Research on Optimization Strategy of Stage Presentation Effect of Dance Works Based on Audience’s Psychological Perception

1)

Retinex Theory

Retinex theory is a theory that explains color perception in the human visual system.Retinex theory explains why the color of an object can be seen to remain relatively stable despite changes in lighting conditions or viewing angle. It also explains why it is possible to distinguish between colors under different lighting conditions, even though these colors may be physically different.

When incident light strikes a reflecting object, it is reflected by the object and forms reflected light, which then enters our eyes and forms the image we see. This process can be accurately described by the following mathematical formula: (1)S(x,y)=R(x,y)*L(x,y)$$S(x,y) = R(x,y)*L(x,y)$$

According to equation (1), it can be understood that the image S of the environment received by the human eye, consists of the product of the light component L and the reflection component R, and S represents the original, unprocessed image, in which all kinds of information are fused. R, which is the reflection component.The Retinex algorithm process is as follows: first the original image is logarithmically operated, which can be obtained according to the light reflection model equation: (2)log[S(x,y)]=log[R(x,y)*L(x,y)]$$\log [S(x,y)] = \log [R(x,y)*L(x,y)]$$

Transforming Eq. (2) and extracting the reflective component yields: (3)log[R(x,y)]=log[S(x,y)]−log[L(x,y)]$$\log [R(x,y)] = \log [S(x,y)] - \log [L(x,y)]$$

Simultaneous exponential operations on both sides of Eq. (3) give the reflected component: (4)R(x,y)=exp{log[S(x,y)]−log[L(x,y)]}$$R(x,y) = \exp \{ \log [S(x,y)] - \log [L(x,y)]\}$$ 2)

Image enhancement algorithm based on Retinex theory

In Eq. (11): i is an index value that corresponds to the red, green, and blue (R, G, and B) channels of the original image. R_MSR(x, y) represents the result of the image processed by the MSR algorithm, while R_MSRCR(x, y) represents the final enhancement effect obtained for the three channel components after the introduction of the color recovery factor. C_i(x, y), on the other hand, represents the matrix of color recovery factors for the different channel components. The specific value of C_i(x, y) can be calculated and derived by a specific mathematical formula as shown in equation (12): (12)Ci(x,y)=αlog[βSi(x,y)∑i=13Si(x,y)]$${C_i}(x,y) = \alpha \log \left[ {\frac{{\beta {S_i}(x,y)}}{{\sum\limits_{i = 1}^3 {{S_i}} (x,y)}}} \right]$$

Where: α and β are the two key gain coefficients, which are usually set to 46 and 125, these two specific values being the optimal solutions validated by many experiments. S_i(x, y), on the other hand, represents the three different color component channels in the original image.

The MSRCR algorithm multiplies the three MSR-processed channels with the color recovery coefficient matrix and then combines the three channel components to obtain the final result. The algorithm not only preserves the detailed information in the original image, but also reaches a new level of color realism and visual effect.

Gamma correction employs a power function transformation to make adjustments to an image [24-25]. This is done by performing a power operation on each pixel value and controlling the brightness and contrast of the image by adjusting the size of the power index. Usually, a Gamma value less than 1 will make the image brighter, while a Gamma value greater than 1 will make the image darker. Here is the specific formula for Gamma correction: (13)F(x,y)=255×(f(x,y)255)γ$$F(x,y) = 255 \times {\left( {\frac{{f(x,y)}}{{255}}} \right)^\gamma }$$

Where f(x, y) represents the input image and F(x, y) is the output image after Gamma correction. In this process, γ is a key exponential parameter that determines how well the image is corrected.

Image evaluation criteria are used to evaluate and compare image processing algorithms, image quality, and image recognition systems. It is mainly divided into subjective evaluation and objective evaluation.

Subjective evaluation criteria mainly rely on the observer’s or evaluator’s direct feelings and subjective judgment of image quality. The research goal in the field of image quality evaluation is to develop objective evaluation algorithms based on mathematical models. This section focuses on the objective evaluation methods. 1)

Peak Signal-to-Noise Ratio

Peak signal-to-noise ratio (PSNR) is an objective evaluation standard for measuring the quality of image reconstruction. It measures the image quality by calculating the logarithm of the mean square error (MSE) between the original image and the processed image.The higher the PSNR value, the better the quality of the processed image. Equation (14) gives the definition of PSNR: (14)MSE=1mn∑i=0m−1∑j=0n−1[I(i,j)−K(i,j)]2$$MSE = \frac{1}{{mn}}\mathop \sum \nolimits_{i = 0}^{m - 1} \mathop \sum \nolimits_{j = 0}^{n - 1} {\left[ {I(i,j) - K(i,j)} \right]^2}$$ (15)PSNR=10×log10(MAX2MSE)$$PSNR = 10 \times {\log _{10}}\left( {\frac{{MA{X^2}}}{{MSE}}} \right)$$ 2)

Structural similarity

Structural similarity (SSIM) is an image quality evaluation criterion based on structural information. It takes into account the brightness, contrast and structural information of the image, and evaluates the image quality by calculating the similarity between the original image and the processed image in these aspects.The closer the SSIM value is to 1, it means the more similar the processed image is to the original image.The formula for calculating SSIM is as follows: (16)SSIM(x,y)=(2μxμy+c1)(σxy+c2)(μx2+μy2+c1)(σx2+σy2+c2)$$SSIM(x,y) = \frac{{\left( {2{\mu _x}{\mu _y} + {c_1}} \right)\left( {{\sigma _{xy}} + {c_2}} \right)}}{{\left( {\mu _x^2 + \mu _y^2 + {c_1}} \right)\left( {\sigma _x^2 + \sigma _y^2 + {c_2}} \right)}}$$

Where: x and y represent the original reference image and enhanced image respectively. σ and μ represent the standard deviation and mean, respectively. c₁, c₂ are constants and generally the two constants are set as shown in equation (17): (17)c1=(K1*L)2,c2=(K2*L)2$${c_1} = {\left( {{K_1}*L} \right)^2},{c_2} = {\left( {{K_2}*L} \right)^2}$$

The network consists of a decomposition module, a multi-scale illumination enhancement module and a reflection component denoising module, with the following three main contributions. 1)

First, a decomposition module is designed and proposed which decomposes images under low and normal illumination based on Retinex theory. Unlike other networks that estimate both components simultaneously, this module first estimates the illumination component Fig. L, and then obtains the reflection component Fig. R in the manner of R = S/L. A loss function with good constraints is designed to stabilize the decomposition process.

This chapter describes the implementation process of the Retinex-Net enhanced network based on multi-scale feature conditioning, and details the framework and functions of the three main modules of the network. 1)

Decomposition Module

By Retinex theory, the input image S is decomposed and obtained the illumination component L and reflection component R, whose expressions are shown in equation (18): (18)S=R⊙L$$S = R \odot L$$

where S denotes the input image, L denotes the illumination component, which is related to the lighting conditions, and R denotes the reflection component, which reflects the inherent intrinsic properties of different objects.

In order to further improve the network generalization capability, a decomposition module (DCM) is proposed using the U-Net network as a framework. Compared to estimating both components simultaneously, this module takes the approach of first estimating the illumination component L and then deriving the reflectance component in R = S/L. The framework structure of the network as well as elements such as the loss function are designed.

The overall loss function of the DCM is shown in equation (19): (19)L=αrsLrs+αisLis+Lre+αilsLils$$L = {\alpha _{rs}}{L_{rs}} + {\alpha _{is}}{L_{is}} + {L_{re}} + {\alpha _{ils}}{L_{ils}}$$

In Eq. (19), L_rs represents the reflectance map similarity loss, L_is represents the illumination smoothing loss, L_re represents the reconstruction loss, and L_ils represents the approximate illumination loss. α_rs, α_is and α_ils are the weighting coefficients corresponding to L_rs, L_is and L_ils, respectively. According to the experiments, these weighting coefficients are 0.05, 0.2, and 0.1, respectively.

The reflectance map similarity loss L_rs and approximate illumination loss L_ils are shown in Eqs. (20) and (21): (20)Lre=‖Rl−Rh‖2$${L_{re}} = {\left\| {{R_l} - {R_h}} \right\|_2}$$ (21)Lils=‖Ll−Lh‖2$${L_{ils}} = {\left\| {{L_l} - {L_h}} \right\|_2}$$

Where, R_l denotes the reflection component of the low light image, R_h denotes the reflection component of the normal light image, L_l denotes the light component of the low light image, and L_h denotes the light component of the normal image [26].

In order to simultaneously ensure the local smoothness of the light component and the clarity of the image structure, a light smoothing loss function is designed for the light component L_is. This loss function is designed to maximize the preservation of details in the edge portion. The definition of this loss function is shown in equation (22): (22)Lis=‖∇Llmax(∇Sl,ε)‖1+‖∇Lhmax(∇Sh,ε)‖1$${L_{is}} = {\left\| {\frac{{\nabla {L_l}}}{{\max \left( {\nabla {S_l},\varepsilon } \right)}}} \right\|_1} + {\left\| {\frac{{\nabla {L_h}}}{{\max \left( {\nabla {S_h},\varepsilon } \right)}}} \right\|_1}$$

where S and L denote the input image and the illumination component maps, and ε is a very small constant avoiding a denominator of zero. Typically, the edge portion of S has a large gradient ∇S and therefore the edge region will also exhibit a large gradient ∇L in the decomposed L.

The reconstruction loss is designed to represent the similarity between the reconstructed image and the original image. The definition of reconstruction loss is shown in equation (23): (23)Lre=‖Sl−RlIl‖1+‖Sh−RhIh‖1$${L_{re}} = {\left\| {{S_l} - {R_l}{I_l}} \right\|_1} + {\left\| {{S_h} - {R_h}{I_h}} \right\|_1}$$

Where S_l is the input low illumination image and S_h is the corresponding normal light image 2)

Multiscale Illumination Enhancement Module

This subsection proposes a multi-scale illumination enhancement module (MIEM). This module enhances the brightness of low-light images while avoiding overexposure or underexposure problems.

where L_spc and L_SSIM denote the spatial consistency loss and structural similarity loss, respectively.

In order to ensure the overall structural feature integrity of the image, the spatial consistency loss function is chosen in this chapter to constrain the spatial consistency before and after enhancement, as shown in Eq. (25): (25)Lspc=∑i=1K∑j∈Ω(i)(|Xi−Xj|−|Yi−Yj|)2$${L_{spc}} = \sum\limits_{i = 1}^K {\sum\limits_{j \in \Omega (i)} {{{\left( {\left| {{X_i} - {X_j}} \right| - \left| {{Y_i} - {Y_j}} \right|} \right)}^2}} }$$

where K is the number of selected local regions in the input image, Ω(i) is the four regions centered on i at the top, bottom, left and right, and X and Y are the average intensity values of a region in the input and output images, respectively.

To avoid image blurring, the structural similarity loss L_SSIM is chosen in this chapter to enhance the protection of image details, whose expression is shown in Equation (26): (26)LSSIM=(2μxμy+C1)(2σxy+C2)(μx2+μy2+C1)(σx2+σy2+C2)$${L_{SSIM}} = \frac{{\left( {2{\mu _x}{\mu _y} + {C_1}} \right)\left( {2{\sigma _{xy}} + {C_2}} \right)}}{{\left( {\mu _x^2 + \mu _y^2 + {C_1}} \right)\left( {\sigma _x^2 + {\sigma _y}^2 + {C_2}} \right)}}$$

Where, μ_x and μ_y are pixel mean, σx2$$\sigma _x^2$$ and σy2$$\sigma _y^2$$ are variance, σ_xy is covariance, C₁ and C₂ are constants. 3)

Reflected component denoising module

This subsection proposes a reflective component denoising module (RCM) that eliminates noise while preserving as much as possible the structure and texture information of the original image.

A multi-scale feature extraction module, MFB, is used in this chapter.The dual attention module, DAB, consists of a feature attention channel and a pixel attention channel, and is able to establish a link between each pixel and feature in the image, and adaptively refine the feature maps of each layer.

The reflection denoising module aims at preserving the image structure, suppressing noise and artifacts, and obtaining a satisfactory visual effect. Therefore, the overall loss function of this module is shown in equation (27): (27)L=Lspc+γtvLtv+‖||∇Rout|−|∇Rint‖22$$L = {L_{spc}} + {\gamma _{tv}}{L_{tv}} + \left\| {\left| {\left| {\nabla {R_{out}}} \right| - } \right|\nabla {R_{\operatorname{int} }}} \right\|_2^2$$

where R_out denotes the reflected component of the enhanced output, ‖⋅‖2$${\left\| \cdot \right\|_2}$$ denotes the L2 paradigm, L_spc is the spatial coherence loss, and L_N is the global variational loss. γ_N is the global variational loss coefficient, which is taken as 10e⁻⁴ according to the experiment.

For the problem of the variability of neighboring pixel values in the image, this chapter adds the global variational loss to the overall loss function of the denoising module, which constrains the gradient changes in the horizontal and vertical directions of the image to make the image smoother. The global variational loss L_tv is defined as shown in equation (28): (28)Ltv=∫ux2+uy2dxdy$${L_{tv}} = \int {\sqrt {u_x^2 + u_y^2} } dxdy$$

where u_x and u_y are the gradients of the image in the horizontal and vertical directions, respectively.