CN111428368A - Automatic shallow relief layout method based on random optimization algorithm - Google Patents
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Abstract
The invention relates to a random optimization algorithm-based automatic layout method of a low relief, which comprises the following steps: arranging and acquiring an image data set of the bas-relief, and making a corresponding information label for each image in the image data set; on the basis of the image data set and the information label, counting indexes influencing the layout of the bas-relief and drawing a distribution curve chart of the indexes; adopting a self-adaptive Gaussian mixture model to perform curve fitting on the distribution curve graph, and expressing the evaluation index as a mathematical expression; constructing an evaluation function based on a weighted geometric mean combination model; optimizing and solving the evaluation function to obtain an optimal evaluation function; and (3) carrying out model layout by utilizing the optimal evaluation function, realizing the curve deformation of the source model, obtaining the optimized bas-relief, attaching the optimized bas-relief on the target curved surface, and finishing automatic layout. The invention can automatically and efficiently layout the bas-relief model, thereby saving the time cost required by the design of professional sculptors and having better layout effect.
Description
Technical Field
The invention belongs to the technical field of computer graphics, and particularly relates to a random optimization algorithm-based automatic layout method for a bas-relief.
Background
The relief is one of sculpture types and also a sculpture culture widely used for thousands of years. Due to its own decorative characteristics, it can be applied to the decoration of various utensils and crafts ranging from ornamental to practical ones, and to indoor and outdoor environments related to buildings, such as interior and exterior wall reliefs, wall decorations, monuments, garden decorations, furniture sculptures, and the like. In recent years, the relief plays an important role in displaying urban culture and beautifying the environment, and becomes an industrial artwork with wide application. With the continuous development of artists' exploration of sculpture spaces, the form of relief does not exist as a complete architectural decoration accessory any more, but begins to show its own unique charm in an independent form, conveying the spiritual connotation of more independent meaning.
At present, the relief can be divided into high relief and low relief due to the difference of height, and the high relief and the low relief are originally defined by the dimension and are currently divided by visual effect and means. The 2.5D high relief is closer to the complete 3D model, while the flatter artwork is called bas-relief, which is also classified as intaglio relief, openwork relief, etc. due to its technical and formal differences. Compared with other types of embossments, the bas-relief has the outstanding characteristic that the space structure is carved into a very narrow bas-relief with a plane characteristic, the image proportion is kept, and the detail outline can be well outlined. Therefore, the bas-relief layout can better use the human visual characteristics and the related evaluation knowledge of the image aesthetics.
In traditional relief making, artists need to adopt complicated technological processes to generate relief models, and aesthetic and creative products of the relief are designed by professional sculptors. Once the relief model is completed, it is difficult to modify and maintain, and therefore artists prefer new digital relief techniques. With the development of artificial intelligence, digitization technology and 3D printing technology, the generation technology of digital relief has become one of the research hotspots in the field of computer graphics in recent years, and is also a basic guarantee for the industrial development of relief artwork. In the process of generating the digital embossment, the research of the embossment layout method becomes a new content of research of numerous scholars due to the reasons that the time cost of the design of artists can be saved, the aesthetic value of the embossment can be automatically and efficiently improved, and the like.
Disclosure of Invention
In view of the above, the present invention provides an automatic layout method of low relief based on a random optimization algorithm to solve the above-mentioned problems.
The technical scheme of the invention is as follows:
a low relief automatic layout method based on a random optimization algorithm comprises the following steps:
arranging and acquiring an image data set of the bas-relief, and making a corresponding information label for each image in the image data set;
on the basis of the image data set and the information label, counting indexes influencing the layout of the bas-relief and drawing a distribution curve chart of the indexes;
performing curve fitting on the obtained distribution curve graph of the index by adopting a self-adaptive Gaussian mixture model, thereby expressing the evaluation index as a mathematical expression;
constructing an evaluation function based on a weighted geometric mean combination model;
optimizing and solving the evaluation function to obtain an optimal evaluation function;
model layout is carried out by utilizing the optimal evaluation function to realize a source model BRObtaining an optimized bas-relief, and attaching the optimized bas-relief to the target curved surface BTAnd (5) finishing automatic layout.
Preferably, the image dataset is marked with L abelmg when creating an information label containing the coordinate position (x) of each model in the bas-relief imagemin,ymin,xmax,ymax)。
Preferably, the plotting of the distribution graph of the index includes the steps of:
various criteria are listed that affect the bas-relief layout: area, separation distance, height difference, boundary rectangle, symmetry, occlusion area, and curvature;
and (3) compressing the reasonable value range of each index into a (0,1) range, counting the proportion of all models occupying the whole relief image by virtue of the coordinate position of each model marked in the image data set, and counting the spacing distance, the height difference, the boundary rectangle and the shielding area among different models in a single relief image to form a distribution curve graph of each index.
Preferably, the unknown distribution curve of the index is p ═ f (x), and the approximate curve of the gaussian mixture model is p ═ f (x)
Calculating the raw data point Pi(xi,yi) I-1, 2, … n and the data point P corresponding to the approximate curvei′(xi,yi) I is the variance σ (p, p') of 1,2, … n;
carrying out threshold judgment on the obtained variance, if sigma is larger than 0.1, averagely dividing original data points, and for the variance, carrying out threshold judgment on the obtained variance
i is 1,2, … n/2 and
and (8) … n, and adopting the adaptive Gaussian function model to segment the approximate curve again until the variance sigma is less than or equal to 0.1.
Preferably, the evaluation function based on the weighted geometric mean combination model is constructed using the following formula:
wherein, C1And C2Is an evaluation function, M denotes the relief layout configuration, NbdBoundary rectangle index function representing fitting, NcuAnd (3) representing a fitted curvature index function, m representing the number of indexes, n representing the number of source models, and w representing the weight of the index function.
Preferably, the step of optimizing the solution to the merit function includes:
optimizing an evaluation function by adopting a simulated annealing method, setting a random value for the distance of each iterative movement to avoid the situation of moving to the same position, performing iterative optimization by using the following formula to avoid the model from exceeding the boundary, synchronously verifying the model position information obtained in the algorithm optimization process, thereby better configuring the relief layout,
pr(Mk′→Mk+1)＝min{1,exp[-(C(Mk′)-C(Mk)/T0-T*k)]}
wherein M iskRepresenting the spatial location coordinates randomly assigned to each source model in the relief during the kth iteration, C being an evaluation function, T0The temperature of the simulated annealing is shown as,Tindicating the rate of temperature decay.
Preferably, the source model B is implementedRThe method for curve deformation comprises the following steps:
traverse BRMiddle vertex
And BTEach vertex
The Euclidean distance of (1) and the vertex with the minimum Euclidean distance is recorded
Establishing
And
is a mapping set of
Computing a set of mapping relationships S1Each vertex in
To correspond to
In BTThe intersecting surfaces of all the adjacent surfaces are calculated according to the space geometric relationship
Mapping vertex on the surface
And recording a mapping relation, wherein the mapping relation is as follows:
wherein the content of the first and second substances,
is a source model BRThe vertex of (a) is,
is a target curved surface BTThe vertex of (a) is,
the vertical axis space coordinate of the vertex of the target curved surface, and a, b and c represent normal vectors on the target curved surface;
according to a set of mapping relationships S2Replacement of the Source model BRHeight information of
And (5) reconstructing the shallow relief to complete curve deformation.
The invention provides a random optimization algorithm-based bas-relief layout method, which has the following beneficial effects:
(1) the invention can automatically and efficiently carry out the layout of the bas-relief model for the given bas-relief and the target curved surface, thereby saving the time cost required by the design of professional sculptors;
(2) according to the method, relevant indexes influencing the layout are extracted according to knowledge such as image aesthetic evaluation, human vision, photographic composition and the like, so that an evaluation function is constructed, and experimental results show that the method has a good layout effect;
(3) the layout bas-relief obtained by the invention can be used as the input of auxiliary manufacturing equipment, provides a new solution for the customization service of relief products, greatly saves the time cost required by artists for designing the artistic layout, has good practicability and is worthy of popularization.
Drawings
FIG. 1 is a flow chart of a method for performing a relief layout based on a stochastic optimization algorithm according to an embodiment of the present invention;
FIG. 2 is a graph of the effect of curve fitting provided by the embodiment of the present invention;
FIG. 3 is a diagram illustrating the effect of a flag identifier according to an embodiment of the present invention;
fig. 4 is a diagram of experimental effects provided by an embodiment of the present invention.
Detailed Description
An embodiment of the method for automatic layout of bas-relief based on random optimization algorithm according to the present invention is described in detail with reference to fig. 1 to 4, but it should be understood that the scope of the present invention is not limited by the embodiment.
Example 1
As shown in fig. 1, the automatic layout method of bas-relief based on random optimization algorithm provided by the invention comprises the following steps:
Using labelImg, a corresponding information label is made for each image in the dataset, marking the coordinate position (x) of each model in the relief image datasetmin,ymin,xmax,ymax) And in a subsequent stepAnd carrying out corresponding statistics by utilizing the coordinate information.
And 2, combining human visual aesthetic habits and aesthetic quality evaluation standards, inspiring by knowledge such as photographic composition and the like, providing seven indexes which influence the layout of the low relief, including area, spacing distance, height difference, boundary rectangle, symmetry, shielding area, curvature and the like, realizing a distribution curve of the indexes by adopting a statistical method, wherein the indexes which can be used for statistics include five types of area, spacing distance, height difference, rectangular boundary and shielding area, and facilitating the fusion of different indexes into an evaluation function.
The index means specifically include:
area: this index describes the area of the model in relief;
the spacing distance is as follows: this index describes the spacing of the different models in the relief layout;
height difference: this index describes the height difference of different models in the relief layout;
boundary rectangle: this index describes the distance from the center of the model in the relief layout to the center of the mapped region;
symmetry: this index describes the symmetry of the different models in the relief layout;
shielding area: the index describes the occlusion situation of different models in the relief layout;
curvature: this index describes the curvature information of the target surface in the relief layout.
And 3, setting the index distribution curve as p ═ f (x) according to the different index distribution curves obtained in the step 2, and adopting an adaptive Gaussian mixture model approximation curve for the unknown index distribution curve p ═ f (x)
The adaptation is represented by calculating the original data point Pi(xi,yi) I-1, 2, … n, and the data point P corresponding to the approximate curvei′(xi,yi) Where i is a variance σ (p, p') of 1,2, … n, and σ > 0.1, the original data point is divided on average, and for the divided data point, the original data point is divided
i is 1,2, … n/2 and
and (8) … n, and re-adopting the Gaussian function model to segment the approximate curve until the sigma is less than or equal to 0.1.
In order to determine the parameters of the gaussian mixture model, the solution is performed by using the least square method, and the gaussian mixture model is shown as formula (1):
wherein, α1,β1,λ1,α2,β2,λ2The coefficients to be determined in the gaussian mixture model need to be solved by a least square method. x represents a variable for different evaluation indexes,
it is a curve fitted to the evaluation index.
The function fitting effect for these four different metrics is shown in fig. 2, where the formula for the bounding rectangle is shown in (2):
a1＝Euclidean(median(v(y))-median(B(y)),median(v(x))-median(B(x)))
wherein V represents the vertex of the source model, and B represents the vertex of the target surface，a1Used for calculating the Euclidean distance k from the source model to the target curved surface1Denotes a1The result of the normalization of (a) is,
it is the fitting function of the boundary rectangle index normalization.
The formula of curvature is shown in (3):
wherein C represents the average curvature of the target curved surface, and n represents the number of vertexes of the source model.
The formula of the separation distance is shown in (4):
wherein v isi(x),viAnd (y) represents coordinates of the ith source model in the x direction and the y direction, and flag represents different layout modes of the two source models. 2, which means that the two models intersect in the x direction and do not intersect in the y direction; 1, which means that the two models intersect in the y direction and do not intersect in the x direction; flag-0 denotes that the two models are all disjoint in the x, y direction; the effect of flag-1, which indicates that the two models intersect in both x and y directions, is shown in fig. 3. k is a radical of3Represents a3Normalized result of (2), Na3Then it is a fitting function normalized by the separation distance index.
The formula of the occlusion region is shown in (5):
in the present invention, only the case where the model is not occluded is considered, and therefore, T is defined as an identifier of whether the models overlap each other. When T ═ 1, the model is not occluded; otherwise, the model will be occluded.
The formula of the height difference is shown in (6):
when T is 1, the two models intersect, and when T is 0, the two models do not intersect. ViDenotes the vertex of the ith model, k5Denotes a5The result of the normalization of (a) is,
it is a fitting function of the height difference indicator normalization.
And 4, constructing an evaluation function based on the weighted geometric mean combination model, wherein the evaluation function of the bas-relief layout can be divided into two types according to the number of the source models: for one source model, the cost function contains two terms; for both models, the cost function contains a total of five terms, and the evaluation function is shown in equation (7):
wherein M represents a relief layout configuration, NbdBoundary rectangle index function representing fitting, NcuAnd (3) representing a fitted curvature index function, m representing the number of indexes, n representing the number of source models, and w representing the weight of the index function.
And 5, optimizing and solving the evaluation function by adopting a simulated annealing algorithm according to the evaluation function provided in the step 4, setting a random value for the distance of each iterative movement to avoid the situation of movement to the same position, and synchronously verifying the position information of the model obtained in the algorithm optimization process to avoid the model from exceeding the boundary, so that the relief layout is better configured. The iterative optimization formula is shown in (8):
pr(Mk′→Mk+1)＝min{1,exp[-(C(Mk′)-C(Mk)/T0-T*k)]} (8)
wherein M iskRepresenting the spatial location coordinates randomly assigned to each source model in the relief during the kth iteration, C being an evaluation function, T0To representThe temperature of the simulated annealing was measured by the temperature control,Tindicating the rate of temperature decay.
Step 6, carrying out model layout according to the optimal result obtained by simulating the annealing algorithm in the step 5, and establishing a source model BRAnd the target curved surface BTThe mapping relationship between the two is shown as the formula (9), and the curve deformation of the model, namely the attachment of the low relief on the target curved surface, is realized.
The method for deforming the curved surface comprises the following steps:
1) traverse BRMiddle vertex
And BTEach vertex
The Euclidean distance of (1) and the vertex with the minimum Euclidean distance is recorded
Establishing
And
is a mapping set of
2) Computing a set of mapping relationships S1Each vertex in
To correspond to
In BTThe intersecting surfaces of all the adjacent surfaces are calculated according to the space geometric relationship
Mapping vertex on the surface
And recording a mapping relation, wherein the mapping relation is as follows:
wherein the content of the first and second substances,
is a source model BRThe vertex of (a) is,
is a target curved surface BTThe vertex of (a) is,
the vertical axis space coordinate of the vertex of the target curved surface is shown, and a, b and c represent normal vectors on the target curved surface.
3) According to a set of mapping relationships S2Replacement of the Source model BRHeight information of
Rebuilding the bas-relief to complete curve deformation, namely rebuilding the source model BRAttached to the target curved surface BTThe above.
The relief layout effect map obtained by the layout method described above is shown in fig. 4, in which fig. 4(a), fig. 4(b) show the relief layout effect of the model on the spherical surface, fig. 4(c) show the relief layout effect of the model on the flat surface, and fig. 4(d) and fig. 4(e) show the relief layout effect of the model on the complex curved surface.
The invention can automatically and efficiently carry out the shallow relief model layout on the given shallow relief and the target curved surface, thereby saving the time cost required by the design of professional sculptors and also improving the aesthetic value of the shallow relief; according to knowledge such as image aesthetic evaluation, human vision, photographic composition and the like, relevant indexes influencing layout are extracted, so that an evaluation function is constructed, and experimental results show that the method has a good layout effect; the layout bas-relief obtained by the invention can be used as the input of auxiliary manufacturing equipment, provides a new solution for the customization service of relief products, greatly saves the time cost required by artists for designing the artistic layout, has good practicability and is worthy of popularization.
The above disclosure is only for the preferred embodiments of the present invention, but the embodiments of the present invention are not limited thereto, and any variations that can be made by those skilled in the art are intended to fall within the scope of the present invention.
Claims (7)
1. A low relief automatic layout method based on a random optimization algorithm is characterized by comprising the following steps:
arranging and acquiring an image data set of the bas-relief, and making a corresponding information label for each image in the image data set;
on the basis of the image data set and the information label, counting indexes influencing the layout of the bas-relief and drawing a distribution curve chart of the indexes;
performing curve fitting on the obtained distribution curve graph of the index by adopting a self-adaptive Gaussian mixture model, thereby expressing the evaluation index as a mathematical expression;
constructing an evaluation function based on a weighted geometric mean combination model;
optimizing and solving the evaluation function to obtain an optimal evaluation function;
model layout is carried out by utilizing the optimal evaluation function to realize a source model BRObtaining an optimized bas-relief, and attaching the optimized bas-relief to the target curved surface BTAnd (5) finishing automatic layout.
2. The method of claim 1, wherein the image data set is marked with L abelmg when creating an information label comprising coordinate positions (x) of each model in the bas-relief imagemin,ymin,xmax,ymax)。
3. The method for automatic layout of bas-relief based on random optimization algorithm as claimed in claim 2, wherein the step of drawing the distribution graph of the index comprises the steps of:
various criteria are listed that affect the bas-relief layout: area, separation distance, height difference, boundary rectangle, symmetry, occlusion area, and curvature;
and (3) compressing the reasonable value range of each index into a (0,1) range, counting the proportion of all models occupying the whole relief image by virtue of the coordinate position of each model marked in the image data set, and counting the spacing distance, the height difference, the boundary rectangle and the shielding area among different models in a single relief image to form a distribution curve graph of each index.
4. The method for automatic layout of bas-relief based on stochastic optimization algorithm of claim 1, wherein the curve fitting of the adaptive Gaussian mixture model to the distribution curve of the obtained index comprises the following steps:
let p ═ f (x) be the unknown distribution curve of the index, and the approximate curve of the Gaussian mixture model be
Calculating the raw data point Pi(xi,yi) I-1, 2, … n and the data point P corresponding to the approximate curvei′(xi,yi) I is the variance σ (p, p') of 1,2, … n;
judging the threshold value of the obtained variance, if sigma is more than 0.1, averagely dividing the original data points, and for Pi T(xi,yi) I is 1,2, … n/2 and Pi V(xi,yi) And i is n/2, … n, and the adaptive Gaussian function model is adopted again to segment the approximate curve until the variance sigma is less than or equal to 0.1.
5. The bas-relief automatic layout method based on stochastic optimization algorithm as claimed in claim 1, wherein the evaluation function based on weighted geometric mean combination model is constructed by the following formula:
wherein, C1And C2Is an evaluation function, M denotes the relief layout configuration, NbdBoundary rectangle index function representing fitting, NcuAnd (3) representing a fitted curvature index function, m representing the number of indexes, n representing the number of source models, and w representing the weight of the index function.
6. The method for automatic layout of bas-reliefs based on stochastic optimization algorithm according to claim 1, wherein the step of optimizing the solution to the merit function comprises:
optimizing an evaluation function by adopting a simulated annealing method, setting a random value for the distance of each iterative movement to avoid the situation of moving to the same position, performing iterative optimization by using the following formula to avoid the model from exceeding the boundary, synchronously verifying the model position information obtained in the algorithm optimization process, thereby better configuring the relief layout,
pr(Mk′→Mk+1)＝min{1,exp[-(C(Mk′)-C(Mk)/T0-T*k)]}
wherein M iskRepresenting the spatial location coordinates randomly assigned to each source model in the relief during the kth iteration, C being an evaluation function, T0The temperature of the simulated annealing is shown as,Tindicating the rate of temperature decay.
7. The method of claim 1, wherein the source model B is implemented by using a random optimization algorithmRThe method for curve deformation comprises the following steps:
traverse BRMiddle vertex
And BTEach vertex
The Euclidean distance of (1) and the vertex with the minimum Euclidean distance is recorded
Establishing
And
is a mapping set of
Computing a set of mapping relationships S1Each vertex in
To correspond to
In BTThe intersecting surfaces of all the adjacent surfaces are calculated according to the space geometric relationship
Mapping vertex on the surface
And recording a mapping relation, wherein the mapping relation is as follows:
wherein the content of the first and second substances,
is a source model BRThe vertex of (a) is,
is a target curved surface BTThe vertex of (a) is,
the vertical axis space coordinate of the vertex of the target curved surface, and a, b and c represent normal vectors on the target curved surface;
according to a set of mapping relationships S2Replacement of the Source model BRHeight information of
And (5) reconstructing the shallow relief to complete curve deformation.
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