The theory of global illumination and computer programs based on it allows calculating the light field accurately in an arbitrary three-dimensional lighting scene. However, the output of the visualization of the light field spatial-angular distribution to the display screen in the form of an image is inevitably associated with scaling the luminance and color of the image pixels to the computer display dynamic range. To date, a color appearance model was created in colorimetry. This model allows recalculating the image pixels' color for viewing conditions other than the original ones preserving the image's visual perception. This model is approved by the CIE (International Commission on Illumination) as a standard model under the name CIECAM02. In this paper, the CIECAM02 algorithm model is implemented, and a study of designing a lighting system for lighting a theater stage to create an atmosphere of sunset is carried out. Modeling the lighting system is performed in the DIALux evo program, which is the de facto standard of design in lighting engineering. The correspondence of the visualization of the stage lighting to the feeling of sunset is analyzed based on expert assessments. The research allows us to recommend the inclusion of the CIECAM02 model in the algorithms for visualizing the image of three-dimensional lighting scenes.
The theory of global illumination allows us to strictly calculate the light field in the lighting scene, considering all the effects in the ray photometric approximation. The calculation of the light field allows generating a realistic synthetic image of the scene from the camera at any point of the scene. However, when displaying this image on the monitor screen, a transition from the real luminance of the light field of a three-dimensional scene to the dynamic range of screen luminance is inevitable. It changes the luminance and color adaptation of the computer user's eye, which inevitably makes the perception of the resulting synthetic image different from the perception of the actual scene. From strength, speech can go only about a photorealistic image.
Currently, the mathematical model CAT/CAM (Chroma adaptation transform/ Color appearance
model) has been developed in colorimetry, which allows describing the perception of an image by the
eye based on stimuli (measurement and description of color) and the synthesis of stimuli based on
perceptions (color reproduction). Thus, the laws of light-color similarity of images are determined,
which preserve its perception when the conditions of luminance and color adaptation change. In 2002,
the CIE (International Commission on Illumination, by the abbreviation of the French name
Commission Internationale de l'éclairage) adopted the CIECAM02 standard [
2021 Copyright for this paper by its authors.
This article aims to implement the CIECAM02 model and test it for stage lighting to create a realistic sunset atmosphere on the stage. Based on expert assessments, the requirements for lighting that creates an atmosphere of sunset are determined. Then, in the standard program for designing lighting installations (LI), a corresponding model is created, based on modeling results in which a synthetic image of this LI is generated. Next, the resulting image is converted according to the CIECAM02 model to a realistic one. By the method of the expert assessments, one determines the discrepancy between the image and the sunset, and appropriate changes are introduced into the LI model. Consequently, we get a model of the LI, which implements the sunset impression on the stage in the lighting.
Thanks to the works of Newton [
The CIECAM02 color appearance model allows determining color perception when observing
conditions change. The color sensation in CIECAM02 is defined in terms of lightness, saturation, and
color tone [
Input data for the CIECAM02 include [
The surround relative luminance is generally taken to be average for reflection prints, dim for CRT displays or televisions, and dark for projected transparencies under the assumption that these media are being viewed in their typical environments. Discounting-the-illuminant is generally assumed to occur for object color stimuli such as prints and not to occur for emissive displays.
Chromatic adaptation is the human visual system’s ability to adjust to illumination changes to preserve the appearance of object colors. It is responsible for the regular appearance of object colors despite the wide variation of light reflected from an object and observed by our eyes. The chromatic adaptation transform (CAT) system emulates this critical aspect of color perception in color appearance models (CAM).
All viable modern chromatic adaptation models can trace their roots, both conceptually and
mathematically, to the hypotheses of Johannes von Kries [
The color-sensitive receptors of the human retina are cones of three types are the most properly referred to as L, M, and S cones. These names refer to the long-wavelength, middle-wavelength, and short-wavelength sensitive cones, respectively. Sometimes the cones are denoted with other symbols such as RGB suggestive of red, green, and blue sensitivities. As seen from their spectral responsivities, this concept is erroneous, and the LMS names are more appropriately descriptive.
Under the RGB color model, we will, as usual, denote an additive color model in which the three main colors (red, green, and blue) of light are combined to reproduce the real color. The RGB model is additive, where colors are obtained by adding to the black color. The RGB color model is device dependent. All pixels in the image file are recorded in RGB format for a standard computer graphics monitor sRGB. Accordingly, in working with images on a computer, the source data will be the colors in the RGB system.
All colors in the CIECAM02 system change in the range [0, 100]. However, since we will implement
this model in the framework of MATLAB, where the color in floating-point format changes in the range
[
Since according to the von Kries hypothesis, the linear adaptation model applies to LMS-cones. The first step of the model is the transition from the RGB values in the image to the values in the LMS system. In the CIECAM02 system, the transition to LMS values is given by the color values in CIE XYZ: L X M MCAT 02 Y , S Z
0.7328 0.4296 0.1624 MCAT 02 0.7036 1.6975 where the transition to XYZ was previously made in the image using the MATLAB rgb2xyz function, and similarly for the white point. Here and further, the column vector will be indicated by an arrow “→”, the rows by a reverse arrow “←”, and the matrices by a double arrow “↔” above the symbol.
Then, following the von Kries hypothesis, the adapted three-stimulus LcMcSc responses representing consistent color stimuli in the reference viewing conditions (equal-energy illuminator) are determined by the expressions:
D D D Lc (1 D) L, Mc (1 D) M , Sc (1 D) S ,
LW MW SW where the coefficient of the adaptation level D is calculated according to the equations:
D F 1 0.28e(LA 42) 92 , F = 0.9 as the dim surround for computer display.
After adaptation, by going to CIE XYZ and back, the cone responses are converted to the Hunt– Pointer–Estévez space that more closely represent cone responsivities: L X c Lc 0.38971 0.68898 0.07868 M MH Yc MH MC1AT 02 Mc , MH 0.22981 1.18340 0.04641 . (4) S Zc Sc 0.00000 0.00000 1.00000
The post-adaptation cone responses (for both the sample and the white) are then calculated using equations:
4(FL L)0.42 4(FL L)0.42 4(FL L)0.42 La 27.13 (FL L)0.42 0.001, Ma 27.13 (FL L)0.42 0.001, Sa 27.13 (FL L)0.42 0.001, (5) where FL k4LA 0.1(1 k4 )2 5LA 1/3 is the luminance-level adaptation factor, k (5LA 1)1 .
The obtained values uniquely determine the parameters of the color perception of JCH. However, from the point of view of the task set in the work, their calculation is not of interest. We simulate the light field in LI in the DIALux evo program, get a synthetic image and the maximum luminance value in the Lmax scene. Let us take the average luminance of the image for the luminance of the adaptation LA. Then using (1)-(5), we can get the visual perception of the image. Nevertheless, as mentioned earlier, we will display the image on the computer display, the average luminance of LAD, and the white point is XWD, YWD, ZWD. Using the same ratios (1)-(5), but in the reverse sequence, we can recalculate the pixel colors of the image Ra, Ga, Ba, which preserved the parameters of the visual perception of the lighting system JCH and adapted for output to the computer display. (1) (2) (3)
The initial data for the task is the layout of the premises of the Vladimir Vysotsky Theater. The DIALux evo software was chosen to implement this model, which includes sufficient functionality for calculating the necessary parameters, visualization, and a large set of lighting devices. Figure 1 shows a visualization of the three-dimensional view of the resulting model. The room's dimensions were calculated based on available information about the number of seats in the hall: eight rows of seats on the first floor of the room and three rows of seats on the balcony.
For illuminating the foreground of the stage and the actors, lighting devices were built on the hall's front part – the balcony. Artemide PICTO LED HIGH FLUX 4000K SPOT ND/AD NERO lighting devices were chosen as spotlights. Lighting fixtures were added to the stage side for the side lighting of the actors and the scenery. The searchlights of the Siemens STAGE PROJECTOR WITH ARM company were chosen as lighting devices. Lighting fixtures were added to the upper part of the stage to illuminate the background. The searchlights of the Siemens MEGAFOCUS company were chosen as lighting devices. All the floodlights added to the model have lamps with a lighting temperature of 3000-4000K. This choice is because the sunset atmosphere assumes low illumination in warm shades.
The sunset atmosphere was created using references taken from the Internet for the request sunset, two of which are shown in Figure 2. Sunset is not a one-time phenomenon. It takes a considerable period, changing from a bright orange color through red to blue and purple. At sunset, the leading color solutions are the predominance of red, red shades if we are talking about early sunset when the sun has not yet set. If we are talking about a later sunset, when the sun has almost set, then the color solutions are replaced by pink shades from the sun side and the predominance of purple and blue shades on the other sunset side.
In this work, several variants of atmospheric lighting were created at different times of sunset. To creating the illusion of the sun shining through the window and adding a textured shadow on the wall, the lighting included a side spotlight placed on the side of the stage. The color filter of this spotlight had a red hue of different saturation.
For illuminating the actor on the stage, front lighting was used with a searchlight placed on the balcony side as the artificial sun (in this work, on the left). For such a searchlight, color filters with the same red shades were used as for side lighting.
The background lighting was created by overhead lighting placed on the top of the stage. In this case, the color filters were of different shades depending on the location of the sun – the farther away from the left part of the scene, the bluer shades prevailed, the closer to the left part, the more yellow and red shades prevailed.
Figure 3 shows the final images of the theatrical stage lighting options model with a sunset atmosphere from early No. 1 to late No. 7.
To create a realistic image, a program was used that implements the CIECAM02 model algorithm described above. The maximum luminance in the lighting scene according to the calculation in the DIALux evo software is =10 / 2. Further, a reverse recalculation was performed according to the ICC profile of the computer display. The results of the images to adapt to the luminance of the display are shown in Figure 4.
The obtained images were evaluated for similarity in the feeling of sunset by the method of
experimental estimates. For conducting surveys, the following sites were used:
https://forms.gle/3KhCJ6mwFZobbuJZ7 and https://forms.gle/oB5z5szssRDAydQ18. To solve this
problem, a scale was introduced by which images were evaluated. The image with the highest number
of positive results is considered the best alternative. In the survey, images were presented in an order
unknown to experts before and after processing. The scale for evaluation includes four options [
Experts are invited to choose one of the most suitable options for each of the proposed images.
Figure 5 shows the response diagrams for each of the image variants before and after transformations.
After summing up the survey results, the best images before the conversion turned out to numbers 1, 5, 6, and after the conversion, the image became the best option number 6. As can be seen from the graph, the total number of responses "Remarkably similar" decreased, which indicates that after processing, the image becomes less suitable for lighting a scene with a sunset atmosphere. In general, the number of answers "Not very similar "and "A little similar" prevails, so we can conclude that the images obtained are not quite suitable for this stage lighting. Therefore, it was decided to conduct a second experiment in which new modified lighting options will be created based on expert comments.
After the first survey, the most similar images for the sunset from the proposed options were identified. An additional survey was created to determine the main points (the selection of color, brightness, and saturation of lighting) that affect experts' decisions. The survey included the three best images. The questions included a scale from 1 to 8, where 1 is not similar, 8 is very similar. The experts were asked to evaluate the selection of the lighting color scheme, brightness, and color saturation on a scale. Also, in addition to each image, it was suggested to add the general opinion of each expert about what is missing for the "perfect sunset" in the image. Let us look at the survey results for the best one. Variant number 6 of the first experiment was selected (Figure 6).
Expert answers on the graphs have a normal distribution. Based on the results, we can conclude that the brightness and saturation almost meet experts' expectations. According to the color solution in the last question, experts believed there are not enough purple shades in the sky.
After processing the survey results, three versions of the images were finalized based on experts' opinions. Figure 7 shows the changes to variant number 6. Purple shades were added in the upper right corner. The color saturation was slightly increased. In the center, Figure 7 shows the changes to variant number 5 - uniformity in shades was added. The primary color of the sunset is pink. After surveys, it was found out that red colors in the lighting positively affect the perception of the sunset atmosphere. Therefore, it was decided to make a third variant with the main color in red shades. For the contrast between the actor and the scenery, the luminance of the front lighting was added. The visualization of the new stage lighting is shown in Figure 7 on the right.
On all models, the luminance index of lighting devices was made at 100% since it was previously found out that after converting images, they become dimmer. To achieve the desired result, it is necessary to make slightly illuminated images in the software.
After receiving the results of the models, the final realistic images of the stage lighting were obtained. These images are shown in Figure 8.
will allow you to realistically evaluate the light and color design of the projected lighting system based on its image.
We want to thank all graduate students and students of the Department of Computer-aided Design and Design at the “National University of Science and Technology “MISiS” and the Department of Light Engineering at the “National Research University “MPEI” for participating in the expert assessment surveys of images based on their similarity to the feeling of sunset.