Koffka Ring Perception in Digital Environments with Brightness Modulation

Abstract

Various parameters and observation conditions contribute to the emergence of color. This phenomenon poses a challenge in modern visual communication systems, which are continuously being enhanced through new insights gained from research into specific psychophysical effects. One such effect is the psychophysical phenomenon of simultaneous contrast. Nearly 90 years ago, Kurt Koffka described one of the earliest illusions related to simultaneous contrast. This study examined the perception of gray tone variations in the Koffka ring against different background color combinations (red, blue, green) displayed on a computer screen. The intensity of the effect was measured using lightness difference ΔL₀₀ across light-, medium-, and dark-gray tones. The results were analyzed using descriptive statistics, while statistically significant differences were determined using the Friedman ANOVA and post hoc Wilcox tests. The strongest visual effect was observed the for dark-gray tones of the Koffka ring on blue/green and red/green backgrounds, indicating that perceptual organization and spatial parameters influence the illusion’s magnitude. The findings suggest important implications for digital media design, where understanding these effects can help avoid unintended color tone distortions caused by simultaneous contrast.

1. Introduction

Psychology of colors is a fundamental element in graphic design because it shapes how people experience perception [1]. Perception is consciousness of things which develops through using physical senses, mostly eyesight, and is a type of “subjective reflection of the objective reality”. Interest in perception dates from the times of the ancient Greek philosophers Aristotle and Plato, who wanted to know how people get to know the world and begin to understand it [2]. Researchers became interested in understanding the different aspects of perception, especially the perception of color, through Leonardo da Vinci, discussions between Newton and Goethe up to the nineteenth century, and Helmholtz theory, which postulates an explanation based on prepositions regarding the human eye’s design [3], and Herning theory, based on the mutual influences of neurons in the retina [4].

In the 1960s, a retinal-based interpretation was used to discover the process of lateral inhibition in the lumens of the retina [5,6]. In the last few decades, studies have shifted towards higher-level theories related to the principles of perceptual organization, although there are exceptions [7,8,9,10,11,12,13], and this is also due to retinal interactions being more difficult to explain. There is a well-known phenomenon studied by Agostini and Galmonte [14] where a gray area surrounded by a darker area is perceived to be darker than an identical gray area surrounded by a lighter area.

Michel Eugene Chevreul looked at color from a practical point of view. He was the first to observe and define simultaneous contrast through black tones, and defined it as the shift of a color in tone and darkness towards the complementary color next to it [15].

In 1935, Gestalt psychologist Kurt Koffka demonstrated and described in his book a simultaneous contrast as a combination of Wertheimer and Benussi patterns [16]. More recently, research related to the perception of brightness/color shift during the occurrence of simultaneous contrast in analog and digital media has taken the direction of developing a recommended model for predicting and reducing the undesirable occurrence of this effect in real graphic production. In their work, Hajdek et al. investigate how the occurrence of simultaneous contrast affects the perception of the observer when changing the background brightness of analog media [17,18,19]. Hajdek et al. also research the simultaneous contrast effect when changing the background brightness in digital media [20], as well as how the changes in the perceptual attributes of color influence the observer’s perception when the simultaneous contrast effect occurs in the digital medium [21].

The image of simultaneous contrast is presented through three different but related variants. The first variant (Figure 1a) consists of a gray ring located on two surfaces colored in different shades of gray. If a ring which affects the color of the background is observed, it will be perceived homogeneously. The second variant (Figure 1b) is divided into two separate segments with equal parts of the ring over different colored backgrounds. One half of the ring is on the darker and the other one is on the brighter side. Parts of the ring will not be perceived homogeneously but will be perceived differently due to the different background colors. The third variant (Figure 1c) is divided into two parts, but there is no gap between the background; only half the ring is vertically moved downwards. The ring is not perceived homogeneously here. However, its perception will be affected, due to spatial organization, by the coloring of the two backgrounds as well as the same coloring of a part of the ring.

Gestalt continuity principles can explain this effect [22]. In complementary colors the effect of simultaneous contrast is more pronounced [23,24,25,26]. Huang et al. showed in their paper that a Koffka ring depends on the thickness, and not the continuity [27]. In their paper, Matijević et al. research the way that the red color influences the perception of the occurrence of the Koffka effect in digital media [28]. The effect of simultaneous contrast, which has been studied for more than a century, is still a poorly understood phenomenon, and agreement between scientists is still far from being reached. The goal of this research is to determine the magnitude of the effect due to the variation in the gray tones of the Koffka ring on different background color combinations (red, blue, green) on a computer screen. In line with that, based on the research results, recommendations will be given to designers regarding which combination of primary and secondary stimuli can be used when creating a conceptual graphic solution in real production, to avoid the unwanted occurrence of the researched effect.

Unlike previous studies, which predominantly focused on analog media or isolated aspects of the simultaneous contrast effect, this study systematically examines how variations in both the spatial arrangement (Koffka ring variants) and background color affect illusion strength in the digital environment. The integration of calibrated Lab* colorimetric measures, multiple digital configurations, and rigorous statistical analysis represents a novel approach that provides new insights relevant for both theoretical understanding and practical applications in digital media.

2. Experimental Part

The Koffka ring (Figure 2) was used for the experiment with three variants. The variants were used to obtain a partial 3D perception of a part of the ring on a different background, as well as to reduce the homogeneity of the ring. There were 27 test samples made with the color combination of primary and secondary stimuli shown in

Table 1. Referent Lab values for primary and secondary stimuli.

Primary Stimuli	Secondary Stimuli (Background): Left Side/Right Side
L: 42; a: 0; b: 0	L: 30; a: 69; b: −114/L: 83; a: −128; b: 87
L: 66; a: 0; b: 0	L: 63; a: 90; b: 78/L: 83; a: −128; b: 87
L: 85; a: 0; b: 0	L: 63; a: 90; b: 78/L: 30; a: 69; b: −114

. The test samples were 80 × 80 mm in size and were created using Photoshop 2020. The dimension of the background surface (secondary stimuli) was 40 × 80 mm (Figure 2). The evaluation of test samples was carried out in defined observation conditions for graphic technology and professional photography ISO 3664:2009 [29,30].

The primary stimulus was a neutral gray color, while the secondary stimuli were complementary color pairs. Lab values of primary and secondary stimuli and design variants are shown in

Table 2. Koffka ring combinations for all brightness values of primary stimuli.

Test Sample	Variant of Koffka Ring
1; 4; 7; 10; 13; 16; 19; 22; 25	variant a
2; 5; 8; 11; 14; 17; 20; 23; 26	variant b
3; 6; 9; 12; 15; 18; 21; 24; 27	variant c

. L, a, and b represent the coordinates in the CIE Lab* color space, where L indicates lightness, a represents the green–red axis, and b represents the blue–yellow axis.

The distance of the examinees from the test samples was 60 cm, while the viewing angle was 10°. The distance, the viewing angle, and height of the test samples are defined using Formula (1) [31].

$$\mathit{tan}{\displaystyle \frac{VA}{2}}={\displaystyle \frac{H}{2D}},$$

(1)

VA stands for the viewing angle, H for height of the test sample, and D for distance of the sample from the observer.

The samples were evaluated under defined environmental conditions (ISO 3664: 2009, viewing angle 10°, examinee distance of 60 cm, naturally matt gray environment, artificial lighting, temperature 5000 K, spectral distribution 300–780 nm). Visual research was conducted on 60 examinees in a mixed population with an average age of 22 years old. Prior to taking the test, all subjects had to take the Munsell Hue Color Vision Test. Only those who passed the test could participate. The inclusion criterion was a Total Error Score (TES) of 16 or less, indicating normal color vision according to test standards. The sample size of 60 observers in this study was determined in accordance with widely accepted statistical criteria for repeated measures designs in perceptual research. The statistical power, calculated according to Cohen’s guidelines for repeated measures, with an effect size of f = 0.25, α = 0.05, and a sample size of n = 60, reached the desired threshold (power ≈ 0.79) for detecting medium effects. The sample size of 60 observers provides sufficient sensitivity to detect relevant differences across repeated measures conditions, thereby enhancing the robustness and reliability of the experimental findings. Although slightly below the typical 0.8 criterion, this sample size is regarded as adequate for studies in this domain, balancing robust statistical inference with the practical constraints of psychophysical experimentation.

Observers were adjusted to D50, and for visual assessment, the simultaneous binocular alignment technique was used [32].

The research was conducted on a computer Asus ET2324IUT with a screen resolution of 1920 × 1080, Full HD and LED backlight, and a 23-inch screen size. The screen was calibrated to white colorD50 and 120 cd/m² using an X-Rite i1 Pro spectrophotometer. The screen calibration was performed using DisplaCAL3 adjusted to the following settings: the white dot temperature was set to 5000 K and the tone curve was Gamma 2.2. The profile type was set to CIELAB LUT and it expanded the Look Up Table profile with 318 test patches on color accuracy and gray balance. The calibrated display values followed the white dot of the media: xy 0.34 0.35, temperature 5011 K, ΔE₀₀ to daylight 0.49, ΔE₀₀ to black body 1.21, and measured brightness 119.75 lx.

The research was carried out on a specially developed program (Figure 3).

The perception of gray fields on colored backgrounds was studied. There was a question at the top of the screen that the respondent had to answer first. The question referred to the gray ring tone on the test sample. The question was the following: “How many tones of gray do you perceive? “, and there were two answers offered: “I see 1 gray tone” or “I see 2 gray tones “. If one shade of gray is perceived, the answer “I see 1 gray tone” is selected and a square opens in the right part of the screen in which the perceived gray tone is adjusted (Figure 3).

If two shades of gray are perceived, the answer “I see 2 gray tones” is selected and two squares open in the right part of the screen in which the perceived gray tone is adjusted. The left perceived gray tone is adjusted in the upper right square, and the right perceived gray tone is adjusted in the lower right square (Figure 4).

After the examinee selected a shade of one gray tone or two gray tones that matched the gray tone of the primary stimulus in the test sample shown, his answer was confirmed. The next stimulus with a different spatial construction and with a different background value would then open and the test would continue.

The deviation in perception caused by the manifestation of the visual effect is shown by the difference in brightness ΔL₀₀. ΔL₀₀ (lightness component of CIEDE2000) was used due to its status as the most perceptually uniform metric for color discrimination in the CIELAB space, especially suited for the fine-grained evaluation of lightness effects. Unlike ΔE94 or CIECAM02, ΔL₀₀ directly quantifies the dimension of brightness that is critical in simultaneous contrast phenomena such as the Koffka ring effect. While CIECAM02 is advantageous for comprehensive color appearance modeling, it introduces additional adaptation and viewing-context variables less relevant for the present paradigm, which focuses on neutral grays and controlled display geometry.

The differences in colors’ ΔE₀₀ as well as the determined differences in brightness ΔL₀₀ in the paper are calculated using Formulas (2) and (3) [33].

$$\Delta E_{00}={\left[{\left({\displaystyle \frac{\Delta L^{\prime }}{k_L{S}_L}}\right)}^2+{\left({\displaystyle \frac{\Delta {C^{\prime }}_{ab}}{k_C{S}_C}}\right)}^2+{\left({\displaystyle \frac{\Delta {H^{\prime }}_{ab}}{k_H{S}_H}}\right)}^2+R_T\left({\displaystyle \frac{\Delta {C^{\prime }}_{ab}}{k_C{S}_C}}\right)\left({\displaystyle \frac{\Delta {H^{\prime }}_{ab}}{k_H{S}_H}}\right)\right]}^{0.5}$$

(2)

$$\Delta L^{\prime }={L^{\prime }}_b-{L^{\prime }}_s$$

(3)

3. Results

This paper presents the results of simultaneous contrasts with three variants of the Koffka rings. Primary stimuli had Lab values as follows: L: 42; a: 0; b: 0; L: 66; a: 0; b: 0; L: 85; a: 0; and b: 0, while the background stimuli were defined by L, a, and b values of L: 30; a: 69; b: −114; L: 83; a: −128; b: 87; L: 63; a: 90; and b: 78. For research purposes, 27 test samples were used, and the results were statistically analyzed using the program Statistica 13 (Stat. Soft. Toulsa). The ΔL₀₀ results were analyzed for three values of the primary stimuli, light, medium, and dark, and for different design variants and different background colors.

3.1. Analysis of the Effect Behavior in Light Primary Stimuli

The results of the statistical effect analysis caused by the stimuli’s Lab values are shown as follows: L: 85; a: 0; and b: 0. These occur in different variants of the Koffka ring design, where test samples 7, 16, and 25 cover variant a of the Koffka ring design; test samples 8, 17, and 26 cover variant b of the Koffka ring design; and test samples 9, 18, and 27 cover variant c of the Koffka ring design (Figure 2). The different background colors are as follows: left side Lab values: L: 30; a: 69; b: −114 and right side: L: 83; a: −128; b: 87 (test samples 7, 8, 9); left side Lab values: L: 63; a: 90; b: 78 and right side: L: 83; a: −128; b: 87 (test samples 16, 17, 18); and left side Lab values: L: 63; a: 90; b: 78 and right side: L: 30; a: 69; b: −114 (test samples 25, 26, 27) (

Table 3. Overview of test samples, Koffka ring design variants (a, b, c), corresponding light primary stimuli, and secondary background colors on the left and right sides for each variant.

Test Sample	Variant of Koffka Ring	Primary Stimuli	Secondary Stimuli (Background)
			Left Side	Right Side
7	variant a	L: 85; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
8	variant b	L: 85; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
9	variant c	L: 85; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
16	variant a	L: 85; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
17	variant b	L: 85; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
18	variant c	L: 85; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
25	variant a	L: 85; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114
26	variant b	L: 85; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114
27	variant c	L: 85; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114

).

The results of descriptive statistics show that the variances and standard deviations are within the limits that are common in the study of visual effects in graphic media, which means that the scattering of data was not significant (

Table 4. Descriptive statistics of the ΔL₀₀ of light primary stimuli on different background colors.

Test Sample	Variant of Koffka Ring	Mean	Med.	Min.	Max.	Var.	St. Dev.	K-S P
7	variant a	−0.179804	0.00000	−6.5057	4.66780	2.60748	1.614770	p < 0.01
8	variant b	−0.845099	0.00000	−9.5906	8.72184	6.46539	2.542714	p < 0.01
9	variant c	−0.136777	0.00000	−5.8303	1.74849	0.80772	0.898734	p < 0.01
16	variant a	−0.140623	0.00000	−6.2271	5.27361	2.29454	1.514773	p < 0.01
17	variant b	−0.655715	0.00000	−6.1587	2.38331	3.22580	1.796050	p < 0.01
18	variant c	−0.728351	0.00000	−25.1413	0.48597	11.25118	3.354278	p < 0.01
25	variant a	0.648876	0.00000	−5.7770	9.22981	4.91420	2.216800	p < 0.01
26	variant b	0.477804	0.00000	−9.3278	16.24118	9.42418	3.069882	p < 0.01
27	variant c	0.159073	0.00000	−2.8589	11.59047	2.36234	1.536990	p < 0.01

Legend: This table includes the arithmetic mean, median, minimum, maximum, variance, and standard deviation as well as Kolmogorov–Smirnov p-values.

). Standard deviations and variances range from the lowest ${\sigma }_9=0.90, {\sigma }_9^2=0.81$, which is obtained for test sample 9, to the highest ${\sigma }_{18}=3.35, {\sigma }_{18}^2=3.35$, on test sample 18. Additionally, the ranges between the minimum and maximum are not big.

The Kolmogorov–Smirnov test showed that no sample was aligned with the normal distribution (Table 4). As samples were not normally distributed, the non-parametric Friedman ANOVA was selected for dependent samples with repeated measurements to examine the existence of statistically significant differences in the strength of the visual effect caused by the Koffka ring measured by the differences in the test samples with a bright stimulus on different colored backgrounds and different variants of the Koffka ring design.

The following results are obtained: The Friedman ANOVA Chi-square has 8 degrees of freedom df = 8, its value is x² = 64.551, and its the corresponding p-value is p = 0.000 < 0.05. This establishes the existence of statistically significant differences between the strengths of the visual effects on the Koffka rings in test samples with a light stimulus on different colored backgrounds and in different Koffka ring design variants. Wilcox tests of equivalent pairs were carried out to identify pairs in which the visual effects differed significantly from a statistical point of view. A significance level of ά = 0.05 was chosen.

The intensity of the visual effect measured by the difference in brightness ΔL₀₀ is small, while the medians for all test samples are equal to zero (Table 4). Therefore, a large number of examinees did not perceive a difference in brightness due to the manifestation of the visual effect in the light stimulus. In test samples 7, 9, 16, and 27, the arithmetic mean of the difference in perceived brightness in relation to the physical value of the brightness is so small that it is not visible (

Table 5. Wilcox tests’ results for light primary stimuli.

Samples	Sample 7	Sample 8	Sample 9	Sample 16	Sample 17	Sample 18	Sample 25	Sample 26
Sample 8	0.015	-
Sample 9	0.958	0.026	-
Sample 16	0.570	0.001	0.789	-
Sample 17	0.092	0.387	0.073	0.055	-
Sample 18	0.492	0.136	0.177	0.332	0.306	-
Sample 25	0.011	0.000	0.014	0.040	0.001	0.002	-
Sample 26	0.112	0.001	0.147	0.271	0.012	0.070	0.601	-
Sample 27	0.151	0.001	0.202	0.441	0.008	0.050	0.090	0.310

Legend: This table contains the Wilcox tests’ p-values.

). This effect is manifested in the opposite direction in test samples 25, 26, and 27.

In the group containing test samples 7, 8, 9, 16, 17, and 18, the effect is manifested in the positive brightness scale direction (Table 5). Statistically significant differences in the strength of the effect were found for test sample 8 in relation to test sample 7 (p = 0.015), test sample 9 (p = 0.026), and test sample 16 (p = 0.001). No statistically significant differences were found between test samples 8 and test samples 17 and 18 (p = 0.387, p = 0.136). On test samples 8, 17, and 18, the difference in brightness was noticeable (Table 5). No difference was observed for test samples 7, 9, and 16.

The effect is manifested in the opposite direction for test samples 25, 26, and 27 (Table 5). A difference is observed for test samples 25 and 26. For test sample 25, the arithmetic mean of brightness difference is the largest compared to the others in this group, and it amounts to ${\mu }_{25}=0.648$ with a median amount ${Med}_{25}=0$ (Table 4). There are statistically significant differences between the strength of the effects on test sample 25 and test samples 7 (p = 0.011), 8 (p = 0.000), 9 (p = 0.014), 16 (p = 0.040), 17 (p = 0.001), and 18 (p = 0.002). There are no statistically significant differences between test sample 25 and 26 (p = 0.601) and test samples 25 and 27 (p = 0.090). No effect was observed for test sample 27.

The results of the statistical analysis clearly show the way the light stimuli are divided into three groups. There are test samples 8, 17, and 18 in the first group, on which the effect can be observed. The effect is most strongly manifested on test sample 8 and it amounts to ${\mu }_8=-0.845$ with a median amount ${Med}_8=0$ (Table 4), which is variant b of the Koffka ring on the blue/green surface. There are test samples 7, 9, and 16 in the second group, on which no difference is observed. In the third group, the effect is manifested in the opposite direction. This group consists of test samples 25, 26, and 27. In this group, the effect is observed on test sample 25, and it amounts to ${\mu }_{25}=0.648$ with a median amount ${Med}_8=0$ (Table 4), which is variant a of the Koffka ring on the red/blue background. The effect is not observed on test samples 26 and 27.

3.2. Analysis of the Effect Behavior in the Medium Primary Stimuli

The effect which occurs on the Koffka ring causes the stimuli Lab values L: 66; a: 0; and b: 0 for different Koffka ring design variants, where test samples 4, 13, and 22 cover Koffka ring design variant a; test samples 5, 14, and 23 Koffka ring design variant b; and test samples 6, 15, and 24 Koffka ring design variant c (Figure 2), and the different background colors are divided as follows: left side Lab values: L: 30; a: 69; b: −114 and right side: L: 83; a: −128; b: 87 (test samples 4, 5, 6); left side Lab values: L: 63; a: 90; b: 78 and right side: L: 83; a: −128; b: 87 (test samples 13, 14, 15); and left side Lab values: L: 63; a: 90; b: 78 and right side: L: 30; a: 69; b: −114 (test samples 22, 23, 24) (

Table 6. Overview of test samples, Koffka ring design variants (a, b, c), corresponding medium primary stimuli, and secondary background colors on the left and right sides for each variant.

Test Sample	Variant of Koffka Ring	Primary Stimuli	Secondary Stimuli (Background)
			Left Side	Right Side
4	variant a	L: 66; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
5	variant b	L: 66; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
6	variant c	L: 66; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
13	variant a	L: 66; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
14	variant b	L: 66; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
15	variant c	L: 66; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
22	variant a	L: 66; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114
23	variant b	L: 66; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114
24	variant c	L: 66; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114

).

The results of the descriptive statistics for the medium-brightness stimuli show that the variances and standard deviations are not high (

Table 7. Descriptive statistics of ΔL₀₀ of medium primary stimuli on different backgrounds.

Test Sample	Variant of Koffka Ring	Mean	Med.	Min.	Max.	Var.	St. Dev.	K-S p
4	variant a	−2.17050	0.000000	−15.7583	8.83015	21.78931	4.667902	p < 0.01
5	variant b	−4.53790	−0.781969	−19.2605	10.36977	38.58277	6.211503	p < 0.01
6	variant c	−0.49132	0.000000	−15.9106	11.35623	12.57916	3.546711	p < 0.01
13	variant a	−2.21468	0.000000	−17.3418	15.00615	28.92547	5.378241	p < 0.01
14	variant b	−2.82521	0.000000	−21.1476	13.65467	33.22954	5.764507	p < 0.01
15	variant c	−0.85072	0.000000	−15.1765	19.55850	19.18819	4.380433	p < 0.01
22	variant a	−0.32957	0.000000	−28.1734	24.19551	35.69081	5.974179	p < 0.01
23	variant b	0.48307	0.000000	−17.0061	26.26080	23.82916	4.881512	p < 0.01
24	variant c	−0.44207	0.000000	−20.7100	4.20868	8.26660	2.875170	p < 0.01

Legend: This table includes the arithmetic mean, median, minimum, maximum, variance, and standard deviation and Kolmogorov–Smirnov p-values.

). The variance is in the range of ${{\sigma }^2}_{24}=0.83$ for test sample 24 to ${{\sigma }^2}_5=3.86$ for test sample 5. The same applies to standard deviations, with the lowest value ${\sigma }_{24}=2.86$ on test sample 24 and the highest ${\sigma }_5=3.86$ on test sample 5. Also, the ranges between minimum and maximum are not big (Table 7), which means there are no deviations in the perception of the visual effect that will have been bigger than expected for the planned experiment.

The Kolmogorov–Smirnov test proved that all samples deviate from normal distribution laws (Table 7). Therefore, the non-parametric Friedman ANOVA was chosen for dependent samples with repeated measurements. The occurrence of statistically significant differences in visual effect strength measured by differences in the brightness of medium-level stimuli on test samples on different colored backgrounds and different variants of the Koffka ring designs was studied.

It was found that Friedman’s ANOVA Chi-square had 8 degrees of freedom df = 8 and its value was x² = 64.551, with a corresponding p-value of the amount p = 0.000 < 0.05. This result points to the existence of statistically significant differences between the strengths of the visual effects on test samples with medium stimuli on different colored backgrounds and in different variants of the Koffka ring design. Wilcox tests of equivalent pairs were chosen as post hoc tests to identify pairs in which the visual effects were statistically significantly different. ά = 0.05 was chosen as the level of significance, which is standard in this type of research.

According to the descriptive statistics results (Table 7), the strength of the visual effect is measured with ΔL₀₀; it is strongest in test sample 5, where the difference in the measured ΔL₀₀ of the amount ${\mu }_5=-4.54$ is clearly visible, with median value ${Med}_5=-0.78$. The strength of the Koffka ring effect is somewhat weaker on test sample 14, where it amounts to ${\mu }_{14}=-2.82$ with a median value ${Med}_{14}=0$, in which the difference in ΔL₀₀ borders between the values when the effect is visible and adequately visible. The Wilcox test did not find statistically significant differences between the strength of the effect on test samples 5 and 14 (

Table 8. Results of the Wilcox medium primary stimuli tests.

Samples	Sample 4	Sample 5	Sample 6	Sample 13	Sample 14	Sample 15	Sample 22	Sample 23
Sample 5	0.006	-
Sample 6	0.014	0.000	-
Sample 13	0.879	0.018	0.008	-
Sample 14	0.455	0.069	0.006	0.480	-
Sample 15	0.129	0.000	0.546	0.106	0.001	-
Sample 22	0.014	0.000	0.569	0.028	0.009	0.289	-
Sample 23	0.001	0.000	0.231	0.003	0.000	0.077	0.212	-
Sample 24	0.008	0.000	0.794	0.018	0.005	0.382	0.605	0.177

Legend: This table contains the p-values of the Wilcox tests.

., p = 0.069). Therefore, in the group where the effect is strongly manifested, or in test samples 5 and 14 where it is adequately visible, that would be variant b of the Koffka ring on a red/green, i.e., blue/green background. There are statistically significant differences between test sample 5 and all other samples except for test sample 14 (Table 8).

In test samples 4 and 13, the visual effect is less manifested than in test samples from the first group. On these test samples, ΔL₀₀ is such that the effect is visible. According to the results of the Wilcox equivalent pairs test, there are no statistically significant differences in the manifestation of this effect on test samples 4 and 13 (Table 8, p = 0.879). Based on the presented results, it can be concluded that test samples 4 and 13 are in the second group, which is a variant of the Koffka ring on a red/green, i.e., blue/green background. The effect strengths on these samples are ${\mu }_4=-2.17$, ${Med}_4=0$ (Table 7) and ${\mu }_{13}=-2.21, {Med}_{13}=0.$

Test samples 6, 15, 22, 23, and 24, on which the effect is observed, are in the third group; the Wilcoxon tests of equivalent pairs did not find statistically significant differences in the strength of the effect on any pair of test samples from this group (Table 8).

3.3. Analysis of the Effect Behavior in Dark Primary Stimuli

The following is a presentation of the statistical analysis results of the effect causing the Lab stimuli with L values of 42; a: 0; and b: 0 for different Koffka ring design variants. Test samples 1, 10, and 19 cover Koffka ring design variant a; test samples 2, 11, and 20 cover Koffka ring design variant b; and test samples 3, 12, and 21 cover Koffka ring design variant c (Figure 2) and the different background colors presented in

Table 9. Overview of test samples, Koffka ring design variants (a, b, c), corresponding dark primary stimuli, and secondary background colors on the left and right sides for each variant.

Test Sample	Variant of Koffka Ring	Primary Stimuli	Secondary Stimuli (Background)
			Left Side	Right Side
1	variant a	L: 42; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
2	variant b	L: 42; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
3	variant c	L: 42; a: 0; b: 0	L: 30; a: 69; b: −114	L: 83; a: −128; b: 87
10	variant a	L: 42; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
11	variant b	L: 42; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
12	variant c	L: 42; a: 0; b: 0	L: 63; a: 90; b: 78	L: 83; a: −128; b: 87
19	variant a	L: 42; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114
20	variant b	L: 42; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114
21	variant c	L: 42; a: 0; b: 0	L: 63; a: 90; b: 78	L: 30; a: 69; b: −114

.

Variances and standard deviations in the dark stimuli are higher than the values of the same indicators in comparison to the light and medium stimuli (

Table 10. Descriptive statistics of ΔL₀₀ of dark primary stimuli on different backgrounds.

Test Sample	Variant of Koffka Ring	Mean	Med.	Min.	Max.	Var.	St. Dev.	K-S P
1	variant a	−4.43659	−2.13522	−20.6536	7.13976	41.35189	6.430543	p < 0.05
2	variant b	−4.58269	−3.89754	−18.3156	10.56289	33.08924	5.752324	p < 0.05
3	variant c	−1.71339	0.00000	−18.1381	9.88852	35.27470	5.939251	p < 0.01
10	variant a	−4.55246	−1.87748	−22.6144	8.22937	40.76960	6.385108	p < 0.01
11	variant b	−4.13296	0.00000	−18.4316	5.28696	33.63150	5.799267	p < 0.01
12	variant c	−2.62506	0.00000	−26.7668	2.47656	32.19058	5.673674	p < 0.01
19	variant a	−1.80000	0.00000	−14.4400	6.54448	17.92289	4.233544	p < 0.01
20	variant b	−1.69553	0.00000	−14.0321	8.64973	20.17079	4.491190	p < 0.01
21	variant c	−1.41859	0.00000	−16.9244	3.43761	16.52070	4.064566	p < 0.01

Legend: This table includes the arithmetic mean, median, minimum, maximum, variance, and standard deviation and Kolmogorov–Smirnov p-values.

). The range of the variance values is from ${{\sigma }^2}_{21}=16.52$ for test sample 21 to ${{\sigma }^2}_1=41.35$ for test sample 1. Consequently, the standard deviation achieves the lowest value, ${\sigma }_{21}=4.06$, on test sample 21 and the highest, ${\sigma }_1=6.43$, on test sample 1. The lowest value of the effect caused by the Koffka ring was determined to be on test sample 12, ${Min}_{12}=-26.25$. The maximum has lower absolute values than the minimum. The highest maximum was found on test sample 2 and amounted to ${Max}_2=10.56$. The data clearly indicates a slightly greater data dispersion. This dispersion is expected because the visual effect caused by the Koffka ring on dark stimuli samples is very strong on some test samples.

Samples are not normally distributed (Table 10). Therefore, non-parametric Friedman ANOVA was carried out for dependent samples with repeated measurements. This determined the existence of a statistically significant difference in the visual effect manifestation measured by differences in brightness on test samples with dark stimuli on different colored backgrounds and different Koffka ring design variants.

Friedman ANOVA Chi-square has 8 degrees of freedom df = 8 and amounts to x² = 37.569, with the corresponding p-value amounting to p = 0.000 < 0.05. There are statistically significant differences between the visual effect strengths on test samples with a dark stimulus on different colored backgrounds and in different Koffka ring design variants. Therefore, post hoc Wilcox tests of equivalent pairs were carried out to identify statistically significantly different pairs. A level of significance of ά = 0.05 was chosen, which is standard in this type of research.

Results of descriptive statistics (Table 10) show that the effect measured by the difference in brightness ΔL₀₀ is most pronounced in test samples 1, 2, 10, and 11, among which statistically significant differences in the strength of the effect were not found. The visual effect that occurs on the Koffka ring is adequately visible in test samples 1, 2, 10, and 11. The effect is manifested most strongly in test sample 2 with the b variant design of the Koffka ring on a blue/green background, with the arithmetic mean amounting to ${\mu }_2=-4.58$ and a median of ${Med}_2=-3.90$. Test sample 10 has almost the same arithmetic mean value, which is variant b on a red/green background. On test sample 10, the arithmetic mean amounts to ${\mu }_{10}=-4.55$ with a median of ${Med}_{10}=-1.88$. The arithmetic mean of the Koffka ring effect strength of test sample 1 is ${\mu }_1=-4.44$, which is variant a on blue/green background, with a median of ${Med}_1=-2.14$. A somewhat weaker effect was observed on test sample 11, which is variant b on a red/green background. The arithmetic mean of test sample 11 is ${\mu }_{11}=-4.13$ while the median value is ${Med }_{11}=0.$ According to the Wilcox tests’ results, there are no statistically significant differences in the manifestation of the effect in this group (

Table 11. Results of Wilcox dark primary stimuli tests.

Samples	Sample 1	Sample 2	Sample 3	Sample 10	Sample 11	Sample 12	Sample 19	Sample 20
Sample 2	0.807	-
Sample 3	0.007	0.002	-
Sample 10	0.947	0.798	0.006	-
Sample 11	0.693	0.639	0.008	0.806	-
Sample 12	0.028	0.009	0.353	0.055	0.030	-
Sample 19	0.004	0.003	0.757	0.000	0.001	0.538	-
Sample 20	0.007	0.005	0.850	0.000	0.010	0.294	0.745	-
Sample 21	0.001	0.000	0.805	0.001	0.002	0.107	0.527	0.661

Legend: This table contains Wilcox tests’ p-values.

). The empirical p-value between test samples 1 and 2 is p = 0.807, between test samples 1 and 10 it is p = 0.947, between test samples 1 and 11 it is p = 0.693, between test samples 2 and 10 it is p = 0.798, between test samples 2 and 11 it is p = 0.639, and between test samples 10 and 11 it is p = 0.806. The visual effect manifested in this group of test samples differed statistically significantly in relation to the visual effects of other test samples (Table 8). A pair of test samples 10 and 12 make an exception, and no statistically significant difference in effect strength was found (p = 0.055).

Test samples 3, 12, 19, 20, and 21 belong to the second group, given the strength of the effect (Table 11). In these test samples, the strength of the visual effect measured by the arithmetic mean is weaker than the one in the first group’s test samples. Wilcox tests show that there are no statistically significant differences in the strength of the effect between pairs of test samples in the second group (Table 11). The empirical p-value between test samples 3 and 12 is p = 0.353, between test samples 3 and 19 it is p = 0.757, between test samples 3 and 20 it is p = 0.850, and between test samples 3 and 21 it is p = 0.805. Furthermore, between test samples 12 and 19, p = 0.538; between test samples 12 and 20, p = 0.294; and between test samples 12 and 21, p = 0.107. Additionally, p = 0.745 between test samples 20 and 21; between test samples 19 and 21, p = 0.527; and between test samples 20 and 21, p = 0.661. The effects differ statistically significantly among pairs of test samples from these groups.

Based on the results of descriptive statistics and ANOVA analysis, it can be concluded that the division of test samples into two groups should be made, given the strength of the visual effects manifested on them. Test samples 1, 2, 10, and 11 form the first group where the manifestation of the effect is stronger. Test samples 3, 12, 19, 20, and 21 form the second group, and on these test samples the manifestation of the effect is significantly weaker than on the first group’s test samples.

4. Discussion

The results of the statistical analysis—including descriptive statistics, Friedman’s ANOVA for dependent samples with repeated measurements, and post hoc Wilcox tests—demonstrate that the visual effect induced by the Koffka ring varies significantly depending on the brightness of the stimuli, the design variant of the Koffka ring, and the color of the background. The strongest effect was observed for dark stimuli, particularly on blue/green and red/green backgrounds in variant b of the Koffka ring design. For middle stimuli, the effect was also pronounced in variant b, while for light stimuli, the effect was generally weak or absent, except for specific combinations where it was noticeable.

Agostini and Galmonte demonstrated that perceptual organization can override local surrounding effects in determining simultaneous lightness contrast, emphasizing the importance of spatial arrangement in visual perception [14]. Our results are consistent with this principle, as variant b of the Koffka ring—where the ring is split between two different backgrounds—showed the strongest effect, suggesting that spatial organization and background color are critical factors in the perception of brightness differences. Chevreul was the first to define simultaneous contrast as a shift in a color’s tone and darkness toward the complementary color adjacent to it [15]. Our results confirm that this effect is most pronounced for dark stimuli, which is in line with Chevreul’s observations. Furthermore, the findings are supported by theories of lateral inhibition in the retina, as discussed by Hartline, Wagner, and Ratliff, which explains how adjacent visual stimuli can inhibit each other, leading to perceived differences in brightness. Hajdek et al. investigated the simultaneous contrast effect in both analog and digital media, and our study extends these findings by demonstrating that, even on digital displays, the effect is robust and depends on the combination of background color and the spatial organization of stimuli [17,18,19,20,21]. The effect was particularly strong for blue/green and red/green backgrounds, while it was weak for red/blue backgrounds across all brightness levels. Huang et al. showed that the Koffka ring effect depends on the thickness of the ring rather than its continuity [27]. Our results indicate that, in addition to thickness, the spatial arrangement and background color play crucial roles. Variant b, with its split design, produced the strongest effect, highlighting the importance of perceptual organization in determining the strength of the simultaneous contrast effect.

In this research, a computer screen was used as a digital medium with the goal of determining the strength of the perceived Koffka effect when using a certain color combination of primary and secondary stimuli in the design of a conceptual graphic solution in real graphic production. The experiment was conducted on a single type of digital display, potentially limiting the applicability of the findings to other devices or display technologies. Further research will focus on displaying the Koffka effect on a wider range of different devices and display technologies such as mobile devices and tablets, with the aim of determining differences in the strength of the perceived effect on three different digital media. If a dark color such as black had been used as the background in this research, the results might be different, but this cannot be stated with certainty; further investigation is needed. In addition, the goal is to achieve reproduction identical to the original in real graphic production in a way that allows designers to predict the strength of the Koffka effect when using certain color combinations in digital media, to avoid unwanted effects on reproduction. In other words, the goal is to achieve a reproduction identical to the display of the image on the digital medium. The application of the obtained results is possible when designing various digital systems for mobile devices, tablets, or all digital media that use the screen to display the image. Our results can guide the selection of color schemes in digital media and UI/UX design. For example, when designing dashboards, buttons, or interactive controls where precise gray tone perception is important (such as in print proofing or visual analytics), the use of gray elements over split backgrounds of red/green or blue/green should be minimized. Effective application of these findings can help avoid situations where the same gray control appears markedly different across sections of an interface, which could lead to an inconsistent user experience or misinterpretation of visual information.

Although this study does not report separate empirical case studies within commercial AR/VR or UI/UX applications, it offers concrete, experimentally backed recommendations directly translating to common design situations. Further work may focus on targeted case studies or prototyping in these technological contexts to deepen the practical guidance.

5. Conclusions

The conclusion based on the research results indicates that the effect of simultaneous contrast is strongest in dark tones, and it is evident that in addition to primary and secondary stimuli, the strength of the effect depends on the perceptual organization and spatial parameters of the stimulus, while perception also depends on our visual system, which sometimes misinterprets information and is not perfect. Further research will focus on displaying the Koffka effect on different devices.