Animation VR scene mosaic modeling based on generalized Laplacian equation

Laplacian equation is a signal analysis method based on time scale, which has the characteristics of multi-resolution analysis and the ability to express local characteristics. This method can decompose the source scene into details of different scales and directions and a lowest approximation. The lowest approximation carries the average information of the scene, that is, it contains most of the energy of the whole scene; The details of different scales and directions contain the high-frequency or edge information of the scene [9]. In the continuous wavelet transform, let f(t) and ψ(t) be square integrable, and ψ (w) be the Fourier transform of mountain ψ(t), which meets the allowable conditions, as shown in equation 1: (1) ∫−∞+∞ψ(ω)ωdω<∞ \int\limits_{ - \infty }^{ + \infty } {{{\psi \left( \omega \right)} \over \omega }} d\omega < \infty (2) Wf(x,y)=1x∫−∞+∞f(t)ψ(t−yx)dt {W_f}\left( {x,y} \right) = {1 \over {\sqrt x }}\int\limits_{ - \infty }^{ + \infty } {f\left( t \right)\psi \left( {{{t - y} \over x}} \right)dt}

Equation 2 is the continuous wavelet transform of f(t). Where, ψ (t) is called the wavelet generating function, a is the scaling factor, and b is the translation parameter. Let the two-dimensional signal of the scene be d. for a given scale function and wavelet coefficient, the wavelet decomposition of the scene is shown in equation 3: (3) { Fk(n,m)=∑n∑mFk−1(n,m)h(2n−i)h(2m−j)dkH(n,m)=∑n∑mFk−1(n,m)h(2n−i)h(2m−j)dkV(n,m)=∑n∑mFk−1(n,m)g(2n−i)h(2m−j)dkD(n,m)=∑n∑mFk−1(n,m)g(2n−i)h(2m−j) \left\{ {\matrix{ {{F_k}\left( {n,\,m} \right) = \sum\limits_n {\sum\limits_m {{F_{k - 1}}\left( {n,\,m} \right)h\left( {2n - i} \right)h\left( {2m - j} \right)} } } \hfill \cr {d_k^H\left( {n,\,m} \right) = \sum\limits_n {\sum\limits_m {{F_{k - 1}}\left( {n,\,m} \right)h\left( {2n - i} \right)h\left( {2m - j} \right)} } } \hfill \cr {d_k^V\left( {n,\,m} \right) = \sum\limits_n {\sum\limits_m {{F_{k - 1}}\left( {n,\,m} \right)g\left( {2n - i} \right)h\left( {2m - j} \right)} } } \hfill \cr {d_k^D\left( {n,\,m} \right) = \sum\limits_n {\sum\limits_m {{F_{k - 1}}\left( {n,\,m} \right)g\left( {2n - i} \right)h\left( {2m - j} \right)} } } \hfill \cr } } \right. Where, F_k, dkH d_k^H , dkV d_k^V and dkD d_k^D are the low-frequency component, horizontal high-frequency component, vertical high-frequency component and diagonal high-frequency component of the source scene at this resolution respectively.

The 3D animation scene splicing system is mainly composed of perception module, emotion module, behavior module and 3D animation generation module [10]. Figure 1 is the overall framework of 3D animation system.

Figure 1

The sensing module extracts simulated information of virtual characters based on different virtual scenes, converts tools in the selected scene and materials of nearby characters into sensing information, and serves the emotion module and action module. The emotion module includes the customized character emotion in the plot description, sets the personalized emotion transformation strategy, updates the emotion in time, and increases the realistic effect of three-dimensional animation characters. The behavior module refers to the behavior selection ability of a 3D cartoon character, and the good or bad of the role acting ability and reaction ability is determined by the design level of the behavior module[11]. The character behavior includes the customized character actions in the plot description. Combined with the perceptual information, it forms a motion library, and forms a series of action sequences according to the online motion control. 3D animation generation module belongs to the core of 3D animation system, which includes character modeling, scene modeling and motion control. Character modeling means that it can not only show the appearance of the virtual character, but also show the physical state of the character's body, such as height and weight.

Scene modeling is to manage and operate according to the way of scene database. The scene database can present all the details of the real environment applied to the virtual scene and build a realistic 3D scene. Motion control makes animation characters move, which belongs to the advanced control method of virtual character motion [12]. Based on the character motion library, when making three-dimensional animation, you can complete the cumbersome motion simulation of virtual characters only by describing the behavior characteristics, without complex partial detail adjustment. Based on the constructed target 3D animation character prototype and action library, users only need to select the character prototype they need and simply change the parameters such as the height and body proportion of the character prototype to obtain the 3D animation target character [13], as shown in Figure 2.

Figure 2

The 3D animation target character is consistent with the original actions in the skeleton, skin, controller and action library of the 3D animation character prototype. The 3D animation character template composed of virtual bone, skin and controller is the 3D animation prototype. A series of basic actions designed for 3D animation character prototype is 3D animation character action library [14]. Users can freely change the proportion and shape of 3D animation characters according to the graphic interface, design target 3D animation characters and build new 3D animation characters. Using motion capture technology to obtain a large number of action examples of character motion, and store them in the corresponding motion library. The obtained motion examples are displayed in three-dimensional form through virtual artificial synthesis software, so that the three-dimensional animation system can realize visualization and facilitate the change of character model action. The rationality of the new action is verified by Newton Euler motion model. The 3D animation system sets the character action as motion (x) and changes the original pose postion (x_i) to obtain a new character pose postion (x_i). the above operations can realize the visual interactive action design. The size of the user window is H × K. move the role model with the mouse. When moving, the change in direction h is Δh and the change in direction k is Δk. according to the Euler theorem, the Euler angle < α, β, γ > represents the rotation in direction l, h, k the relationship after reasoning is as follows: (4) sinα=zΔh/F(1−z)Δk/Hsinβ=xΔh/F(1−x)Δk/Hsinγ=yΔh/F(1−y)Δk/H \matrix{ {\sin \alpha = z\Delta h/F\left( {1 - z} \right)\Delta k/H} \hfill \cr {\sin \beta = x\Delta h/F\left( {1 - x} \right)\Delta k/H} \hfill \cr {\sin \gamma = y\Delta h/F\left( {1 - y} \right)\Delta k/H} \hfill \cr } Where: z, x, y are the influence factors respectively, representing the influence degree of Δh and Δk on Euler angle < α, β, γ > in the three directions of l, h, k. The new pose of the character model is obtained through calculation, and the simulation of the three-dimensional animation character model is realized. Animation scene modeling technology uses computer graphics to abstract the real scene and build the three-dimensional geometric model of virtual landscape in the form of polygons, including terrain and architecture. At the same time, it also needs to build the lighting and material model in the virtual scene.

After the 3D animated character and scene construction is complete, you need to set up texture maps and control parameters for the model to improve realism. Texture mapping technology can simulate figures (objects) such as elaborate and irregular color textures. Using texture mapping technology, any plane graphics (scene) can be covered on the surface of 3D animation model, so that the model surface can generate more real color texture, increase the authenticity of 3D animation and simplify the modeling process. Texture mapping technology has two steps: 1)

Determining the texture properties determines which parameters of the person's (object) surface should be defined in the form of a texture;

Only basic contour features and lack of surface texture details will reduce the realism. This requires texture mapping for each module to increase the realism of the model. The overall direction of the surface patch determines which spatial plane the surface patch is projected to, and it is projected to the plane with the smallest angle between the overall direction of the surface patch and the plane [15]. Since some parts of the surface of the person (object) are curved, the total direction of the curved surface needs to be calculated. The calculation method is as follows:

Suppose that the three vertices of a triangular patch are v₁, v₂, v₃ respectively, [v₁ – v₂] * [v₂ – v₃] is perpendicular to the patch. After normalizing it, obtain the normal vector V of the triangular patch, calculate the sum and mean of the normal vectors of all patches, obtain the average vector sum representing the module, and master the overall direction of the module, as shown in equation 5: (5) W=sinα∑i=1vi−F(1−a)ΔgG W = \sin \alpha \sum\limits_{i = 1} {{v_i} - {{F\left( {1 - a} \right)\Delta g} \over G}}

To find out the mapping relationship between the surface patch and the corresponding texture coordinates, the texture coordinates of the grid points can be calculated using the perspective projection transformation. As shown in equations 6 and 7: (6) k[ u v 1 ]T=kX′=HX k{\left[ {u\,v\,1} \right]^T} = kX^\prime = HX (7) H=[ h100h40h20h500h30 ] H = \left[ {\matrix{ {{h_1}} & 0 & 0 & {{h_4}} \cr 0 & {{h_2}} & 0 & {{h_5}} \cr 0 & 0 & {{h_3}} & 0 \cr } } \right] Where: h₁, h₂, h₃, h₄, h₅ are unknown parameters; The texture coordinate is (u, v), and the corresponding homogeneous texture coordinate is X^′; X-coordinate is homogeneous grid; The perspective projection matrix of 3 × 4 is H, and the constant coefficient is k. According to equations 6 and 7, it is found that each group of corresponding mesh vertices and texture vertices have two independent linear equations. To transform matrix H, three groups of feature points need to be selected. By analyzing the whole texture mapping process and combining the obtained texture image size, the texture image size is set to m × n, which can simplify equation 7.

Laplacian operator is a second-order differential operator, which has a good effect on the detection of scene edge position. Use wavelet transform to decompose the scene to obtain low-frequency coefficient N(n, m), and convolute N(n, m) with two Laplacian operators to obtain equation 8: (8) Mi(n,m)=q1⊗N(n,m)Nj(n,m)=q2⊗N(n,m) \matrix{ {{M_i}\left( {n,m} \right) = {q_1} \otimes N\left( {n,m} \right)} \hfill \cr {{N_j}\left( {n,m} \right) = {q_2} \otimes N\left( {n,m} \right)} \hfill \cr }

Then compare the corresponding M_i(n, m) and N_j(n, m) (when i = j), and select the one with the largest value of each two as the candidate coefficient, as shown in equation 9: (9) K(n,m)={ Mi(n,),Mi(n,m)≥Nj(n,m)Nj(n,m),Mi(n,m)<Nj(n,m) K\left( {n,m} \right) = \left\{ {\matrix{ {{M_i}\left( {n,} \right),{M_i}\left( {n,m} \right) \ge {N_j}\left( {n,m} \right)} \hfill \cr {{N_j}\left( {n,m} \right),{M_i}\left( {n,m} \right) < {N_j}\left( {n,m} \right)} \hfill \cr } } \right.

Finally, the scene entropy function and evaluation function are used to determine the final splicing coefficient, as shown in equation 10: (10) Hω(n,m)=−∑n∑mKn(n,m)ln[ Kn(n,m) ] {H_\omega }\left( {n,m} \right) = - \sum\limits_n {\sum\limits_m {{K_n}\left( {n,m} \right)\ln \left[ {{K_n}\left( {n,m} \right)} \right]} }

Compare the H_ω(n, m) value of the high-frequency coefficient corresponding to the two images to be spliced, and take the largest one as the high-frequency coefficient of the spliced scene. This experiment is run on a computer with win7 system, Intel (R) core (TM) i3cpu, main frequency of 2.26GHz and memory of 4G. Matlab r2010b is used for programming simulation experiment. In order to verify the validity of the modified algorithm presented in this article, an experiment was conducted using a scene with a different focus. The scenes to be spliced are compared, simulated and analyzed with three traditional wavelet transform algorithms and the improved algorithm proposed in this paper, specifically, as shown in Figure 3 and Figure 4.

Figure 3

Figure 4

Algorithm 1 uses weighted average rules for both high-frequency and low-frequency coefficients, algorithm 2 uses absolute maximum rules for both high-frequency and low-frequency coefficients, and algorithm 3 uses weighted average and absolute maximum rules for high-frequency and low-frequency coefficients respectively. After comparison and application, the stitching effect of the improved algorithm in this paper is more ideal. It does not have virtual shadow like the stitching scene of the traditional algorithm, but also improves the brightness and contrast, and the details are more complete. It can be seen that the numbers on the dial and the letters on the box are clearer than other methods. After subjectively evaluating the splicing scenes obtained by several methods, this paper introduces several common objective evaluation indexes to compare and analyze the splicing results: ①

Average gradient: the average gradient can reflect the clarity of the scene and reflect the variation characteristics of texture and the contrast of details in the scene. The larger its value is, the clearer the scene is.

In order to verify the smoothness of the movement connection of the animated characters in this system, an experiment was conducted using a video of a basketball player as an example. The number of video frames is 60, and every 10 frames is a segment. This system can not only make the motion segments have better smoothness at the connection, but also inherit the original motion details. In this paper, the connection effect of the system at the junction of the two segments is relatively smooth. Not only can you successfully connect the movements of the two segments, but you can also retain the details of the first movement and take over the first movement data. Experiments show that the connection effect of each part of the system is relatively smooth. In order to further verify the realistic effect of the system, multiple motion segments of the heel joint are selected to compare the connection effects of the three systems. The systems herein are relatively smooth at the motion segment connections, but the remaining two systems are not sufficiently smooth at the motion segment connections and may perfectly show the behavior of the entire motion segment. Can not. The connection of motion clips is not smooth enough, which will produce flashing effect in the process of playing 3D animation, resulting in the action of 3D animation characters is not realistic enough. Experiments show that the system can connect the motion segments well and make the action effect of 3D animation characters more realistic.