Understanding the image cues driving the switch from brightness to lightness responses in the Adelson checker-block illusion

Abstract

Adelson's checker-block illusion is an engaging demonstration of the difference between lightness and brightness. The illusory nature of the stimulus derives from participants’ experience of the discrepancy between perceived lightness of two test patches (A, B) despite their physical luminance being identical. The identical nature of the test patches becomes apparent when cues informing the viewer of the scene's illumination and 3D structure are removed. Here we explore which cues drive the transition from ‘brightness’ pixel-based responses to ‘lightness’ material-based responses. Participants (n = 123) viewed versions of the stimulus with various components deleted (top, left and right-sides, shadows, outline-edges) under four between-subjects scenarios: with lighting direction varied (from left or right) and with the scene orientation varied (upside-down or correctly oriented). Participants indicated the perceived difference between A and B by responding on a Likert scale. Generalised linear mixed effects models were used to estimate the strength of each cue in driving the change of responses from brightness towards lightness. The lightness responses were strongest for upright images illuminated from the top-left, with panels adjacent to the test patches present. The stimuli, responses and model fits are shared as a dataset that can be tested against existing models of lightness perception.

How to cite this article

Lovell, P. G., Scott-Brown, K. C., & Smart, I. E. (2026). Understanding the image cues driving the switch from brightness to lightness responses in the Adelson checker-block illusion. i-Perception, 17(1), 1–16. https://doi.org/10.1177/20416695251410895

Introduction

There exists a broad class of lightness and brightness illusions which can involve low-, mid- and high-level factors (e.g., Adelson, 2000; Gilchrist, 2007). Many lightness stimuli are rendered in only two dimensions, that is, test patches within the stimulus are usually co-planar with one another and generally orthogonal to the viewer and/or image-plane (see Kingdom, 2011 for a review). The Adelson checker-shadow (Adelson, 1995) is a useful extension to these stimuli because it presents a scene with a clear three-dimensional structure, featuring directional lighting and solid objects with surfaces that are either directly illuminated or in shadow. The illusion features two panels (A and B) that are squares on a checkerboard. The ‘A’ panel is a ‘dark’ tile that is directly illuminated, while the ‘B’ panel is a ‘light’ tile beneath a cast-shadow. The A and B panels match one another in brightness, but not in lightness, that is, perceptually they appear different, due to the observers’ material perception, yet the identical brightness of ‘A’ and ‘B’ becomes apparent when the 3D structure of the scene is occluded. To elaborate: by brightness we mean the ‘perceived’ intensity of light coming from that part of an image irrespective of what the surface is (a low-level judgement of light reaching the eye). On the other hand, by lightness we mean the perceived inherent reflectance of a surface, that is, how much light that surface reflects (a judgement by the visual system that tries to take account of surrounding light and shade to estimate the true surface). The illusion happens when the three-dimensional structure of the scene and its illumination become apparent to the observer. So, when these contextual cues are removed, the observer's relative judgments between the two panels converge so that the patch A no longer appears darker than B.

Adelson's ‘checker-blocks’ illusion (Adelson, 1993) differs from its younger and more famous sibling the ‘checker-shadow’ illusion (Adelson, 1995). While both illusions provide a powerful illustration of our ability to judge the lightness of material properties implied in shaded 3D scenes, in the checker-blocks illusion the ‘A’ and ‘B’ test panels are no longer co-planar, instead they lie on different faces of a rectangular object. Furthermore, the ‘A’ and ‘B’ panels are now spatially distinct from the cast shadow and the ‘B’ face is in shade due to the light source being behind the rectangle, while the ‘A’ panel faces upwards towards the light-source. The Adelson Checker-Blocks Illusion (Adelson, 1993) has been cited more than 750 times to date, and featured in countless demonstrations, lectures and conference presentations. Adelson was able to make the A panel appear darker than the B panel, despite their physically identical luminance. In the illusion, a directly illuminated surface appears darker than a shadowed surface, the illusion is constructed with a checkerboard pattern presented with a cast shadow. The combination of local and global contextual cues (namely of edges and cast-shadows) makes the illusion compelling because knowledge of its effect does not diminish its strength. It is a particularly memorable and convincing demonstration of the way the brain treats lightness and brightness, and how the brain can discount effects of lighting.

The current study utilises the Adelson checker-block illusion because it allows the widest range of contextual factors to be included in the assessment of those cues that drive lightness judgements. In particular, the checker-block stimulus facilitates the deletion of each of the three visible surfaces and, in addition the cast-shadow cue can be manipulated to encourage perception of the scene's three-dimensional structure and light field (Koenderink et al., 2007). Figure 1 shows two examples of the checker-blocks stimuli created for the current study, that are illuminated from different directions. When the whole scene is visible most participants would respond that panel ‘A’ within the stimuli is darker than panel ‘B’. So, participants viewing the whole stimulus will respond by pressing ‘4’, ‘3’ or even ‘2’ on the scale (Figure 1, bottom). These participants are responding to the perceived lightness of the material in the ‘scene’ rather than the brightness of the pixels. If you take a sheet of paper and create two holes that align with panels A and B and place the paper over the image, you will see that A and B actually have the same brightness. The pixel values are identical in terms of brightness (RGB = [138, 138, 138]) and when the 3D shape and illumination cues are concealed, participants respond to pixel brightness alone and perceive the two patches to be identical. The illusion demonstrates the limitation of the naïve belief that we make judgements based upon pixel brightness when in fact we can make judgements based upon the perceived reflectance of materials – which we term lightness.

Figure 1.

Examples of radiance rendered versions of the Adelson checker-block illusion. (Top left) The complete scene illuminated from the left. (Top right) The complete scene illuminated from the right. (Bottom) The response template used to guide keyboard presses. In both examples the areas adjacent to ‘A’ and ‘B’ have the same RGB value of 138.

There are several types of theoretical and computational models used to explain lightness and brightness illusions. Contrast theories are based upon relatively simple, low-level mechanisms such as lateral inhibition (see Kingdom, 2011 for a 25-year review, and Rudd, 2020 for a recent further appraisal) and Oriented Difference-of-Gaussians (Blakeslee & McCourt, 1999; McCourt et al., 2016). While these explanations are mechanistic and well defined, proving effective for many lightness illusions, they are less able to cope with the display of more complex stimuli or additional cues to scene context, such as implied depth or shading. Rudd and Shareef’s (2025) theory is a recently described exemplar, expanding on previous work (Rudd, 2020). In Intrinsic Image Theories (e.g., Murray, 2013, 2021), cues such as local contrast, texture and shading are used to isolate an object's brightness (perceived luminance) from lightness (reflectance). This is known as inverse optics to many because it attempts to ‘reverse engineer’ the lighting to reveal the object's true properties (see Murray, 2021 for a review). In both contrast theories and intrinsic image theories, the sorts of lightness illusions modelled tend to focus on stimuli that are viewed under highly specialised situations often with unusual lighting. This then limits the role of context in the explanations. In the same way, lightness anchoring theory (Gilchrist, 2006; Gilchrist et al., 1999) has been used to explain many lightness illusions such as the famous staircase Gelb (1929) effect. Robilotto and Zaidi (2006) argue that most explanations of these type of illusion use flat plain, non-patterned stimuli viewed under laboratory conditions, limiting the scope of additional cues (e.g., 3D, patterning) to influence illusion strength. Allred and Olkkonen (2013) make a similar case for background illumination in 3D to improve colour identification, while Fleming et al. (2003) make an empirical case for the importance of realistic illumination in estimation of perception of surface reflectance.

Here we address the question of which pictorial components of the Adelson ‘checker-blocks’ Illusion (Adelson, 1993 (Figure 1); Adelson, 2000 (Figure 24.7)) elicit the perceptual transition from (simple) brightness perception, to (illusory) lightness perception. We present a dataset comprising perceptual responses to a series of increasingly deconstructed and disrupted stimuli to enable the predictions from models of lightness perception to be tested against perceptual data from all permutations.

The motivation for the current study is based on the explanatory gaps emerging between current explanations for the illusion. On the one hand, theories of lightness and brightness have sought to emphasise the importance of retinal/cortical processing (e.g., so-called ‘retinex’ theories; Land, 1977); on the other, the 3D class of illusions developed by Adelson demonstrate the need for wider image viewing context to be included in explanations of lightness and brightness perception. For the latter, lightness differences become apparent when the three-dimensional object is directionally illuminated by a point source. Our motivation is to determine the parts of the Adelson checker-block (Adelson, 1993, Figure 1) stimulus that drive the switch from simple brightness responses to lightness responses. In this study we develop the assessment of the resilience of the Adelson checker-block illusion in several, progressive, related ways. We examine the role of lighting source (e.g., Sun & Perona, 1998), whether it is assumed to come from above or below; or from one side or the other. We simultaneously examine the role of scene complexity (sometimes referred to as articulation; Gilchrist et al., 1999), and the extent to which edges, panels, and shadows influence the way in which participants perceive the relative lightness of the two target panels of the Adelson stimulus.

The choice of conditions for the study emerged from a teaching exercise with a cohort of Junior Honours undergraduates enrolled on a BSc Psychology degree. Students selected an illusion that they wanted to design an experiment for, and while they initially chose the Adelson checker-shadow illusion, we eventually decided upon the checker-blocks illusion as it was considered more appropriate for an experimental design. Implementing a problem-based learning (e.g., Barrows & Tamblyn, 1980) approach with the students had the benefit of being able to include conditions inspired by the literature available, but also to include conditions inspired by insights, inferences, and deductions from the class. For example, in the class discussions, one explanation for the illusion from students was that perhaps observers may prefer illumination from the left since (for right handers at least), this would make handwriting visible rather than shaded. There is evidence for a left-side preference for illumination in art (McManus et al., 2004).

The observer's heuristic that light can be generally assumed to come from above as a cue to illumination was documented by Brewster (1826), in the 19th century. Sun and Perona (1998) explain how 3D scene interpretation often requires the visual system to guess the position of a light source to interpret concavities. In the current study, our primary stimulus manipulation is to include inverted stimuli–as used for example by Kobayashi and Morikawa (2019). By ‘flipping’ the stimulus pattern upside down, the normal assumptions about lighting from shadows are challenged and the resilience of the illusion to such high-level disruption (uprightness) tested. In addition to the light from above prior, Adams (2007) argued that ‘above left’ lighting can guide behaviour in some reflectance tasks. In this study, in addition to light from above (and inverted), we introduced variants of the checker blocks ‘lit from the left’, and ‘lit from the right’; thus, creating four different primary lighting scenarios for the stimulus.

The second avenue of investigation, scene complexity, is designed to gradually remove three-dimensional pictorial elements within the stimulus to titrate the illusion down to test which aspects of the three-dimensional scene are required for participants to perceive lightness differences. Here our systematic removal of shadow cues, edge cues and individual panels from the checker-block stimulus array directly manipulates those cues which might enable an observer to judge the illumination and structure of the three-dimensional scene. This may relate to articulation which is defined at the degree of complexity within the scene (Gilchrist and Annan, 2002; Katz, 1935). Katz's argues that the greater the complexity, the more reliable the lightness judgement. Henneman (1935, cited in Gilchrist et al., 1999) suggested that when more objects were set in different planes (tridimensionality) this led to more reliable lightness responses.

These pictorial cues inform judgements of the three-dimensional structure of the scene; however, they also provide cues towards an understanding of illumination upon the scene. To ensure that observers could parse the checker-block stimulus with or without pictorial elements, we incorporated a coloured background (green) (see Figure 1). The green background was revealed when picture elements were removed, allowing observers to better understand the structure of the checker-blocks. From the classic Adelson (1993) pattern we varied the presence or absence of the top panel adjacent to A; the right side of the canonical stimulus (i.e., the panels adjacent to B); the left side of the canonical stimulus; the shadow. We introduced an additional pictorial cue on top of Adelson's original which was the tracing of each of the pictorial elements with edges. This served to maintain the overall outline of the Adelson checker-block stimuli even in the absence of many of the elements.

We generated multiple versions of this stimulus and deconstructed the rendered scene, and measured participant responses to judgements of lightness matches. Edges and colour panels in the upright and inverted images are locally identical, only their global arrangement is varied in the inverted versus upright images. By assessing the strength or weakness of the illusion in observers, that is, the perceived lightness difference between the two target panels A and B, we identify the key drivers of lightness responses. The responses reflect a deeper understanding of the scene's structure and illumination by establishing the extent to which observers discount each cue in the Adelson Illusion. Figure 1 shows the fully dressed stimulus, and Figures 4 and 5 show the illusion in differing states of deconstruction.

Figure 4.

Generalised linear mixed effect model fits compared to averaged participant responses; each symbol represents the mean response across participants compared to the mean response for the model. The symbols were chosen to represent the key stimulus properties – see key to the right. The inset exemplar images show the stimuli that correspond to symbols. To view each stimulus in sequence, view the GIF shared on OSF (https://osf.io/k4agx). Open symbols indicate scenes that are lit from the left and closed symbols indicate scenes lit from the right.

Figure 5.

The lower-diagram shows the presence or absence of key stimulus parameters (right-side, top and lit-from-left). The greatest shift from brightness to lightness responses is shown to the right-hand side of the upper plot, this corresponds to the stimulus with each of the components present and presented in an upright configuration (i.e., three solid black circles on the lower stave). (Upper plot) Mean responses for key stimulus conditions. Black symbols represent participant responses. The upright triangles represent averaged responses for upright stimuli, where the triangles point downwards, they represent the responses for inverted (upside-down) stimuli. Error bars show 95% bootstrapped confidence intervals.

Method

Participants

Participants (N = 123) were undergraduate students enrolled on a BSc Psychology degree programme. All participants had normal or corrected-to-normal vision and gave their informed consent to take part in the study. Ethical approval (SHS_S_2014-15_41) for this study was granted by the Abertay University Social and Applied Sciences Ethics committee. After completing the study participants would receive a course credit. We did not record any demographic information.

Stimuli were rendered in Radiance (Ward, 1994) which is reported to reliably simulate lighting and shadows in virtual scenes (Ruppertsberg & Bloj, 2006). Stimuli creation was automated using a scripted wrapper written in Matlab (Mathworks, 2018). We began by creating a scene matching that presented by Adelson (2000, Figure 24.7). The scene featured a green [RGB: 158 190 158] ground plane so that deletions from the scene would be more easily interpretable by the viewer, when a surface was removed the green ground plane would become visible – when pilot images featured a grey ground-plane removed surfaces would result in images that looked largely unchanged. The scene featured cubes arranged as a wall. Two blocks had a lighter level of reflectance while two more had a darker level of reflectance (see Table 1). The images were rendered iteratively with varying levels of reflectance until the pixel values of the key surfaces (marked by ‘A’ and ‘B’ in Figure 1) were the same [138, 138, 138]. This process was repeated for two scenes, one illuminated from the left and another illuminated from the right. Additionally, these scenes were inverted (i.e., flipped upside-down), and as a result different groups of participants encountered the four scenes: inverted and lit from the left (n = 34), inverted and lit from the right (n = 21), not inverted and lit from the left (n = 39), not inverted and lit from the right (n = 29).

Table 1.

Key values in scene models and final RGB values for the A and B panels.

Condition	Sun elevation	Sun azimuth	Dark cube reflectance	Light cube reflectance	Patch (A and B) RGB
LitLeft = 0	55°	108°	0.1500	0.1200	138, 138, 138
LitLeft = 1	55°	−24°	0.4099	0.5627	138, 138, 138

The introduction of the lit from left/lit from right contrast involved the change in the direction of the light source and variations in the reflectance of the cubes within the scene. The experiment requires the maintenance of the identical irradiance of panels A and B, therefore by changing the light, the illumination changes the background. It should be emphasised that this is an essential change in the scene which has the effect of making the top panel adjacent to the target panel appear whiter in the lit from left conditions.

After the two illumination scenes were created, each pictorial component of the image was isolated (right-side, left-side, top, shadow). A line drawn version of each scene was created which featured the visible outline of each block and the outline of the shadow (referred to as edges). Subsequently stimuli were created by combining the different pictorial elements in all (full-factorial) combinations – see examples in Figure 4. The ‘A’ and ‘B’ panels, that participants were asked to compare, were present in all stimuli, apart from a control stimulus where the ‘A’ and ‘B’ panels were replaced with similarly sized gray circles with the same brightness levels. The latter stimulus was included to assess any response bias participants might have when comparing the brightness of the two image regions. Such a bias could be due to both cognitive processes and due to inhomogeneities of the brightness levels across the participant's screen.

The stimulus presentation software was created using PsychoPy 1.90.3 (Peirce et al., 2019) and compiled for online presentation. Clearly, presenting carefully calibrated stimuli online is problematic, as we have no control of the exact brightness settings of an individual screen, nor of the screen's linearity. Images created by Radiance are linearised, we encoded the images with a gamma curve (exp = 0.45) to match-up with the standard display decoding exponent of 2.2. We did not attempt to linearise each participant's individual screen as this seemed more likely to result in display errors (see Epicoco et al., 2024 for a useful discussion of such issues). Regardless of calibration, the Adelson illusion is very robust to variations in display characteristics, it is effective on website demonstrations and within textbooks. To counter any potential problems, all stimuli were created as whole uncompressed .png images, so all pictorial parts of the images would be subject to the same brightness lookup table and presentation timing. The response images, illustrating grey panels with varying brightness differences, were also complete images, featuring colour values sampled from the stimulus scene. Thus, the pixel levels in the stimuli and the response image would both co-vary exactly with any screen peculiarities. Finally, we included control stimulus which just featured grey circles replacing the ‘A’ and ‘B’ panels, removing the final pictorial cue, the shape of the ‘A’ and ‘B’ panels, any peculiar responses to these stimuli should reveal observer biases or peculiarities in screen characteristics.

In the current study the instructions stated that: ‘In this study you will be shown a series of different images. In each image there will always be a pair of coloured grey areas to the left of the letters “A” and “B”, your task is to decide whether the area “A” is lighter or darker than the area “B”. If the appearance of A is lighter than B, then you would press a key from 6 to 9. If you think A appears darker, then you would press a key from 1 to 4. If you think that A and B have equal lightness, then you would press key 5’ (see Figure 2). The colours of the A and B panels upon the response grid were a 9-step linear progression from the lightest to the darkest panels present within the stimulus image.

Figure 2.

The instructions that were presented to the participants prior to the experiment commencing.

For each trial the stimulus was displayed and after four seconds the response image (Figure 2, bottom) was presented. The stimulus and response image remained on screen until a participant responded via a key press.

Results

Anonymised raw data and analysis scripts are available on the Open Science Framework (Lovell et al., 2025). Our dataset of responses provides a rich set of 3,597 observer responses spread across the 128 unique experimental conditions. The dataset affords three levels of analysis:

1. We can explore the averaged response to each unique condition, investigation how each stimulus property influences the participants choice of response (see Figure 3).

2. To investigate the relative strength of each stimulus property in driving responses we will present a generalised linear mixed effects model, allowing us to identify the strongest drivers of the switch from brightness to lightness responses. This analysis will seek the minimally adequate model (MAM) based upon the BIC measure of model performance.

3. While 1 and 2 may provide some insights into the factors responsible for the change in participants responses, the most effective use of the current dataset would be to present the stimuli to image-based models of lightness processing, this final step is facilitated by the sharing of the whole set of stimuli and responses and image-values in order that they can be processed by visual models.

Figure 3.

(Lower-panel) The pattern of black circles represents the structure of the stimulus image shown, the presence of a black circle means the stimulus element was visible – for ‘isInverted’ a black circle means the whole image was flipped upside-down. (Upper-panel) The circles show how averaged participant responses vary as components of the stimuli were manipulated, error bars represent bootstrapped 95% confidence intervals. Data are sorted by the participant responses (leftmost are the stimuli that result in panel ‘A’ being visibly darker than panel ‘B’. ‘x’ marks the stimuli-components that correspond to the right-most stimuli presented in Figure 5.

For each scenario (inverted on/off and lit from left/right), each participant viewed each of the stimuli five times. We first calculated the average response to each of these five presentations, giving 32 values for the 2⁵ combinations of each scene feature (top, rightside, leftside, edges and shadow) plus another averaged response for the baseline condition which simply featured two circles with brightness values corresponding to the key panels within the Adelson scenes. Stimulus levels for each scene property were coded with a binary representation, that is, if the rightside was visible then rightside = 1 if it was deleted then rightside = 0. The between-subjects factors were coded similarly, with a binary coding of inverted=1 representing situations where the scene images were presented flipped in the y-axis. Data were imported into Jamovi (version 2.5; The jamovi project, 2024) where all subsequent analyses were conducted.

Participant responses for the baseline stimuli (just coloured circles) across the upright or inverted and lit-from-left or lit-from-right conditions violated the assumptions of normality (W = 0.915, p < .001). Lighting direction and inversion were computed into a variable that encoded all four combinations of the between-subject conditions. A Kruskal–Wallis test revealed no significant differences between the participants responses (χ² = 5.97, df = 3, p = 0.113) across the lighting direction and inversion conditions. Participants’ responses across these conditions were generally close to 5 which corresponded to the no-colour-difference on the response image. The non-significant result confirms that participants in each between-subjects group had no obvious biases (e.g., due to cognitive processes or inhomogeneities of the brightness levels across the participant's screen) that might undermine the subsequent analyses.

With the baseline (just coloured circles) condition excluded we have a total of 128 different scene presentations (4 between × 32 within-participants levels) to analyse. The simplest analysis would be to calculate the mean response for each experimental level and then to rank those responses in each condition (see Figure 3) and to explore those factors which result in a shift from a brightness response to one that reflects lightness, that is, a shift from ‘5’ responses towards ‘1’ on the graphical response scale (see Figure 1 bottom).

While our intention was to offer a dataset for future perceptual modelling, here we provide a parsimonious statistical summary of the key drivers of responses in our study. The mean participant response was fitted to a generalised linear mixed effects model (GAMLj jamovi module; Gallucci, 2019), with a Gamma distribution and an identity link function. The data corresponding with the baseline condition, approximately 3.03% of the total dataset, were not included in the modelling. Participant was fitted as a random intercept, with fixed effects top, rightside, leftside, edges, shadow, isInverted and litLeft.

To begin with, all fixed effects and their interactions were fitted, starting with the highest order interactions, and the BIC values of each model evaluated. Across each level, we identified that the model with the lowest BIC had a combination of two-way and three-way interactions (each modelling stage is shared on OSF). From a model with every three-way interaction, we sequentially deleted the fixed-effects with the lowest χ², which were also not involved in a higher-order interaction, until the BIC stopped decreasing. We followed the convention that models with a BIC difference of 2.0 or less do not differ in their fit of the data (Fabozzi et al., 2014). When BIC values were less than 2.0, we made the parsimonious choice of selecting the simpler model. The model which results in the lowest overall BIC (i.e., the minimally adequate model; MAM) is adopted as the best available model, thereby balancing the number of free parameters and quality of fit. The final model (BIC: 5019.145) had the following formula:

$$\begin{array}{rl}& \mathrm{meanKey}\sim \mathrm{isInverted}*\mathrm{edges}+\mathrm{rightside}*\mathrm{edges}+\mathrm{litLeft}*\mathrm{shadow}+\mathrm{litLeft}\\ & *\mathrm{leftside}+\mathrm{isInverted}*\mathrm{top}+\mathrm{isInverted}*\mathrm{litLeft}*\mathrm{rightside}+(1|\mathrm{Participant})\end{array}$$

The final model showed a significant three-way interaction between the orientation of the stimuli, the three panels adjacent to B and the direction of the lighting (χ²(1) = 19.83, p < .001). The model also showed significant two-way interactions between the orientation of the stimuli and the panel adjacent to A (χ²(1) = 69.25, p < .001), the presence of edges (χ²(1) = 12.92, p < .001) and the three panels adjacent to B (χ²(1) = 980.13, p < .001). The lighting direction did not significantly interact with the orientation of the stimuli (χ²(1) = 1.07, p = .30). However, the direction of lighting significantly interacted with the presence of shadows (χ²(1) = 25.25, p < .001), the presence of the left side (χ²(1) = 29.64, p < .001), and the three panels adjacent to B (χ²(1) = 37.13, p < .001). There was also a significant interaction between the three panels adjacent to B and the presence of edges (χ²(1) = 20.32, p < .001). The presence of edges, the lighting direction and the presence of the left side did not have a significant main effect on the participant's response (χ²(1) = 2.46, p = .117; χ²(1) = 0.07, p = .794; χ²(1) = 3.72, p = .05, respectively). There were significant main effects of the orientation of the stimuli (χ²(1) = 34.84, p < .001), the presence of the three panels adjacent to B (χ²(1) = 1531.89, p < .001), the presence of the panel adjacent to A (χ²(1) = 115.59, p < .001), and the presence of a shadow (χ²(1) = 38.52, p < .001). These results and the estimates from the generalised liner mixed effects model are presented in Table 2. Model fits are compared to mean participant responses in Figure 4, below.

Table 2.

Results from the generalised linear mixed effects model of the minimally adequate model.

						95% confidence intervals
Names	χ 2	df	Effect	Estimate	SE	Lower	Upper	z	p
(Intercept)			(Intercept)	4.80	0.05	4.71	4.90	96.22	<.001
top1	115.59	1	1 - 0	−0.15	0.01	−0.18	−0.12	−10.75	<.001
leftside1	3.72	1	1 - 0	−0.03	0.01	−0.05	4.43 × 10−4	−1.93	0.054
litLeft1	0.07	1	1 - 0	0.03	0.10	−0.17	0.22	0.26	0.794
edges1	2.46	1	1 - 0	0.02	0.01	−0.01	0.05	1.57	0.117
shadow1	38.52	1	1 - 0	−0.09	0.01	−0.11	−0.06	−6.21	<.001
isInverted1	34.84	1	1 - 0	0.59	0.10	0.39	0.78	5.90	<.001
rightside1	1531.89	1	1 - 0	−0.57	0.01	−0.60	−0.54	−39.14	<.001
isInverted1 * rightside1	980.13	1	(1 - 0) * (1 - 0)	0.92	0.03	0.86	0.97	31.31	<.001
litLeft1 * rightside1	37.13	1	(1 - 0) * (1 - 0)	−0.18	0.03	−0.24	−0.12	−6.09	<.001
edges1 * isInverted1	12.92	1	(1 - 0) * (1 - 0)	−0.10	0.03	−0.16	−0.05	−3.59	<.001
edges1 * rightside1	20.32	1	(1 - 0) * (1 - 0)	0.12	0.03	0.07	0.18	4.51	<.001
leftside1 * litLeft1	29.64	1	(1 - 0) * (1 - 0)	−0.15	0.03	−0.21	−0.10	−5.44	<.001
top1 * isInverted1	69.25	1	(1 - 0) * (1–0)	0.24	0.03	0.18	0.29	8.32	<.001
litLeft1 * shadow1	25.25	1	(1 - 0) * (1 - 0)	−0.14	0.03	−0.19	−0.08	−5.03	<.001
litLeft1 * isInverted1	1.07	1	(1 - 0) * (1 - 0)	0.21	0.20	−0.18	0.60	1.04	0.300
litLeft1 * isInverted1 * rightside	19.83	1	(1 - 0) * (1 - 0) * (1 - 0)	0.26	0.06	0.15	0.38	4.45	<.001

The table presents both omnibus tests for fixed effects and parameter estimates. Note that the p-values are shared across both fixed effects and parameter estimates. The χ² value represents the likelihood ratio tests, which assess whether each predictor or interaction significantly improves the model fit. The estimate column provides the fixed effect coefficients, where negative values indicate a decrease in response (i.e., a lightness response), relative to the reference level. Significant factors (p < .05) are presented as bold.

The inclusion of participant as a random intercept significantly improves the model fit (χ²(1) = 2620, p < .001), suggesting that responses varied between participants. The model explains 97% of the variance in the data (R² = 0.97, see Figure 4) when including participant as a random intercept. When examining the model's fit of the data with only the fixed effects, it explains 85% of the variance (R² = 0.846), indicating that the fixed effects are the main driver of the participant's response.

The estimates in Table 2 indicate that the four main factors that drive participant's response are the orientation of the stimuli (isInverted), the presence of the panel adjacent to panel ‘A’ (top), the presence of the three panels adjacent to panel ‘B’ (rightside) and the lighting direction (litleft). When the stimulus is inverted, participant's response increases (i.e., towards a brightness response; β = 0.59, SE = 0.10, 95% CI [0.39 0.78], p < .001). However, when the panels adjacent to ‘A’ and ‘B’ were present the participant's response decreases (i.e., towards a lightness response; β = −0.15, SE = 0.01, 95% CI [−0.18 −0.12], p < .001; β = −0.57, SE = 0.10, 95% CI [−0.60 −0.54], p < .001, respectively). Notwithstanding this, lighting direction does not have a significant main effect and only influences the participant's response when interacting with other factors (see Table 2). When fitting a model (BIC 5126.094) that involves only these main factors, that is, dropping leftside, edges and shadows, the fixed effects explain 84% of the variance. The averaged participant responses over these main factors are presented in Figure 5.

Discussion

We found that the relevant drivers of the responses indicating a difference in perceived brightness of the A and B panels are ‘uprightness’; the surface shading adjacent to the ‘A’ and ‘B’ panels and lighting direction. Lesser factors include the cast shadow and non-adjacent surface shading.

One of the main factors driving a lightness response is the presence of the right-hand side of the blocks (i.e., the three panels adjacent to ‘B’) in the stimulus, which is consistent with the co-planar ratio principle (Gilchrist, 1977). These blocks neighbour the shaded surface and extend to the top surface, which, assuming the lightest upper block is uniformly coloured, gives an indication of the direction and diffuseness of the illumination. This effect, however, is overridden when the stimulus is inverted, which drives participants towards a brightness response. The reduction in perceived differences could be due to difficulties participants might have interpreting the ambiguous images when inverted. However, it is likely due to light-from-above biases (Brewster, 1826; Johnston et al., 2013; Sun & Perona, 1998). The top surface, adjacent to the upper directly illuminated horizontal surface, is also influential. This surface, in concert with the upper right-hand surface (i.e., panel ‘A’) gives further information of the light-field.

The effect of lighting direction on the illusion is highly context dependent. In particular, the effect is dependent upon the orientation of the stimulus and the presence of the right-hand side. Lighting direction accentuates the effect that the right-hand side has on the participant's response. However, the modulation of the effect of the right-hand side by lighting direction is contingent upon whether the stimulus is inverted or not. This further indicates that participant responses are driven by a light-from-above bias (Brewster, 1826; Johnston et al., 2013; Sun & Perona, 1998). Furthermore, when lighting direction is combined with the presence of the left-hand side of the blocks and a shadow, participants were driven towards a lightness response. These components provide additional cues which give the viewer an indication of the light field. It is worth noting, however, that lighting direction has no independent effect on the participant's response: suggesting that lighting direction means nothing if there are not additional cues that inform the viewer of the structure of illumination.

While we explored the drivers of lightness responses by breaking the stimulus into key image components [right-side, top, etc.] a reappraisal of our models reveals how the key drivers of the lightness response may relate to a higher category of indirectly and directly illuminated areas that are proximate to the test panels or are non-adjacent [left-side panels, the leftward cast shadow]. For example, the strongest cues within upright stimuli were right-side and top (see Figure 5). The right-side panels are important as they reveal the right-side surface is shaded, but they also reveal that the four blocks have a checkerboard pattern. The additional adjacent panel top is directly illuminated and reveals the nature of the direct illumination, this is helpful in revealing the nature of the light field overall when presented in-concert with the right-side panels. However, neither the right-side nor top panels help drive a lightness response when the image is inverted, it seems participants simply did not establish reliable understanding of the scene lighting in the upside-down stimulus, even when all image components were present.

The wireframe presentation, when panels were omitted but edges included, could provide a cue towards the global shape of the scene. However, the shape cue alone does not seem to result in lightness responses, possibly because the outline on its own, without cues towards panel shading does not help in the interpretation of the light field. This is true even when there are edges, shadows and the distal surface away from the ‘A’ and ‘B’ panels (left-side) were present (e.g., see inset image at Figure 4, location x = 4.4 y = 5.2). Additionally, where outlines (edges) are added to shadows they look rather more like a plinth. It arguably makes the illusion more like a drawing and less like a photo-realistic rendering of a scene.

Conclusions

For most of human evolution, it has been a useful working assumption that light originates from above (Sun & Perona, 1998), excepting campfires, sunrises and sunsets. The strong effect of stimulus orientation in our results is likely to reflect the interaction of this prior with the contents of the image. Therefore, it is curious that the lightness and brightness community often chooses to disregard this fact and instead work with highly atypical lighting conditions and explanations that operate at the neural level in the retina and the early visual cortex. Our findings indicate that future studies may need to include conditions that widen the lighting and viewing contexts. Such conditions could include the scene inversion and variations in lighting directions that we have used in the current study. Further stimulus conditions manipulating lighting could include creating a negative stimulus image by colour inversion, that is, an image with reversed tones – dark areas appear light, light areas appear dark and colours shifted to their complementary counterparts. Bearing in mind that Felleman and van Essen (1991) and subsequent authors have pointed out that 40% of connections in the early visual system are descending, it would be prudent to assume a top-down influence in lightness and brightness perception, even in judgments whose physiological location would apparently be retinal or early in the visual cortex. Given our results show a very strong flipping effect, it seems worthwhile to include light from above biases within even the simplest models.

Limitations

It is possible that the deletion of some surfaces within the stimuli made the objects sometimes less plausible in terms of physical entities, for example leaving floating panels unsupported by lower structures, or removing panels while the shadows they cast remained unchanged. While these may be questionable in terms of physical plausibility, we have many consistent participant responses to these stimuli and comparing their responses to model responses to these images should reveal where models respond implausibly to peculiar stimuli.

The nine-step response mechanism was relatively coarse in nature, however the precision of the responses was improved by averaging responses to five repeated trials for each unique stimulus.

Clearly, it is the nature of online studies that we give-up some control over screen brightness, linearisation and colour calibration when running such a study online. However, each stimulus was presented on screen as a single-image, so any peculiarities of screen brightness were shared by all pictorial aspects of the image, including the response-scale image. It is likely that attempts to calibrate individual screens without supervision can result in gamma corrections that are incorrect (Epicoco et al., 2024).

Summary

Adelson's Checker-Block illusion provides a challenge for models of brightness and lightness, which have been developed to explain simpler two-dimensional stimuli successfully. Our dataset offers the additional complexity of 3D elements and cast shadows, as well as systematic removal of elements articulating the scene. The key drivers of lightness perception in the illusion are scene structure and illumination and not patch luminance (as RGB values, which were always identical across all trials). Perceived surface uprightness, and adjacent luminance (irradiance) are most significant, while cast shadows and non-adjacent luminance contribute less. The data challenge pure ‘brightness only’ explanations or models; and demonstrate the importance of both spatial and contextual cues. We hope the deconstruction of the stimulus paired with the participant responses, individually and in aggregate can permit the testing and development of models to enhance their validity and extend their generalisability.

• Those shaded surfaces co-planar to panel A principally drive the switch from brightness to lightness.

• The shaded surface is more important than the upper surface, though both are necessary for the strongest ‘lightness’ response. NB. The shaded surface has a larger area.

• Inversion of the stimulus seems to largely eliminate the effect of the Adelson Checker-Block Illusion.