CN106204714A - Video fluid illumination calculation method based on Phong model - Google Patents

Abstract

A kind of method that the invention discloses video fluid illumination calculation, the method is intended to utilize Phong model, utilizes flow surface geological information, quickly calculates Phong model illumination parameter.First, ambient light and irreflexive composition are obtained by the method for linear fit.On this basis, update flow surface geological information, further according to ambient light composition, diffuse-reflectance composition and flow surface geological information, by the means of cluster, obtain the direct reflection index of fluid scene.Finally according to the intensity of flow surface, it is calculated the specular reflection component of fluid scene.By experiment test and error analysis, it was demonstrated that the method studied in the present invention is the most effective.The present invention can be effectively applied in research and the application of the reverse engineering of fluid, can obtain the lighting effect consistent with sample fluid outward appearance, overcome computationally intensive in existing fluid illumination calculation and need the problems such as user's initialization in heavily emulation.

Description

Video fluid illumination calculation method based on Phong model

Technical Field

The invention relates to a method for calculating illumination in video fluid re-simulation. And (3) calculating the ambient light and diffuse reflection components of the fluid scene by using a Phong model and a result of height calculation of a fluid video sample frame and using a linear fitting method, updating the height information of the fluid surface on the basis, and further obtaining the specular reflection index of the scene by using a clustering method, so that the specular reflection components of the scene can be calculated.

Background

The real fluid-sensitive weight simulation is widely applied to the fields of game design, fluid animation simulation, special effect design of movies, fluid military simulation and the like, and research on video fluid illumination calculation has achieved a lot of results. The complexity of particle motion limited to fluid scenes has led to a complication in the problem of video fluid illumination calculations, which has been the subject of much recent research. How to fully utilize the intensity in the fluid video and the geometric information of the fluid surface, and further effectively calculate the illumination parameters of the video fluid, thereby realizing the realistic drawing, which is a problem to be solved urgently in the video fluid reverse engineering.

In recent years, some research works are based on Bidirectional Reflectance Distribution Function (BRDF), torance-spark illumination model, or Phong model, but how to automatically calculate the illumination of a scene is still a difficult problem in research, and especially, the complexity of fluid motion brings difficulty to the research of the scene illumination problem.

In the research of people's illumination calculation problem of video fluid at present, the problem that exists is mainly: some works are to obtain the illumination information of the fluid scene by using an optimization method and means, such research measures are mainly inconvenient for practical application, and ideal results are difficult to obtain when the illumination of the fluid scene is calculated by using the existing methods. In the recently developed research methods, a pretreatment is required by people, which is inconvenient to solve the problem of fluid scene illumination calculation. Therefore, the method for rapidly and conveniently calculating the illumination parameters of the fluid scene still is a practical problem to be solved urgently, and particularly in the research of the reverse engineering problem of the video fluid, the calculation problem of the illumination parameters of the fluid scene is a crucial problem.

Disclosure of Invention

The invention aims to provide a video fluid illumination calculation method aiming at the defects of the prior art and the requirements of realistic re-simulation in video fluid reverse engineering.

The specific technical scheme for realizing the purpose of the invention is as follows: a method for calculating illumination of a video fluid based on Phong model, characterized in that, an RGB color model is used for the video fluid, and the color components of any pixel P in a sample frame F of the fluid video are represented as R, G and B, then according to Phong model:

$R=C_a^R+k_d^R(L_m\·N)i_{m,d}^R+k_s^R{(R_m\·V)}^{\mathrm{\α}}{i}_{m,s}^R---\left(1\right)$

$G=C_a^G+k_d^G(L_m\·N)i_{m,d}^G+k_s^G{(R_m\·V)}^{\mathrm{\α}}{i}_{m,s}^G---\left(2\right)$

$B=C_a^B+k_d^B(L_m\·N)i_{m,d}^B+k_s^B{(R_m\·V)}^{\mathrm{\α}}{i}_{m,s}^B---\left(3\right)$

wherein,andis the component of ambient light in three channels of RGBAndis an ambient light component;

andis the rate of the diffuse reflectance and,andthe intensities of diffuse reflection in three channels of RGB are respectively;is marked asIs marked asIs marked asCombined balanceAndis a diffuse reflection component;

L_mis a unit normal vector from any point in the scene to the light source direction, N is a unit normal vector from any point on the fluid surface, V is a unit vector in the line of sight direction, L is a unit vector in the line of sight direction_mThe direction of an angle bisector between the V and the V is E and R_mIs the unit vector of the reflected light direction at any point on the fluid surface, and V is the unit vector of the sight line direction according to V and R_mThe included angle between N and E is twice of the included angle between N and E, and the use ofCalculating L in equations (1) to (3)_mDot product L with N_m·N；Andis the reflection of a mirror surface, and, andα is the index of specular reflection;is marked asIs marked asIs marked asBalanceAndis a specular reflection component;

by the height h of the pixel P_PInstead of R in the formulae (1) to (3)_mAnd V dot product R_mV, then, from (1) to (3):

$R=C_a^R+(2h_p^2-1)C_d^R+C_s^R{h}_P^{\mathrm{\α}}---\left(4\right)$

$G=C_a^G+(2h_p^2-1)C_d^G+C_s^G{h}_P^{\mathrm{\α}}---\left(5\right)$

$B=C_a^B+(2h_p^2-1)C_d^B+C_s^B{h}_P^{\mathrm{\α}}---\left(6\right)$

the illumination parameters of the fluid scene are effectively calculated by the following steps:

(1) calculating the ambient light component and the diffuse reflection component of the Phong illumination model, specifically:

(a) constructing a set L by using all pixels satisfying the formula (7) in the fluid video sample frame F;

D_p≤T_L(7)

D_pis the intensity of the pixel P, D_pThe calculation is as follows:

D_p＝0.299*R+0.587*G+0.114*B (8)

t in formula (7)_LIs an intensity threshold, which is calculated as T_L＝(D_max-D_min)*2/9+D_min,D_maxAnd D_minThe maximum value and the minimum value of the intensities of all pixels in the F are respectively;

(b) calculating ambient light and diffuse reflectance components of the fluid scene using the set L, specifically:

for any one of the pixels Q in L, it can be obtained according to equations (4) to (6):

$C_a^R+(2h_Q^2-1)C_d^R-I_Q^R=0---\left(9\right)$

$C_a^G+(2h_Q^2-1)C_d^G-I_Q^G=0---\left(10\right)$

$C_a^B+(2h_Q^2-1)C_d^B-I_Q^B=0---\left(11\right)$

wherein,andis the intensity component of Q in the three RGB channels;

calculating the height h of the fluid surface_QAnd use ofInformation of all pixels in L for the ambient light component in (9), (10) and (11)Andand a diffuse reflection componentAndsolving by adopting a linear fitting method;

(2) updating the fluid surface height information

The ambient light component of the R channel obtained in the step (1)And a diffuse reflection componentSubstituting into equation (9), recalculate the height h of each particle_QH is to be_QIs marked as h_R(ii) a The ambient light component of G channelAnd a diffuse reflection componentSubstituting into equation (10), recalculate the height h of each particle_QH is to be_QIs marked as h_G(ii) a Mixing the ambient light component of the B channelAnd a diffuse reflection componentSubstituting into equation (11), recalculate each particle height h_QH is to be_QIs marked as h_B(ii) a Finally, the height information of the particle is updated to h_n＝(h_R+h_G+h_B)/3；

(3) Specular reflection index and specular reflection component calculation

(a) Constructing a set H by using all pixels satisfying the formula (12) in the F;

D_p≥T_H(12)

T_His an intensity threshold, calculated as T_H＝(D_max-D_min)*8/9+D_min；

(b) Calculating specular reflection index and specular reflection component using H

For any two pixels P in H₁And P₂If P is₁Is of color R₁、G₁And B₁，P₂Is of color R₂、G₂And B₂，P₁Is assumed to be h₁，P₂Is assumed to be h₂(ii) a According to Phong illumination model:

$C_s^R{h}_1^{\mathrm{\α}}=R_1-C_a^R-C_d^R(2h_1^2-1)---\left(13\right)$

$C_s^R{h}_2^{\mathrm{\α}}=R_2-C_a^R-C_d^R(2h_2^2-1)---\left(14\right)$

$C_s^G{h}_1^{\mathrm{\α}}=G_1-C_a^G-C_d^G(2h_1^2-1)---\left(15\right)$

$C_s^G{h}_2^{\mathrm{\α}}=G_2-C_a^G-C_d^G(2h_2^2-1)---\left(16\right)$

$C_s^B{h}_1^{\mathrm{\α}}=B_1-C_a^B-C_d^B(2h_1^2-1)---\left(17\right)$

$C_s^B{h}_2^{\mathrm{\α}}=B_2-C_a^B-C_d^B(2h_2^2-1)---\left(18\right)$

the results α of the specular reflection index can be obtained from the R channel by equations (13) and (14)_R：

${\mathrm{\α}}_R=\frac{\lg (f_1/f_2)}{\lg (h_1/h_2)}---\left(19\right)$

Wherein

Calculating the specular reflection index of an R channel by using any pair of pixels in the H; get N_RFor the pixel, then use (13), (14) and (19) to get N_RCalculation results of R channelsAnd form a setN_RIs a natural number, N is more than or equal to 1000_RLess than or equal to 5000; clustering by adopting a k-means method to obtain the specular reflection index of the R channelSpecifically, for any pair S_RAny two ofAndif so:

$|{\mathrm{\&alpha;}}_R^U-{\mathrm{\&alpha;}}_R^V|<T_R^{\mathrm{\&alpha;}}---\left(20\right)$

thenAndare grouped into the same class;andis a setAre two different elements of (A), U and V are serial numbers, andand satisfies that U is more than or equal to 0 and less than or equal to N_R-1，0≤V≤N_R-1, while U ≠ V;a threshold value that is the difference between the specular reflection indices; finally, the mean value of all the specular reflection indexes in the class with the most collected samples is used as the average valuec represents clustering;

by the same token, the specular reflection indexes of the G channel and the B channel can be obtainedAnd

in calculating the specular reflection index of three channelsAndthen, the threshold value of the difference between the specular reflection indexes is a set value and is set to be 0.1;

finally, the specular reflection index is calculated as:

$\mathrm{\&alpha;}=({\mathrm{\&alpha;}}_R^C+{\mathrm{\&alpha;}}_G^C+{\mathrm{\&alpha;}}_B^C)/3---\left(21\right)$

for any pixel P in F, the specular reflection component is calculated as followsAnd

from equations (4), (5) and (6):

$C_s^R=(R-C_a^R-(2h_p^2-1\left)C_d^R\right)/h_P^{\mathrm{\&alpha;}}---\left(22\right)$

$C_s^G=(G-C_a^G-(2h_p^2-1\left)C_d^G\right)/h_P^{\mathrm{\&alpha;}}---\left(23\right)$

$C_s^B=(B-C_a^B-(2h_p^2-1\left)C_d^B\right)/h_P^{\mathrm{\&alpha;}}---\left(24\right)$

the average value of the R-channel specular reflection components calculated for all pixels is used asAs a result, similarly, a result of obtaining a G-channel specular reflection component can be obtainedAnd the result of specular component in the B channel

(4) Application in re-simulation

In the fluid simulation, for each frame in the fluid simulation, the height h of any fluid particle is obtained_rCalculating the color component R of the particle using (25) to (27)_r,G_rAnd B_r

$R_r=C_a^R+(2h_r^2-1)C_d^R+C_s^R{h}_r^{\mathrm{\&alpha;}}---\left(25\right)$

$G_r=C_a^G+(2h_r^2-1)C_d^G+C_s^G{h}_r^{\mathrm{\&alpha;}}---\left(26\right)$

$B_r=C_a^R+(2h_r^2-1)C_d^B+C_s^B{h}_r^{\mathrm{\&alpha;}}---\left(27\right)$

By utilizing an effective method of video fluid illumination calculation, a realistic illumination result can be obtained in real time in fluid weight simulation.

The method has the characteristics of simplicity and practicality, can effectively realize the illumination calculation of the video fluid, overcomes the problems of user intervention and high complexity in the conventional illumination parameter calculation research, and further demonstrates the effectiveness of the method. The method can realize the problem of relighting in the re-simulation of the fluid scene, and the researched illumination calculation method is suitable for various fluid types including advection, sea waves and the like.

Drawings

FIG. 1 is a graph of the results of fluid scene illumination calculations according to an embodiment of the present invention;

FIG. 2 is a graph of a fluid scene relighting result, obtained by testing in a re-simulation, according to an embodiment of the present invention;

fig. 3 is a graph of a fluid scene relighting result obtained in a re-simulation boundary test according to an embodiment of the present invention.

Detailed Description

Examples

The invention is further described below with reference to the accompanying drawings.

The embodiment adopts the fluid video (for example, the fluid video such as 54ab 110) in the DynTex dynamic texture library to perform fluid scene illumination calculation. The method is implemented under the Windows7 operating system on a PC, and the hardware configuration is 2.66GHz Intel core (TM)2Duo CPU and 4GB RAM.

Video fluid illumination calculation based on Phong model is characterized in that: using the RGB color model for video streaming, representing the color components of any pixel P in a sample frame F of streaming video as R, G and B, then according to the Phong model there are: a method for calculating illumination of a video fluid based on Phong model, characterized in that, an RGB color model is used for the video fluid, and the color components of any pixel P in a sample frame F of the fluid video are represented as R, G and B, then according to Phong model:

$R=C_a^R+k_d^R(L_m\&CenterDot;N)i_{m,d}^R+k_s^R{(R_m\&CenterDot;V)}^{\mathrm{\&alpha;}}{i}_{m,s}^R---\left(1\right)$

$G=C_a^G+k_d^G(L_m\&CenterDot;N)i_{m,d}^G+k_s^G{(R_m\&CenterDot;V)}^{\mathrm{\&alpha;}}{i}_{m,s}^G---\left(2\right)$

$B=C_a^B+k_d^B(L_m\&CenterDot;N)i_{m,d}^B+k_s^B{(R_m\&CenterDot;V)}^{\mathrm{\&alpha;}}{i}_{m,s}^B---\left(3\right)$

wherein,andis the component of ambient light in three channels of RGBAndis an ambient light component;

andis the rate of the diffuse reflectance and,andthe intensities of diffuse reflection in three channels of RGB are respectively;is marked asIs marked asIs marked asCombined balanceAndis a diffuse reflection component;

L_mis a unit normal vector from any point in the scene to the light source direction, N is a unit normal vector from any point on the fluid surface, V is a unit vector in the line of sight direction, L is a unit vector in the line of sight direction_mThe direction of an angle bisector between the V and the V is E and R_mIs the unit vector of the reflected light direction at any point on the fluid surface, and V is the unit vector of the sight line direction according to V and R_mThe included angle between N and E is twice of the included angle between N and E, and the use ofCalculating L in equations (1) to (3)_mDot product L with N_m·N；Andis the reflection of a mirror surface, and, andα is the index of specular reflection;is marked asIs marked asIs marked asBalanceAndis a specular reflection component;

by the height h of the pixel P_PInstead of R in the formulae (1) to (3)_mAnd V dot product R_mV, then, from (1) to (3):

$R=C_a^R+(2h_p^2-1)C_d^R+C_s^R{h}_P^{\mathrm{\&alpha;}}---\left(4\right)$

$G=C_a^G+(2h_p^2-1)C_d^G+C_s^G{h}_P^{\mathrm{\&alpha;}}---\left(5\right)$

$B=C_a^B+(2h_p^2-1)C_d^B+C_s^B{h}_P^{\mathrm{\&alpha;}}---\left(6\right)$

the illumination parameters of the fluid scene are effectively calculated by the following steps:

(1) calculating the ambient light component and the diffuse reflection component of the Phong illumination model, specifically:

(a) constructing a set L by using all pixels satisfying the formula (7) in the fluid video sample frame F;

D_p≤T_L(7)

D_pis the intensity of the pixel P, D_pThe calculation is as follows:

D_p＝0.299*R+0.587*G+0.114*B (8)

t in formula (7)_LIs an intensity threshold, which is calculated as T_L＝(D_max-D_min)*2/9+D_min,D_maxAnd D_minThe maximum value and the minimum value of the intensities of all pixels in the F are respectively;

(b) calculating ambient light and diffuse reflectance components of the fluid scene using the set L, specifically:

for any one of the pixels Q in L, it can be obtained according to equations (4) to (6):

$C_a^R+(2h_Q^2-1)C_d^R-I_Q^R=0---\left(9\right)$

$C_a^G+(2h_Q^2-1)C_d^G-I_Q^G=0---\left(10\right)$

$C_a^B+(2h_Q^2-1)C_d^B-I_Q^B=0---\left(11\right)$

wherein,andis the intensity component of Q in the three RGB channels;

calculating the height h of the fluid surface_QAnd using the information of all pixels in L for the ambient light components in (9), (10) and (11)Andand a diffuse reflection componentAndsolving by adopting a linear fitting method;

(2) updating the fluid surface height information

The ambient light component of the R channel obtained in the step (1)And a diffuse reflection componentSubstituting into equation (9), recalculate the height h of each particle_QH is to be_QIs marked as h_R(ii) a The ambient light component of G channelAnd a diffuse reflection componentSubstituting into equation (10), recalculate the height h of each particle_QH is to be_QIs marked as h_G(ii) a Mixing the ambient light component of the B channelAnd a diffuse reflection componentSubstituting into equation (11), recalculate each particle height h_QH is to be_QIs marked as h_B(ii) a Finally, the height information of the particle is updated to h_n＝(h_R+h_G+h_B)/3；

(3) Specular reflection index and specular reflection component calculation

(a) Constructing a set H by using all pixels satisfying the formula (12) in the F;

D_p≥T_H(12)

T_His an intensity threshold, calculated as T_H＝(D_max-D_min)*8/9+D_min；

(b) Calculating specular reflection index and specular reflection component using H

For any two pixels P in H₁And P₂If P is₁Is of color R₁、G₁And B₁，P₂Is of color R₂、G₂And B₂，P₁Is assumed to be h₁，P₂Is assumed to be h₂(ii) a According to Phong illumination model:

$C_s^R{h}_1^{\mathrm{\&alpha;}}=R_1-C_a^R-C_d^R(2h_1^2-1)---\left(13\right)$

$C_s^R{h}_2^{\mathrm{\&alpha;}}=R_2-C_a^R-C_d^R(2h_2^2-1)---\left(14\right)$

$C_s^G{h}_1^{\mathrm{\&alpha;}}=G_1-C_a^G-C_d^G(2h_1^2-1)---\left(15\right)$

$C_s^G{h}_2^{\mathrm{\&alpha;}}=G_2-C_a^G-C_d^G(2h_2^2-1)---\left(16\right)$

$C_s^B{h}_1^{\mathrm{\&alpha;}}=B_1-C_a^B-C_d^B(2h_1^2-1)---\left(17\right)$

$C_s^B{h}_2^{\mathrm{\&alpha;}}=B_2-C_a^B-C_d^B(2h_2^2-1)---\left(18\right)$

the results α of the specular reflection index can be obtained from the R channel by equations (13) and (14)_R：

${\mathrm{\&alpha;}}_R=\frac{\lg (f_1/f_2)}{\lg (h_1/h_2)}---\left(19\right)$

Wherein

Calculating the specular reflection index of an R channel by using any pair of pixels in the H; get N_RFor the pixel, then use (13), (14) and (19) to get N_RCalculation results of R channelsAnd form a setN_RIs a natural number, N is more than or equal to 1000_RLess than or equal to 5000; clustering by adopting a k-means method to obtain the specular reflection index of the R channelSpecifically, for any pair S_RAny two ofAndif so:

$|{\mathrm{\&alpha;}}_R^U-{\mathrm{\&alpha;}}_R^V|<T_R^{\mathrm{\&alpha;}}---\left(20\right)$

thenAndare grouped into the same class;andis a setU and V are serial numbers, and satisfy that U is greater than or equal to 0 and is less than or equal to N_R-1，0≤V≤N_R-1, while U ≠ V;a threshold value that is the difference between the specular reflection indices; finally, all classes with the most samples are gatheredMean value of specular reflection index asc represents clustering;

by the same token, the specular reflection indexes of the G channel and the B channel can be obtainedAnd

in calculating the specular reflection index of three channelsAndthen, the threshold value of the difference between the specular reflection indexes is a set value and is set to be 0.1;

finally, the specular reflection index is calculated as:

$\mathrm{\&alpha;}=({\mathrm{\&alpha;}}_R^C+{\mathrm{\&alpha;}}_G^C+{\mathrm{\&alpha;}}_B^C)/3---\left(21\right)$

for any pixel P in F, the specular reflection component is calculated as followsAnd

from equations (4), (5) and (6):

$C_s^R=(R-C_a^R-(2h_p^2-1\left)C_d^R\right)/h_P^{\mathrm{\&alpha;}}---\left(22\right)$

$C_s^G=(G-C_a^G-(2h_p^2-1\left)C_d^G\right)/h_P^{\mathrm{\&alpha;}}---\left(23\right)$

$C_s^B=(B-C_a^B-(2h_p^2-1\left)C_d^B\right)/h_P^{\mathrm{\&alpha;}}---\left(24\right)$

the average value of the R-channel specular reflection components calculated for all pixels is used asAs a result, similarly, a result of obtaining a G-channel specular reflection component can be obtainedAnd the result of specular component in the B channel

(4) Application in re-simulation

In the fluid weight simulation, the 2D movement speed of the first frame of the video is calculated by using the existing method, and then the Lattice Boltzmann Methods (LBM) are initialized, and in the deduction process of the fluid weight simulation, for each frameCalculating the height h of the fluid particles in one frame_rCalculating the color component R of the particle using (25) to (27)_r,G_rAnd B_r

$R_r=C_a^R+(2h_r^2-1)C_d^R+C_s^R{h}_r^{\mathrm{\&alpha;}}---\left(25\right)$

$G_r=C_a^G+(2h_r^2-1)C_d^G+C_s^G{h}_r^{\mathrm{\&alpha;}}---\left(26\right)$

$B_r=C_a^R+(2h_r^2-1)C_d^B+C_s^B{h}_r^{\mathrm{\&alpha;}}---\left(27\right)$

FIG. 1 is the result of illumination calculation, where the first column is the sample frame of the original video (taking the first frame as the sample frame); the second column is the result of illumination calculation in the present invention, and the relighting intensity of the fluid surface is obtained using the calculated ambient light component, diffuse reflection component, specular reflection component, and specular reflection index. It can be seen from the illustration of fig. 1 that the video fluid illumination calculation method of the present invention is very efficient, with the recalculated illumination very close to the appearance of the sample frame.

Comparing the method of the invention with existing methods: in order to verify the effectiveness of the video fluid illumination calculation method in the invention, the method is compared with the illumination parameter calculation method of Thiago research. The errors of the illumination parameter calculation of the invention and the Thiago method are respectively calculated by adopting the following methods:

$E_a=\left(0.299\underset{i=0}{\overset{N_p-1}{\&Sigma;}}\right|R_i-R_i^r|+0.587\underset{i=0}{\overset{N_p-1}{\&Sigma;}}|G_i-G_i^r|+0.114\underset{i=0}{\overset{N_p-1}{\&Sigma;}}|B_i-B_i^r\left|\right)/N_p---\left(28\right)$

$E_r=\frac{0.299\underset{i=0}{\overset{N_p-1}{\&Sigma;}}|R_i-R_i^r|+0.587\underset{i=0}{\overset{N_p-1}{\&Sigma;}}|G_i-G_i^r|+0.114\underset{i=0}{\overset{N_p-1}{\&Sigma;}}|B_i-B_i^r|}{0.299\underset{i=0}{\overset{N_p-1}{\&Sigma;}}{R}_i+0.587\underset{i=0}{\overset{N_p-1}{\&Sigma;}}{G}_i+0.114\underset{i=0}{\overset{N_p-1}{\&Sigma;}}{B}_i}---\left(29\right)$

wherein N is_pIs the number of pixels in the scene, R_i,G_iAnd B_iIs the color component of the ith pixel in the sample frame in the RGB color space,andis the illumination result recalculated according to the illumination model, i is a non-negative integer and the value range is that i is more than or equal to 0 and less than or equal to N_p-1。

TABLE 1 error comparison of illumination calculations for two different methods

Table 1 shows the results of the comparative error, where the first column in the results is the name of the fluid sample; the second and third columns are the Thiago research method and the absolute error E of the invention, respectively_a(ii) a The fourth and fifth columns are the Thiago research method and the relative error E of the present invention, respectively_r. Compared with the existing method, the error result of the method has the characteristic of obviously smaller error, no matter the absolute error E_aOr relative error E_rThe effectiveness of the illumination calculation method of the present invention is clearly demonstrated.

Verifying relighting in the fluid weight simulation: the method for calculating the illumination parameters provided by the invention is applied to the application of fluid weight simulation.

The 2D motion velocity of the first frame of the video is calculated by using the existing method, then the Lattice Boltzmann Methods (LBM) model is initialized, and the simulation fluid is relighted by using the method according to the height of the fluid particles of each frame in the deduction process of the fluid re-simulation, wherein fig. 2 shows the result of the relighting. As can be seen from the relighting effect in the figure, the illumination calculation method is very effective, can be applied to the fluid re-simulation process, and is convenient and practical.

The application of the illumination calculation method in the re-simulation relighting is as follows: the method is applied to the boundary test process of the fluid weight simulation, and a satisfactory illumination result is obtained. The effectiveness of the present invention can be seen in fig. 3.

Claims (1)

1. A method for calculating illumination of a video fluid based on Phong model, characterized in that, an RGB color model is used for the video fluid, and the color components of any pixel P in a sample frame F of the fluid video are represented as R, G and B, then according to Phong model:

$R=C_a^R+k_d^R(L_m\&CenterDot;N)i_{m,d}^R+k_s^R{(R_m\&CenterDot;V)}^{\mathrm{\&alpha;}}{i}_{m,s}^R---\left(1\right)$

$G=C_a^G+k_d^G(L_m\&CenterDot;N)i_{m,d}^G+k_s^G{(R_m\&CenterDot;V)}^{\mathrm{\&alpha;}}{i}_{m,s}^G---\left(2\right)$

$B=C_a^B+k_d^B(L_m\&CenterDot;N)i_{m,d}^B+k_s^B{(R_m\&CenterDot;V)}^{\mathrm{\&alpha;}}{i}_{m,s}^B---\left(3\right)$

wherein,andis the component of ambient light in three channels of RGBAndis an ambient light component;

andis the rate of the diffuse reflectance and,andthe intensities of diffuse reflection in three channels of RGB are respectively;is marked as Is marked as Is marked asCombined balanceAndis a diffuse reflection component;

L_mis a unit normal vector from any point in the scene to the light source direction, N is a unit normal vector of any point on the fluid surface, and V is a sight lineUnit vector of direction, L_mThe direction of an angle bisector between the V and the V is E and R_mIs the unit vector of the reflected light direction at any point on the fluid surface, and V is the unit vector of the sight line direction according to V and R_mThe included angle between N and E is twice of the included angle between N and E, and the use ofCalculating L in equations (1) to (3)_mDot product L with N_m·N；Andis the reflection of a mirror surface, and, andα is the index of specular reflection;is marked as Is marked as Is marked asBalanceAndis a specular reflection component;

by the height h of the pixel P_PInstead of R in the formulae (1) to (3)_mAnd V dot product R_mV, then, from (1) to (3):

$R=C_a^R+(2h_p^2-1)C_d^R+C_s^R{h}_P^{\mathrm{\&alpha;}}---\left(4\right)$

$G=C_a^G+(2h_p^2-1)C_d^G+C_s^G{h}_P^{\mathrm{\&alpha;}}---\left(5\right)$

$B=C_a^B+(2h_p^2-1)C_d^B+C_s^B{h}_P^{\mathrm{\&alpha;}}---\left(6\right)$

the illumination parameters of the fluid scene are effectively calculated by the following steps:

(1) calculating the ambient light component and the diffuse reflection component of the Phong illumination model, specifically:

(a) constructing a set L by using all pixels satisfying the formula (7) in the fluid video sample frame F;

D_p≤T_L(7)

D_pis the intensity of the pixel P, D_pThe calculation is as follows:

D_p＝0.299*R+0.587*G+0.114*B (8)

t in formula (7)_LIs an intensity threshold, which is calculated as T_L＝(D_max-D_min)*2/9+D_min,D_maxAnd D_minThe maximum value and the minimum value of the intensities of all pixels in the F are respectively;

(b) calculating ambient light and diffuse reflectance components of the fluid scene using the set L, specifically:

for any one of the pixels Q in L, it can be obtained according to equations (4) to (6):

$C_a^R+(2h_Q^2-1)C_d^R-I_Q^R=0---\left(9\right)$

$C_a^G+(2h_Q^2-1)C_d^G-I_Q^G=0---\left(10\right)$

$C_a^B+(2h_Q^2-1)C_d^B-I_Q^B=0---\left(11\right)$

wherein,andis the intensity component of Q in the three RGB channels;

calculating the height h of the fluid surface_QAnd using the information of all pixels in L for the ambient light components in (9), (10) and (11)Andand a diffuse reflection componentAndsolving by adopting a linear fitting method;

(2) updating the fluid surface height information

The ambient light component of the R channel obtained in the step (1)And a diffuse reflection componentSubstituting into equation (9), recalculate the height h of each particle_QH is to be_QIs marked as h_R(ii) a The ambient light component of G channelAnd a diffuse reflection componentSubstituting into equation (10), recalculate the height h of each particle_QH is to be_QIs marked as h_G(ii) a Mixing the ambient light component of the B channelAnd a diffuse reflection componentSubstituting into equation (11), recalculate each particle height h_QH is to be_QIs marked as h_B(ii) a Finally, the height information of the particle is updated to h_n＝(h_R+h_G+h_B)/3；

(3) Specular reflection index and specular reflection component calculation

(a) Constructing a set H by using all pixels satisfying the formula (12) in the F;

D_p≥T_H(12)

T_His an intensity threshold, calculated as T_H＝(D_max-D_min)*8/9+D_min；

(b) Calculating specular reflection index and specular reflection component using H

For any two pixels P in H₁And P₂If P is₁Is of color R₁、G₁And B₁，P₂Is of color R₂、G₂And B₂，P₁Is assumed to be h₁，P₂Is assumed to be h₂(ii) a According to Phong illumination model:

$C_s^R{h}_1^{\mathrm{\&alpha;}}=R_1-C_a^R-C_d^R(2h_1^2-1)---\left(13\right)$

$C_s^R{h}_2^{\mathrm{\&alpha;}}=R_2-C_a^R-C_d^R(2h_2^2-1)---\left(14\right)$

$C_s^G{h}_1^{\mathrm{\&alpha;}}=G_1-C_a^G-C_d^G(2h_1^2-1)---\left(15\right)$

$C_s^G{h}_2^{\mathrm{\&alpha;}}=G_2-C_a^G-C_d^G(2h_2^2-1)---\left(16\right)$

$C_s^B{h}_1^{\mathrm{\&alpha;}}=B_1-C_a^B-C_d^B(2h_1^2-1)---\left(17\right)$

$C_s^B{h}_2^{\mathrm{\&alpha;}}=B_2-C_a^B-C_d^B(2h_2^2-1)---\left(18\right)$

the results α of the specular reflection index can be obtained from the R channel by equations (13) and (14)_R：

${\mathrm{\&alpha;}}_R=\frac{\lg (f_1/f_2)}{\lg (h_1/h_2)}---\left(19\right)$

Wherein

Calculating the specular reflection index of an R channel by using any pair of pixels in the H; get N_RFor the pixel, then use (13), (14) and (C)19) To obtain N_RCalculation results of R channelsAnd form a setN_RIs a natural number, N is more than or equal to 1000_RLess than or equal to 5000; clustering by adopting a k-means method to obtain the specular reflection index of the R channelSpecifically, for any pair S_RAny two ofAndif so:

$|{\mathrm{\&alpha;}}_R^U-{\mathrm{\&alpha;}}_R^V|<T_R^{\mathrm{\&alpha;}}---\left(20\right)$

thenAndare grouped into the same class;andis a setU and V are serial numbers, and satisfy that U is greater than or equal to 0 and is less than or equal to N_R-1，0≤V≤N_R-1, while U ≠ V;a threshold value that is the difference between the specular reflection indices; finally, the mean value of all the specular reflection indexes in the class with the most collected samples is used as the average valuec represents clustering;

by the same token, the specular reflection indexes of the G channel and the B channel can be obtainedAnd

in calculating the specular reflection index of three channelsAndthen, the threshold value of the difference between the specular reflection indexes is a set value and is set to be 0.1;

finally, the specular reflection index is calculated as:

$\mathrm{\&alpha;}=({\mathrm{\&alpha;}}_R^C+{\mathrm{\&alpha;}}_G^C+{\mathrm{\&alpha;}}_B^C)/3---\left(21\right)$

for any pixel P in F, the specular reflection component is calculated as followsAnd

from equations (4), (5) and (6):

$C_s^R=(R-C_a^R-(2h_p^2-1\left)C_d^R\right)/h_P^{\mathrm{\&alpha;}}---\left(22\right)$

$C_s^G=(G-C_a^G-(2h_p^2-1\left)C_d^G\right)/h_P^{\mathrm{\&alpha;}}---\left(23\right)$

$C_s^B=(B-C_a^B-(2h_p^2-1\left)C_d^B\right)/h_P^{\mathrm{\&alpha;}}---\left(24\right)$

the average value of the R-channel specular reflection components calculated for all pixels is used asAs a result, similarly, a result of obtaining a G-channel specular reflection component can be obtainedAnd the result of specular component in the B channel