, b) are the verticesThe color three-dimensional vector of (1). Calculating to obtain the color attribute error E of the edge to be folded by the formula (13)c。
Step 3.2: calculating the geometric attribute error E of the edge to be foldedg。
Step 3.2.1: and (4) calculating by using a formula (14) to obtain the geometric quadratic error measure of each vertex in the normalized mesh three-dimensional model.
Qvg(a)＝ΣQfg(a) (14)
Wherein Q isvg(a) Representing the geometric quadratic error measure of any vertex a in the normalized mesh three-dimensional model; qfg(a) Representing the geometric quadratic error measure of a certain adjacent triangular surface of a vertex a in the normalized mesh three-dimensional model; sigma Qfg(a) And representing the sum of geometric quadratic error measures of all adjacent triangular surfaces of the vertex a in the normalized mesh three-dimensional model.
Step 3.2.2: calculating the edge (v) to be folded by the formula (15)k,vk′) Point v ofkAnd vk′Vertex obtained after foldingGeometric quadratic error measure of (Q)g。
Dividing edges in the normalized grid three-dimensional model into three types: internal edges, simple edges and boundary edges; points in the normalized grid three-dimensional model are divided into two types: interior points and boundary points. Both end points of the inner edge are inner points; one end point of the simple side is an internal point, and the other end point is a boundary point; both end points of the boundary edge are boundary points. The boundary edge has only one abutment surface and the other edges have two abutment surfaces.
If the edge (v) is to be foldedk,vk′) Is a simple side or an inner side, the side to be folded (v) is calculated by the formula (15)k,vk′) Point v ofkAnd vk′Vertex obtained after foldingGeometric quadratic error measure of (Q)g。
Qg＝Qvg(k)+Qvg(k′) (15)
Wherein Q isvg(k) And Qvg(k') can be calculated by the formula (14).
If the edge (v) is to be foldedk,vk′) Is a boundary edge, the edge (v) to be foldedk,vk′) Point v ofkAnd vk′Vertex obtained after foldingGeometric quadratic error measure of (Q)gThe calculation method comprises the following steps:
edge to be folded (v)k,vk′) Making a vertical plane of its associated plane, and forming a quadratic matrix Q of the vertical planepIncorporated into the edge to be folded (v)k,vk′) In a quadratic matrix of the upper boundary points, the edge (v) to be folded is obtainedk,vk′) Geometric quadratic error measure of (Q)gAs shown in equation (16).
Wherein Q istTo be folded (v)k,vk′) A quadratic matrix of any one of the upper boundary points; t denotes the edge to be folded (v)k,vk′) The upper boundary points are numbered sequentially, and t is a positive integer;indicating the edge to be folded (v)k,vk′) The sum of quadratic matrixes of all upper boundary points; w is a constant which has the function of ensuring that the boundary edge is properly simplified and simultaneously enabling the position of the target point to be close to the boundary edge when the simple edge is folded; w is 100.
Step 3.2.3: calculating the geometric attribute error E of the edge to be folded by the formula (17)g。
Step 3.3: the folding cost of the edge to be folded is calculated by equation (18).
Wherein, S (v)k) And S (v)k′) Is calculated by the formula (8).
And step four, sequencing all the edges to be folded according to the folding cost from small to large.
And step five, selecting the edge to be folded with the minimum cost from the results of the step five to perform folding operation, so as to obtain a new model.
And step six, repeating the operations from the step two to the step six until the simplification requirement is met.
Corresponds to sigmatThe model diagrams obtained for ε,2 ε, and 3 ε are shown in FIG. 4(a), FIG. 4(b), and FIG. 4(c), respectively. The results of different specifications were combined to obtain model diagrams as shown in fig. 4 (d).
To illustrate the effect of the present invention, the method of QEM (secondary error metric, only geometric features are considered) and the method of the present invention are used together to simplify the automobile model shown in fig. 1 and 2, and the comparison graph is shown in fig. 5.
Fig. 5(a) shows an original colored automobile model. FIGS. 5(b) and 5(c) are both models at a 90% reduction rate; FIG. 5(b) is a simplified result of the QEM method, which does not take into account color attribute characteristics; FIG. 5(c) is a simplified result of using the method of the present invention. It can be seen that the method of the present invention achieves simplification of the color attribute model. Second, FIG. 5(c) retains the salient features of the mesh better than FIG. 5(b) under the guidance of the saliency of the model color attributes. The lamp portion is well retained up to a 90% reduction. The light in the right door region has disappeared in fig. 5(b) and remains in fig. 5 (c). The color boundaries of the front mirror portion of the automobile in fig. 5(c) are also clearer than in fig. 5 (b). The method has the advantages that the algorithm can not only well realize the grid simplification of the grids with the attributes, but also effectively keep the obvious attribute characteristics of the grids.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it will be apparent to those skilled in the art that various modifications may be made without departing from the principles of the invention, and these should be construed as falling within the scope of the invention.
Claims (2)
1. A model simplification method based on salient color attribute feature preservation is characterized in that: the method comprises the following concrete steps:
step one, normalizing an original grid three-dimensional model; the original mesh three-dimensional model comprises color attributes of vertices; the method specifically comprises the following steps:
step 1.1: processing the color attribute of the vertex of the three-dimensional model of the original mesh;
representing the color attribute of the vertex of the three-dimensional model of the original mesh as a three-dimensional vector consisting of red, green and blue (RGB) color components to obtain the color attribute of the vertexColor attribute coordinates; then, calculating the color difference of any two vertexes of the original mesh three-dimensional model by adopting a weighted color component method through a formula (1); by the symbol ciAnd cjAny two vertices representing the three-dimensional model of the original mesh, denoted by the symbol ci(ri,gi,bi) And cj(rj,gj,bj) Any two vertexes c of original mesh three-dimensional modeliAnd cjA color three-dimensional vector of (a);
wherein D (c)i,cj) Any two vertices c representing the three-dimensional model of the original meshiAnd cjThe color difference of (a); w is ar、wg、wbRespectively representing the weighting coefficients, w, for red, green and bluer＞wb，wg＞wb；
Any two vertexes c of original mesh three-dimensional modeliAnd cjColor difference D (c) ofi,cj) May adopt a vertex ciAnd cjEuclidean distance between them, but with the proviso that the RGB space is a uniform color space: namely, the color with equal color difference of each color should form a spherical surface in the RGB space; and the colors at different positions on the spherical surface and the color at the center of the sphere should show the same difference; the RGB space obviously does not meet the condition, and the Euclidean distance is used for measuring the chromatic aberration in the RGB space and the chromatic aberration does not meet the human visual sense; research shows that human eyes have different sensitivities to the three primary colors of red, green and blue and are more sensitive to the red and the green, so that the three primary colors need to be treated differently when calculating color difference, and the calculation is more accurate; to compensate for the non-uniformity of the RGB space, a weighted color component method is adopted for the calculation of the color difference: i.e. adding wr、wg、wbThree weighting coefficients;
step 1.2: the geometrical coordinates and color attribute coordinates of each vertex of the original mesh three-dimensional model are normalized to be in the same range;
on the basis of the operation of step 1.1, the coordinate ranges of the geometric coordinates and the color attribute coordinates of each vertex of the original mesh three-dimensional model may be different, and in order to enable the spatial position and the color attribute information to play an equal role in calculating the folding cost, the geometric coordinates and the color attribute coordinates of each vertex of the original mesh three-dimensional model are normalized to be in the same range, that is: three components of the vertex color coordinate of the original grid three-dimensional model are all in the range of [0, m ], so that three dimensions of the geometric coordinate of the vertex of the original grid three-dimensional model need to be specified in the range of [0, m ], and m belongs to [1,10 ];
setting the coordinate ranges of three dimensions of bounding boxes of the original grid three-dimensional model as xmin,xmax]，[ymin,ymax]，[zmin,zmax]Calculating the coordinate value of any vertex in the original grid three-dimensional model after normalization through a formula (2);
wherein (x)b,yb,zb) Representing the geometric coordinate of any vertex in the original mesh three-dimensional model; (x'b,y′b,z′b) Representing the geometric coordinate of any vertex in the original mesh three-dimensional model after normalization; d ═ max { xmax-xmin,ymax-ymin,zmax-zmin}；
Obtaining a normalized grid three-dimensional model through the operation of the first step;
step two, obtaining the color attribute significance of all vertexes of the normalized grid three-dimensional model;
on the basis of the operation of the first step, calculating the color attribute significance of all the vertexes of the normalized mesh three-dimensional model, specifically:
step 2.1: calculating the gray value of each vertex in the normalized grid three-dimensional model;
by the symbol (r)a,ga,ba) Representing a three-dimensional model of a normalized grid of a computerColor attribute coordinates of any vertex in the model; for the convenience of research, the color vector of the vertex is reduced to a one-dimensional vector; the use of gray scale enables conversion of a color model into a high quality black and white model, with different colors in the RGB space corresponding to different gray scale values, and different gray scale values corresponding to different RGB vectors; the original color information is represented by the gray value of the vertex, so that the dimensionality of the original model can be reduced, and the original model can be represented without distortion; calculating the gray value of each vertex in the normalized mesh three-dimensional model through formula (3), and expressing the gray value by gray (a);
gray(a)＝0.299ra+0.587ga+0.114ba(3)
a color model can be converted into a high-quality gray model through the conversion;
step 2.2: calculating the neighborhood gray value of each vertex in the normalized grid three-dimensional model;
calculating the neighborhood with the radius of the vertex a being sigma through a formula (4), wherein sigma is an artificial set value; the neighborhood of vertex a is defined using the euclidean distance;
N(a,σ)＝{x|||x-a||＜σ,x∈U} (4)
wherein N (a, σ) represents a neighborhood of vertex a with radius σ; u represents a normalized grid three-dimensional model;
then, calculating the neighborhood gray value of the vertex a through a formula (5); adopting a Gaussian weighted average gray value of the vertex gray value to the neighborhood gray value of the vertex a;
wherein G (gray (a), σ) represents the neighborhood gray value of vertex a; exp (·) represents the power of the natural base e;
step 2.3: calculating the color attribute significance of each vertex in the normalized grid three-dimensional model; calculating the color attribute significance of the vertex by the difference value of the gray scales of different radii, as shown in formula (6);
S(a)＝|G(gray(a),2σ)-G(gray(a),σ)| (6)
s (a) represents the color attribute significance of a vertex a in the normalized mesh three-dimensional model;
in order to calculate the significance of the grid attribute in the neighborhoods with different specifications, the color attribute significance of the vertex a in a certain specification is calculated by using a formula (7);
St(a)＝|G(gray(a),2σt)-G(gray(a),σt)| (7)
wherein S ist(a) Representing the color attribute significance of the vertex a under the specification t; sigmatRepresenting the neighborhood radius of the vertex a under the specification t; t belongs to {1,2,3 }; sigmatE is left to be { epsilon, 2 epsilon, 3 epsilon }, and the value of epsilon is 0.3% -0.8% of the diagonal length of the bounding box of the normalized grid three-dimensional model;
in order to synthesize results of different specifications, a nonlinear suppression operator is adopted to synthesize the color attribute significance S of the vertex a under different specificationst(a) Further rewriting the formula (6) to the formula (8);
wherein M istRepresents S calculated under the specification tt(a) Maximum value of (1);represents S calculated under the specification tt(a) In, except for MtAn average value of;
obtaining the color attribute significance of all vertexes of the normalized mesh three-dimensional model through a formula (8);
step three, calculating the geometric attribute error and the color attribute error of each edge to be folded and the folding cost of the edge to be folded in sequence; symbol for edge to be folded (v)k,vk′) Represents;
step 3.1: calculating the color attribute error of the edge to be folded, using the symbol EcRepresents;
step 3.1.1: calculating to obtain the color quadratic error measure of each vertex in the normalized grid three-dimensional model through a formula (9);
Qvc(a)＝∑Qfc(a) (9)
wherein Q isvc(a) Representing the color quadratic error measure of any vertex a in the normalized grid three-dimensional model; qfc(a) Representing the color quadratic error measure of a certain adjacent triangular surface of the vertex a in the normalized mesh three-dimensional model; sigma Qfc(a) Representing the sum of color quadratic error measures of all adjacent triangular surfaces of a vertex a in the normalized grid three-dimensional model;
calculating color quadratic error measure Q of certain adjacent triangular surface of vertex a in normalized mesh three-dimensional modelfc(a) In the method, because the three vertexes of the same triangular surface have the same color or two vertexes have the same color, the three color vectors of the triangular surface cannot form a plane; thus, for a triangular surface with three vertices of the same color or two vertices of the same color, the color quadratic error measure Qfc(a) The calculation method comprises the following steps:
when the three vertices of a triangular patch are of the same color, it corresponds to a point in color space, denoted by the symbol v1Color of the point, v1＝(r1,g1,b1)，(r1,g1,b1) Values representing three components in the RGB space, respectively; the color quadratic error measure Q for the three vertices of a triangle of the same colorfc(a) Calculated by formula (10);
wherein I is an identity matrix;
when the colors of any two vertexes in one triangular patch are the same, the color plane where the triangle is located is degenerated into a straight line; by the symbol vc1、vc2And vc3Respectively representing the colors of three vertices, vc1＝(r1,g1,b1)，vc2＝vc3＝(r2,g2,b2)，(r1,g1,b1) And (r)2,g2,b2) Values that each represent three components in the RGB space; the color quadratic error measure Q of the triangular surface having the same color for the two verticesfc(a) Calculated by equation (11);
wherein,
by the operation of this step, the edge (v) to be folded is obtainedk,vk′) Vertex v ofkAnd vk′The color quadratic error measure of (2);
step 3.1.2: calculating the edge to be folded (v) by the formula (12)k,vk′) Point v onkAnd vk′Folded color quadratic error measure Q represented by vertex vc；
Qc＝Qvc(k)+Qvc(k′) (12)
Wherein Q isvc(k) And Qvc(k') can be calculated by the formula (9);
step 3.1.3: calculating the color attribute error E of the edge to be foldedc；
Edge to be folded (v)k,vk′) Point v onkAnd vk′Vertex obtained after foldingHaving geometric propertiesRepresentation and color feature attributesIt is shown that,(x, y, z) is the vertex(r, g, b) are the verticesA color three-dimensional vector of (a); calculating to obtain the color attribute error E of the edge to be folded by the formula (13)c；
Step 3.2: calculating the geometric attribute error of the edge to be folded, using the symbol EgRepresents;
step 3.2.1: calculating by a formula (14) to obtain the geometric quadratic error measure of each vertex in the normalized grid three-dimensional model;
Qvg(a)＝∑Qfg(a) (14)
wherein Q isvg(a) Representing the geometric quadratic error measure of any vertex a in the normalized mesh three-dimensional model; qfg(a) Representing the geometric quadratic error measure of a certain adjacent triangular surface of a vertex a in the normalized mesh three-dimensional model; sigma Qfg(a) Representing the sum of geometric quadratic error measures of all adjacent triangular surfaces of a vertex a in the normalized mesh three-dimensional model;
step 3.2.2: calculating the edge (v) to be folded by the formula (15)k,vk′) Point v ofkAnd vk′The geometrical quadratic error measure of the vertex v obtained after folding is represented by the symbol QgRepresents;
dividing edges in the normalized grid three-dimensional model into three types: internal edges, simple edges and boundary edges; points in the normalized grid three-dimensional model are divided into two types: interior points and boundary points; both end points of the inner edge are inner points; one end point of the simple side is an internal point, and the other end point is a boundary point; both end points of the boundary edge are boundary points; the boundary edge has only one abutment surface and the other edges have two abutment surfaces;
if the edge (v) is to be foldedk,vk′) Is a simple side or an inner side, the side to be folded (v) is calculated by the formula (15)k,vk′) Point v ofkAnd vk′Folded geometric quadratic error measure Q of vertex vg；
Qg＝Qvg(k)+Qvg(k′) (15)
Wherein Q isvg(k) And Qvg(k') can be calculated by the formula (14);
if the edge (v) is to be foldedk,vk′) Is a boundary edge, the edge (v) to be foldedk,vk′) Point v ofkAnd vk′Folded geometric quadratic error measure Q of vertex vgThe calculation method comprises the following steps:
edge to be folded (v)k,vk′) Making a vertical plane of its associated plane, and forming a quadratic matrix Q of the vertical planepIncorporated into the edge to be folded (v)k,vk′) In a quadratic matrix of the upper boundary points, the edge (v) to be folded is obtainedk,vk′) Geometric quadratic error measure of (Q)gAs shown in equation (16);
wherein Q ist′To be folded (v)k,vk′) A quadratic matrix of any one of the upper boundary points; t' represents the edge to be folded (v)k,vk′) The upper boundary points are numbered sequentially, and t' is a positive integer;indicating the edge to be folded (v)k,vk′) The sum of quadratic matrixes of all upper boundary points; w is a constant which has the function of ensuring that the boundary edge is properly simplified and simultaneously enabling the position of the target point to be close to the boundary edge when the simple edge is folded; w is equal to 100,1000]；
Step 3.2.3: calculating the edge to be folded by equation (17)Geometric attribute error Eg；
Step 3.3: the folding cost of the edge to be folded is calculated by equation (18).
Wherein, S (v)k) And S (v)k′) Is calculated by the formula (8);
step four, sequencing all edges to be folded according to the folding cost from small to large;
step five, selecting the edge to be folded with the minimum cost from the results of the step four to carry out folding operation, so as to obtain a new model;
and step six, repeating the operations from the step two to the step six until the simplification requirement is met.
2. The method of claim 1, wherein the model reduction method based on the significant color attribute feature preservation comprises: w is ar＝3、wg＝4、wb＝2。
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