CN115759175A - Approximation method of detail level grid model based on approximate global optimization - Google Patents
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Abstract
The invention discloses a detail level grid model approximation method based on approximate global optimization. The method comprises the steps of firstly calculating a movable range of each point of a simplified detail level grid model, determining the range through a variable geometric space based on nearest neighbor joints, then constructing a collaborative learning sparrow-grey wolf optimization algorithm by combining the global exploration capability of the sparrow algorithm and the local exploration capability of the grey wolf algorithm, searching the optimal vertex position combination by using the sparrow-grey wolf optimization algorithm under the condition of keeping the surface structure of the detail level grid model, and globally optimizing all vertexes of the detail level grid to approximate to an original grid model. According to the method, the optimal three-dimensional mesh approximation effect with the minimum approximation error can be obtained through mesh optimization.
Description
Technical Field
The invention belongs to the technical field of computer application, computer graphics and intelligent optimization, and particularly relates to a detailed level grid model approximation method based on approximate global optimization.
Background
With the development of three-dimensional technology, three-dimensional mesh models have been widely applied in many fields, such as entertainment industry, virtual reality, three-dimensional reconstruction, urban modeling, and the like. However, large-scale grid models consume large computational costs and storage resources, making storage, rendering, and transmission of these operations very difficult. Meanwhile, under different application scenes, the accuracy requirements on the grid model are different. It is therefore desirable to simplify the three-dimensional mesh model and generate a level-of-detail mesh model that approximates the original model.
The generation of the detail-level mesh model refers to that under the premise that the overall appearance and the topological structure of the model are basically unchanged, the number of vertexes and patches in the model is reduced, namely, the detail-level mesh model approximate to the original model is generated under the condition that points and faces are reduced. For a detail-level mesh model with a specified number of vertices, the key problem is how to reduce the approximation error of the detail-level mesh model and the original model. The traditional simplification method is mostly based on a greedy algorithm and local optimization, namely, the simplification method is realized by controlling local errors in the simplification process, and the vertex of the model can only be simplified without optimization.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a detail level grid model approximation method and a calculation system based on approximate global optimization, which comprises the following steps:
step 2, calculating the movable range of each point of the detail level grid model in the step 1;
step 3, combining the global exploration capability of the sparrow algorithm and the local exploration capability of the grey wolf algorithm, constructing a cooperative learning sparrow-grey wolf optimization algorithm, comprising the following substeps:
step 3.1, randomly initializing a population within the vertex movable range, wherein each individual in the population is a possible vertex position set, and recording the position of the ith individual in the population as X i ；
Step 3.2, in the global search stage, updating the vertex position by using a producer, a follower and a detection and early warning mechanism in a sparrow algorithm;
3.3, taking the optimal solution found by the sparrow algorithm as the alpha wolf of the grey wolf algorithm to continue to guide search;
and 3.4, in the local searching stage, updating the vertex position by utilizing a hunting and hunting mechanism of the grey wolf algorithm.
And 4, under the condition of keeping the surface structure of the detail level grid model, performing global optimization on all vertexes of the detail level grid by using a sparrow-wolf optimization algorithm to enable the detail level grid model to approach the original grid model.
Furthermore, in step 2, the movable range of each point is calculated by using the variable geometric space of the nearest neighboring point, and for a certain vertex v (x, y, z) of the detail-level mesh model, its variable geometric space based on the nearest neighboring point is defined as:
R(v)＝{min v′∈N(v) |x-x′|,min v′∈N(v) |y-y′|,min v′∈N(v) |z-z′|} (1)
in the formula, R (v) represents the movable range of each point, N (v) is a set of adjacent points in the v neighborhood, v ' is an adjacent point in N (v), and x ', y ', and z ' are coordinates of v ' in the directions of the x axis, the y axis, and the z axis, respectively.
Moreover, the producer in step 3.2 refers to an individual in the population whose fitness value is smaller than the set threshold, and the location update formula is as follows:
in the formula, X i (t)、X i (T + 1) denotes the position of the ith individual in the population for the T, T +1 iterations, T max Denotes the maximum number of iterations, α ∈ (0, 1)]Is a uniform random number, Q is a random number following normal distribution, and L is 1 XN d All one matrix of, N d In order to simplify the number of vertexes of the model, R is a current early warning value, and ST is a preset safety threshold value.
Followers are individuals in the population other than the producer, and the location update formula is:
in the formula, X i (t)、X i (t + 1) represents the position of the ith individual in the population of the t, t +1 iterations; x w And X b Is the current worst and best position; q is a random number which follows normal distribution; n is the number of individuals in the population; n is a radical of hydrogen d Simplifying the number of the top points of the model; a is N d ×N d Each element in the matrix is randomly assigned to be 1 or-1; l is 1 XN d All of the matrices of (a).
The detection and warning mechanism is that assuming that a certain proportion of producers and followers can sense danger in advance, their positions are updated again as follows:
in the formula, X i (t)、X i (t + 1) denotes the position of the ith individual in the population at the t, t +1 iterations, X b Is the best current position, beta is a random number representing the step size, and K e [ -1,1]Is a uniform random number, f i Is the fitness value of the ith individual, f b And f w Is the current best and worst fitness value, and epsilon is a very small constant to avoid a divisor of 0.
Moreover, the optimal solution found by the sparrow algorithm in the step 3.3 is a vertex position set with the minimum fitness value.
Moreover, when the graywolves search for prey in step 3.4, they will gradually form an enclosure around the prey target, and the locations are updated with the locations of α, β and δ wolves as guidance, and α, β and δ wolves as the three individuals with the minimum fitness value in the population:
D α ＝|C 1 X α (t)-X(t)| (5)
D β ＝|C 2 X β (t)-X(t)| (6)
D δ ＝|C 3 X δ (t)-X(t)| (7)
X 1 (t+1)＝X α (t)-A 1 D α (8)
X 2 (t+1)＝X β (t)-A 2 D β (9)
X 3 (t+1)＝X δ (t)-A 3 D δ (10)
wherein X (t + 1) represents the position of the gray wolf in the t +1 th iteration, X α (t)、X β (t)、X δ (t) the positions of the alpha, beta and delta wolfs for the t-th iteration, X (t) the position of the grey wolf for the t-th iteration, D α 、D β And D δ Is the distance from the other wolf to alpha, beta and delta wolf, A 1 、A 2 、A 3 And C 1 、C 2 、C 3 Are coefficient vectors.
Moreover, the global optimization problem in the step 4 is modeled as follows: given an original three-dimensional mesh model M o (V o ,F o ) And a simplified level of detail model M s (V s ,F s ) On the patch set F s Under the condition of unchanging structure, searching an optimal vertex set
So that
And M o The error of (c) is minimal:
in the formula, V and F respectively represent a vertex set and a patch set of the corresponding mesh model, D () represents a fitness function, and the calculation method is as follows:
in the formula (I), the compound is shown in the specification,
represents the shortest distance from point p to model M, and d (p, p ') represents the euclidean distance between p and p'.
Compared with the prior art, the invention has the following advantages:
1) Calculating a movable range of each point of the detail level grid model based on a variable geometric space of nearest neighbor joints, maintaining a grid geometric topological structure and avoiding overlarge deviation between an optimized grid vertex and an original vertex;
2) Under the condition of keeping the surface structure of the detail level mesh model, all vertexes of the detail level mesh are optimized globally, all possible combinations of vertex positions can be searched in a maximum range, and the situation that the local optimization is trapped is avoided;
3) And searching an optimal vertex position set by using a sparrow-grayish wolf optimization algorithm to obtain an optimized three-dimensional grid model with the minimum approximation error.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
FIG. 2 is a diagram showing the optimization effect of the method provided by the present invention on four detail level mesh models with different resolutions.
Fig. 3 is a comparison graph of the convergence of the optimization method based on Sparrow-Grey Wolf (SSA-GWO) and Sparrow optimization Algorithm (SSA optimization, SSA) and Grey Wolf optimization Algorithm (Grey Wolf Optimizer, GWO) on three mesh model approximations.
Fig. 4 is a graph of the comparison effect of the visual quality before and after optimization by the method of the present invention.
Detailed Description
The invention provides a detail level mesh model approximation method based on approximate global optimization, and the technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, the process of the embodiment of the present invention includes the following steps:
And 2, calculating the movable range of each point of the detail level grid model in the step 1.
Calculating the movable range of each point by using the variable geometric space of the nearest adjacent point, wherein for a certain vertex v (x, y, z) of the detail level mesh model, the variable geometric space based on the nearest adjacent point is defined as:
where R (v) represents the movable range of each point, N (v) is the set of adjacent points in the v neighborhood, v ' is the adjacent point in N (v), and x ', y ', and z ' are the coordinates of v ' in the directions of the x, y, and z axes, respectively.
Step 3, combining the global exploration ability of the sparrow algorithm and the local exploration ability of the grey wolf algorithm, constructing a collaborative learning sparrow-grey wolf optimization algorithm, which comprises the following substeps:
step 3.1, randomly initializing a population in a vertex movable range, wherein each individual in the population is a possible vertex position set, and marking the position of the ith individual in the population as X i 。
And 3.2, in the global search stage, updating the vertex position by using a producer, a follower and a detection and early warning mechanism in a sparrow algorithm.
The producer refers to an individual with the fitness value smaller than a set threshold value in the population, and the position updating formula is as follows:
in the formula, X i (t)、X i (T + 1) denotes the position of the ith individual in the population for the T, T +1 iterations, T max Denotes the maximum number of iterations, α ∈ (0, 1)]Is a uniform random number, Q is a random number following normal distribution, and L is 1 XN d All one matrix of, N d In order to simplify the number of vertexes of the model, R is a current early warning value, and ST is a preset safety threshold value.
The followers are other individuals except the producer in the population, and the position updating formula is as follows:
in the formula, X i (t)、X i (t + 1) represents the position of the ith individual in the population of the t, t +1 iterations; x w And X b Is the current worst and best position; q is a random number which follows normal distribution; n is the number of individuals in the population; n is a radical of d Simplifying the number of the top points of the model; a is N d ×N d Each element in the matrix is randomly assigned to 1 or-1; l is 1 XN d All of the matrices of (a).
The detection and early warning mechanism is that assuming that a certain proportion of producers and followers are able to sense danger in advance, their locations are updated again as follows:
in the formula, X i (t)、X i (t + 1) denotes the position of the ith individual in the population at the t, t +1 iterations, X b Is the best current position, beta is a random number representing the step size, and K e [ -1,1]Is a uniform random number, f i Is the fitness value of the ith individual, f b And f w Is the current best and worst fitness value, and epsilon is a very small constant to avoid a divisor of 0.
And 3.3, taking the optimal solution found by the sparrow algorithm as the alpha wolf of the grey wolf algorithm to continuously guide search.
The optimal solution found by the sparrow algorithm is a vertex position set with the minimum fitness value.
And 3.4, updating the vertex position by utilizing the hunting and hunting mechanism of the wolf algorithm in the local searching stage.
As the sirius find prey (i.e., the best location), they gradually form a containment around the prey target, with location updates directed to the locations of α, β, and δ wolves (i.e., the three individuals in the population with the least fitness value):
D α ＝|C 1 X α (t)-X(t)| (5)
D β ＝|C 2 X β (t)-X(t)| (6)
D δ ＝|C 3 X δ (t)-X(t)| (7)
X 1 (t+1)＝X α (t)-A 1 D α (8)
X 2 (t+1)＝X β (t)-A 2 D β (9)
X 3 (t+1)＝X δ (t)-A 3 D δ (10)
wherein X (t + 1) represents the position of Grey wolf at the t +1 iteration, and X α (t)、X β (t)、X δ (t) the positions of alpha, beta and delta wolf in the t-th iteration, X (t) the position of grey wolf in the t-th iteration, D α 、D β And D δ Is the distance from the other wolf to alpha, beta and delta wolf, A 1 、A 2 、A 3 And C 1 、C 2 、C 3 Are coefficient vectors.
And 4, under the condition of keeping the surface structure of the detail level grid model, performing global optimization on all vertexes of the detail level grid by using a sparrow-wolf optimization algorithm to enable the detail level grid model to approach the original grid model.
The global optimization problem can be modeled as: given an original three-dimensional mesh model M o (V o ,F o ) And a QEM algorithm simplified detail level model M s (V s ,F s ) On the patch set F s Under the condition of unchanged structure, searching an optimal vertex set
So that
And M o The error of (2) is minimal:
in the formula, V and F respectively represent a vertex set and a patch set of the corresponding mesh model, D () represents a fitness function, and the present embodiment uses a hausdov distance, which is calculated as follows:
in the formula (I), the compound is shown in the specification,
represents the shortest distance from point p to model M, and d (p, p ') represents the euclidean distance between p and p'.
Table 1 shows the comparison of the optimization results of the method of the present invention on 13 mesh models, N o And N d Respectively representing the number of vertices before and after simplification, err * Respectively representing the approximate errors before and after optimization, err/Err * To be the ratio of the approximation errors before and after optimization.
TABLE 1
From table 1, it can be known that the method provided by the present invention achieves good optimization effects for grids with different topologies and sizes. In terms of size, the smaller model "Horse" with the number of vertexes of only 233 and the large model "Buddha" with the number of vertexes reaching 61512 have the ratio of approximation error before and after optimization of 1.41 and 1.43 respectively, and the optimization effect is not reduced due to the increase of the size. In terms of topology, the optimization effects of the "Hammer" model with sharp edges and the "knock 108s" model with complex curvature changes are also not affected by the particular topology.
FIG. 2 is a schematic diagram of the optimization effect of the method provided by the present invention on four kinds of detail level grid models of Teddy, teapot, kitten, and Bunny under different resolutions. The solid line is the approximate error before optimization, and the dotted line is the approximate error after optimization. Because the error of the detail level grid model and the original grid model under different resolutions is greatly different, in order to visually display the optimization effect under high resolution and low resolution, the optimization effect under high resolution is specially displayed at the upper right corner. As can be seen from fig. 2, the method provided by the present invention can achieve a better optimization effect under different resolutions, and the optimization effect is not affected by the resolution.
Table 2 shows the optimization effect of the detail level Mesh model generated by the method of the present invention and 5 different Mesh simplification Algorithms, where MD (Mesh simplification), PM (Progressive Meshes), and CGAL (Computational Geometry Algorithms) are three classical Mesh simplification Algorithms, and Lescoat and Liang represent two latest Mesh simplification Algorithms.
TABLE 2
N o And N d Representing the number of vertices before and after simplification, respectively, using the approximation errors Err, err before and after optimization * The ratio Err/Err of the pre-optimization and post-optimization approximation errors / The optimization effect evaluation was performed as an evaluation index. It can be seen from table 2 that the method provided by the present invention is not limited to a specific mesh simplification algorithm, and can achieve a certain optimization effect for detail level models generated by different simplification methods.
Fig. 3 is a comparison graph of convergence of the optimization method based on Sparrow-Grey Wolf (SSA-GWO) and Sparrow optimization Algorithm (SSA optimization, SSA) and Grey Wolf optimization Algorithm (GWO) to the three grid models of char, pig and Teddy. As can be seen from fig. 3, the sparrow optimization algorithm SSA can quickly find a vertex set with smaller error than the given detail level grid, which indicates that its global exploration capability and solution efficiency are particularly excellent, but the population diversity decreases in the late stage of iteration. The grey wolf optimization algorithm GWOO has good local development capability and optimization performance, but has a low convergence rate. The optimization method SSA-GWOL based on sparrow-Grey wolf can make up the respective defects of SSA and GWO, and can give full play to the global exploration capability of SSA and the local exploration capability of GWO.
TABLE 3
Table 3 shows the minimum approximation error Min and the average approximation error Avg of the optimization method based on Sparrow-Grey Wolf (SSA-GWO) and the Sparrow optimization Algorithm (SSA ) and the Grey Wolf optimization Algorithm (greenwolf Optimizer, GWO) for the mesh model approximation problem. As can be seen from Table 3, the minimum error and the average error of the optimization method SSA-GWOO based on the sparrow-grayish wolf are obviously smaller than those of the other two optimization algorithms.
Fig. 4 shows the visual quality effect before and after optimization by the method of the present invention, using the perceptually driven evaluation matrix MSDM2 as a fitness evaluation function, and plotting the degree of deformation of each vertex relative to the original mesh model, the darker the color represents the greater the degree of deformation. As can be seen from the deformation diagram, the method provided by the invention can avoid large deformation and improve the visual quality.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or scope of the invention as defined in the appended claims.
Claims (9)
1. A detail level mesh model approximation method based on approximate global optimization is characterized by comprising the following steps:
step 1, carrying out preliminary simplification on any original three-dimensional mesh model by using a simplification algorithm to obtain a detail level mesh model with fewer vertexes and patches;
step 2, calculating the movable range of each point of the detail level grid model in the step 1;
step 3, combining the global exploration capability of the sparrow algorithm and the local exploration capability of the grey wolf algorithm to construct a collaborative learning sparrow-grey wolf optimization algorithm;
and 4, under the condition of keeping the surface structure of the detail level grid model, performing global optimization on all vertexes of the detail level grid by using a sparrow-wolf optimization algorithm to enable the detail level grid model to approach the original grid model.
2. The method of approximating a hierarchical-of-detail mesh model based on approximate global optimization of claim 1, wherein: in step 2, the movable range of each point is calculated by using the variable geometric space of the nearest neighbor point, and for a certain vertex v (x, y, z) of the detail level mesh model, the variable geometric space based on the nearest neighbor point is defined as:
R(v)＝{min v′∈N(v) |x-x′|,min v′∈N(v) |y-y′|,min v′∈N(v) |z-z′|} (1)
where R (v) represents the movable range of each point, N (v) is the set of adjacent points in the v neighborhood, v ' is the adjacent point in N (v), and x ', y ', and z ' are the coordinates of v ' in the directions of the x, y, and z axes, respectively.
3. The approximation method of the hierarchical-of-detail mesh model based on approximate global optimization as claimed in claim 1, wherein: the step 3 comprises the following steps:
step 3.1, randomly initializing a population within the vertex movable range, wherein each individual in the population is a possible vertex position set, and recording the position of the ith individual in the population as X i ；
Step 3.2, in the global search stage, updating the vertex position by using a producer, a follower and a detection and early warning mechanism in a sparrow algorithm;
3.3, taking the optimal solution found by the sparrow algorithm as the alpha wolf of the grey wolf algorithm to continue to guide search;
and 3.4, in the local searching stage, updating the vertex position by utilizing a hunting and hunting mechanism of the grey wolf algorithm.
4. The method of approximating a hierarchical-of-detail mesh model based on approximate global optimization of claim 3, wherein: in step 3.2, the producer refers to an individual with a fitness value smaller than a set threshold in the population, and the position updating formula is as follows:
in the formula, X i (t)、X i (T + 1) denotes the position of the ith individual in the population for the T, T +1 iterations, T max Represents the maximum number of iterations, α ∈ (0, 1)]Is a uniform random number, Q is a random number following normal distribution, and L is 1 XN d All one matrix of (N) d In order to simplify the number of vertexes of the model, R is a current early warning value, and ST is a preset safety threshold value.
5. The method of approximating a hierarchical-of-detail mesh model based on approximate global optimization of claim 4, wherein: in step 3.2, the followers are other individuals except for the producer in the population, and the position updating formula is as follows:
in the formula, X i (t)、X i (t + 1) represents the position of the ith individual in the population of the t, t +1 iterations; x w And X b Is the current worst and best position; q is a obedience positiveRandom numbers of state distributions; n is the number of individuals in the population; n is a radical of hydrogen d Simplifying the number of vertexes of the model; a is N d ×N d Each element in the matrix is randomly assigned to 1 or-1; l is 1 XN d All of the matrices of (a).
6. The approximation method of the hierarchical-of-detail mesh model based on approximate global optimization as claimed in claim 5, wherein: the detection and early warning mechanism in step 3.2 is that assuming that a certain proportion of producers and followers can sense danger in advance, their positions are updated again as follows:
in the formula, X i (t)、X i (t + 1) denotes the location of the ith individual in the population for the t, t +1 iterations, X b Is the best current position, beta is a random number representing the step size, and K ∈ -1,1]Is a uniform random number, f i Is the fitness value of the ith individual, f b And f w Is the current best and worst fitness value and epsilon is a very small constant to avoid divisor 0.
7. The approximation method of the hierarchical-of-detail mesh model based on approximate global optimization as claimed in claim 3, wherein: and 3.3, the optimal solution found by the sparrow algorithm is a vertex position set with the minimum fitness value.
8. The method of approximating a hierarchical-of-detail mesh model based on approximate global optimization of claim 3, wherein: in step 3.4, when the gray wolves search for the prey, the gray wolves gradually form an enclosure around the prey target, and the positions of the alpha, the beta and the delta wolves are used as guidance, and the alpha, the beta and the delta wolves are three individuals with the minimum fitness value in the population, so that the positions are updated:
D α ＝|C 1 X α (t)-X(t)| (5)
D β ＝|C 2 X β (t)-X(t)| (6)
D δ ＝|C 3 X δ (t)-X(t)| (7)
X 1 (t+1)＝X α (t)-A 1 D α (8)
X 2 (t+1)＝X β (t)-A 2 D β (9)
X 3 (t+1)＝X δ (t)-A 3 D δ (10)
wherein X (t + 1) represents the position of the gray wolf in the t +1 th iteration, X α (t)、X β (t)、X δ (t) the positions of the alpha, beta and delta wolfs for the t-th iteration, X (t) the position of the grey wolf for the t-th iteration, D α 、D β And D δ Is the distance from the other wolf to alpha, beta and delta wolf, A 1 、A 2 、A 3 And C 1 、C 2 、C 3 Are coefficient vectors.
9. The method of approximating a hierarchical-of-detail mesh model based on approximate global optimization of claim 1, wherein: the global optimization problem in the step 4 is modeled as follows: given an original three-dimensional mesh model M o (V o ,F o ) And a simplified level of detail model M s (V s ,F s ) On the patch set F s Under the condition of unchanging structure, searching an optimal vertex set V s * So that
And M o The error of (c) is minimal:
in the formula, V and F respectively represent vertex sets and patch sets of the corresponding mesh models, D () represents a fitness function, and the calculation method is as follows:
in the formula (I), the compound is shown in the specification,
represents the shortest distance from point p to model M, and d (p, p ') represents the euclidean distance between p and p'.
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