What are lightness illusions and why do we see them?

Lightness Perception in Complex Scenes

Lightness perception is the perception of achromatic surface colors: black, white, and shades of grey. Lightness has long been a central research topic in experimental psychology, as perceiving surface color is an important visual task but also a difficult one due to the deep ambiguity of retinal images. In this article, I review psychophysical work on lightness perception in complex scenes over the past 20 years, with an emphasis on work that supports the development of computational models. I discuss Bayesian models, equivalent illumination models, multidimensional scaling, anchoring theory, spatial filtering models, natural scene statistics, and related work in computer vision. I review open topics in lightness perception that seem ready for progress, including the relationship between lightness and brightness, and developing more sophisticated computational models of lightness in complex scenes. Expected final online publication date for the Annual Review of Vision Science, Volume 7 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Dynamic decorrelation as a unifying principle for explaining a broad range of brightness phenomena

The visual system is highly sensitive to spatial context for encoding luminance patterns. Context sensitivity inspired the proposal of many neural mechanisms for explaining the perception of luminance (brightness). Here we propose a novel computational model for estimating the brightness of many visual illusions. We hypothesize that many aspects of brightness can be explained by a dynamic filtering process that reduces the redundancy in edge representations on the one hand, while non-redundant activity is enhanced on the other. The dynamic filter is learned for each input image and implements context sensitivity. Dynamic filtering is applied to the responses of (model) complex cells in order to build a gain control map. The gain control map then acts on simple cell responses before they are used to create a brightness map via activity propagation. Our approach is successful in predicting many challenging visual illusions, including contrast effects, assimilation, and reverse contrast with the same set of model parameters.

Themes of advanced information processing in the primate brain

Here is a review of several empirical examples of information processing that occur in the primate cerebral cortex. These include visual processing, object identification and perception, information encoding, and memory. Also, there is a discussion of the higher scale neural organization, mainly theoretical, which suggests hypotheses on how the brain internally represents objects. Altogether they support the general attributes of the mechanisms of brain computation, such as efficiency, resiliency, data compression, and a modularization of neural function and their pathways. Moreover, the specific neural encoding schemes are expectedly stochastic, abstract and not easily decoded by theoretical or empirical approaches.

More than noise: context-dependent luminance contrast discrimination in a coral reef fish (Rhinecanthus aculeatus)

Achromatic (luminance) vision is used by animals to perceive motion, pattern, space and texture. Luminance contrast sensitivity thresholds are often poorly characterised for individual species and are applied across a diverse range of perceptual contexts using over-simplified assumptions of an animal's visual system. Such thresholds are often estimated using the receptor noise limited model (RNL). However, the suitability of the RNL model to describe luminance contrast perception remains poorly tested. Here, we investigated context-dependent luminance discrimination using triggerfish (Rhinecanthus aculeatus) presented with large achromatic stimuli (spots) against uniform achromatic backgrounds of varying absolute and relative contrasts. 'Dark' and 'bright' spots were presented against relatively dark and bright backgrounds. We found significant differences in luminance discrimination thresholds across treatments. When measured using Michelson contrast, thresholds for bright spots on a bright background were significantly higher than for other scenarios, and the lowest threshold was found when dark spots were presented on dark backgrounds. Thresholds expressed in Weber contrast revealed lower thresholds for spots darker than their backgrounds, which is consistent with the literature. The RNL model was unable to estimate threshold scaling across scenarios as predicted by the Weber-Fechner law, highlighting limitations in the current use of the RNL model to quantify luminance contrast perception. Our study confirms that luminance contrast discrimination thresholds are context dependent and should therefore be interpreted with caution.

Color illusions also deceive CNNs for low-level vision tasks: Analysis and implications

The study of visual illusions has proven to be a very useful approach in vision science. In this work we start by showing that, while convolutional neural networks (CNNs) trained for low-level visual tasks in natural images may be deceived by brightness and color illusions, some network illusions can be inconsistent with the perception of humans. Next, we analyze where these similarities and differences may come from. On one hand, the proposed linear eigenanalysis explains the overall similarities: in simple CNNs trained for tasks like denoising or deblurring, the linear version of the network has center-surround receptive fields, and global transfer functions are very similar to the human achromatic and chromatic contrast sensitivity functions in human-like opponent color spaces. These similarities are consistent with the long-standing hypothesis that considers low-level visual illusions as a by-product of the optimization to natural environments. Specifically, here human-like features emerge from error minimization. On the other hand, the observed differences must be due to the behavior of the human visual system not explained by the linear approximation. However, our study also shows that more 'flexible' network architectures, with more layers and a higher degree of nonlinearity, may actually have a worse capability of reproducing visual illusions. This implies, in line with other works in the vision science literature, a word of caution on using CNNs to study human vision: on top of the intrinsic limitations of the L + NL formulation of artificial networks to model vision, the nonlinear behavior of flexible architectures may easily be markedly different from that of the visual system.

Effect of Spatial Structure Defined by Binocular Disparity with Uniform Luminance on Lightness

We examined whether lightness is determined based on the experience of the relationship between a scene’s illumination and its spatial structure in actual environments. For this purpose, we measured some characteristics of scene structure and the illuminance in actual scenes and found some correlations between them. In the psychophysical experiments, a random-dot stereogram consisting of dots with uniform distribution was used to eliminate the effects of local luminance and texture contrasts. Participants matched the lightness of a presented target patch in the stimulus space to that of a comparison patch by adjusting the latter’s luminance. Results showed that the matched luminance tended to increase when the target patch was interpreted as receiving weak illumination in some conditions. These results suggest that the visual system can probably infer a scene’s illumination from a spatial structure without luminance distribution information under an illumination–spatial structure relation.

Colorful glares: Effects of colors on brightness illusions measured with pupillometry

We hypothesized that pupil constrictions to the glare illusion, where converging luminance gradients subjectively enhance the perception of brightness, would be stronger for 'blue' than for other colors. Such an expectation was based on reflections about the ecology of vision, where the experience of dazzling light is common when one happens to look directly at sunlight through some occluders. Thus, we hypothesized that pupil constrictions to 'blue' reflect an ecologically-based expectation of the visual system from the experience of sky's light and color, which also leads to interpret the blue gradients of illusory glare to act as effective cues to impending probable intense light. We therefore manipulated the gradients color of glare illusions and measured changes in subjective brightness of identical shape stimuli. We confirmed that the blue resulted in what was subjectively evaluated as the brightest condition, despite all colored stimuli were equiluminant. This enhanced brightness effect was observed both in a psychophysical adjustment task and in changes in pupil size, where the maximum pupil constriction peak was observed with the 'blue' converging gradients over and above to the pupil response to blue in other conditions (i.e., diverging gradients and homogeneous patches). Moreover, glare-related pupil constrictions for each participant were correlated to each individual's subjective brightness adjustments. Homogenous blue hues also constricted the pupil more than other hues, which represents a pupillometric analog of the Helmholtz-Kohlrausch effect on brightness perception. Together, these findings show that pupillometry constitutes an easy tool to assess individual differences in color brightness perception.

Stripping #The Dress: the importance of contextual information on inter-individual differences in colour perception

In 2015, a picture of a Dress (henceforth the Dress) triggered popular and scientific interest; some reported seeing the Dress in white and gold (W&G) and others in blue and black (B&B). We aimed to describe the phenomenon and investigate the role of contextualization. Few days after the Dress had appeared on the Internet, we projected it to 240 students on two large screens in the classroom. Participants reported seeing the Dress in B&B (48%), W&G (38%), or blue and brown (B&Br; 7%). Amongst numerous socio-demographic variables, we only observed that W&G viewers were most likely to have always seen the Dress as W&G. In the laboratory, we tested how much contextual information is necessary for the phenomenon to occur. Fifty-seven participants selected colours most precisely matching predominant colours of parts or the full Dress. We presented, in this order, small squares (a), vertical strips (b), and the full Dress (c). We found that (1) B&B, B&Br, and W&G viewers had selected colours differing in lightness and chroma levels for contextualized images only (b, c conditions) and hue for fully contextualized condition only (c) and (2) B&B viewers selected colours most closely matching displayed colours of the Dress. Thus, the Dress phenomenon emerges due to inter-individual differences in subjectively perceived lightness, chroma, and hue, at least when all aspects of the picture need to be integrated. Our results support the previous conclusions that contextual information is key to colour perception; it should be important to understand how this actually happens.

Perceptual Dominance in Brief Presentations of Mixed Images: Human Perception vs. Deep Neural Networks

Visual perception involves continuously choosing the most prominent inputs while suppressing others. Neuroscientists induce visual competitions in various ways to study why and how the brain makes choices of what to perceive. Recently deep neural networks (DNNs) have been used as models of the ventral stream of the visual system, due to similarities in both accuracy and hierarchy of feature representation. In this study we created non-dynamic visual competitions for humans by briefly presenting mixtures of two images. We then tested feed-forward DNNs with similar mixtures and examined their behavior. We found that both humans and DNNs tend to perceive only one image when presented with a mixture of two. We revealed image parameters which predict this perceptual dominance and compared their predictability for the two visual systems. Our findings can be used to both improve DNNs as models, as well as potentially improve their performance by imitating biological behaviors.

Coral reef fish perceive lightness illusions

Visual illusions occur when information from images are perceived differently from the actual physical properties of the stimulus in terms of brightness, size, colour and/or motion. Illusions are therefore important tools for sensory perception research and from an ecological perspective, relevant for visually guided animals viewing signals in heterogeneous environments. Here, we tested whether fish perceived a lightness cube illusion in which identical coloured targets appear (for humans) to return different spectral outputs depending on the apparent amount of illumination they are perceived to be under. Triggerfish (Rhinecanthus aculeatus) were trained to peck at coloured targets to receive food rewards, and were shown to experience similar shifts in colour perception when targets were placed in illusory shadows. Fish therefore appear to experience similar simultaneous contrast mechanisms to humans, even when targets are embedded in complex, scene-type illusions. Studies such as these help unlock the fundamental principles of visual system mechanisms.

Perception and Reality: Why a Wholly Empirical Paradigm is Needed to Understand Vision

A central puzzle in vision science is how perceptions that are routinely at odds with physical measurements of real world properties can arise from neural responses that nonetheless lead to effective behaviors. Here we argue that the solution depends on: (1) rejecting the assumption that the goal of vision is to recover, however imperfectly, properties of the world; and (2) replacing it with a paradigm in which perceptions reflect biological utility based on past experience rather than objective features of the environment. Present evidence is consistent with the conclusion that conceiving vision in wholly empirical terms provides a plausible way to understand what we see and why.

An exponential filter model predicts lightness illusions

Lightness, or perceived reflectance of a surface, is influenced by surrounding context. This is demonstrated by the Simultaneous Contrast Illusion (SCI), where a gray patch is perceived lighter against a black background and vice versa. Conversely, assimilation is where the lightness of the target patch moves toward that of the bounding areas and can be demonstrated in White's effect. Blakeslee and McCourt (1999) introduced an oriented difference-of-Gaussian (ODOG) model that is able to account for both contrast and assimilation in a number of lightness illusions and that has been subsequently improved using localized normalization techniques. We introduce a model inspired by image statistics that is based on a family of exponential filters, with kernels spanning across multiple sizes and shapes. We include an optional second stage of normalization based on contrast gain control. Our model was tested on a well-known set of lightness illusions that have previously been used to evaluate ODOG and its variants, and model lightness values were compared with typical human data. We investigate whether predictive success depends on filters of a particular size or shape and whether pooling information across filters can improve performance. The best single filter correctly predicted the direction of lightness effects for 21 out of 27 illusions. Combining two filters together increased the best performance to 23, with asymptotic performance at 24 for an arbitrarily large combination of filter outputs. While normalization improved prediction magnitudes, it only slightly improved overall scores in direction predictions. The prediction performance of 24 out of 27 illusions equals that of the best performing ODOG variant, with greater parsimony. Our model shows that V1-style orientation-selectivity is not necessary to account for lightness illusions and that a low-level model based on image statistics is able to account for a wide range of both contrast and assimilation effects.

Noise masking of White's illusion exposes the weakness of current spatial filtering models of lightness perception

Spatial filtering models are currently a widely accepted mechanistic account of human lightness perception. Their popularity can be ascribed to two reasons: They correctly predict how human observers perceive a variety of lightness illusions, and the processing steps involved in the models bear an apparent resemblance with known physiological mechanisms at early stages of visual processing. Here, we tested the adequacy of these models by probing their response to stimuli that have been modified by adding narrowband noise. Psychophysically, it has been shown that noise in the range of one to five cycles per degree (cpd) can drastically reduce the strength of some lightness phenomena, while noise outside this range has little or no effect on perceived lightness. Choosing White's illusion (White, 1979) as a test case, we replicated and extended the psychophysical results, and found that none of the spatial filtering models tested was able to reproduce the spatial frequency specific effect of narrowband noise. We discuss the reasons for failure for each model individually, but we argue that the failure is indicative of the general inadequacy of this class of spatial filtering models. Given the present evidence we do not believe that spatial filtering models capture the mechanisms that are responsible for producing many of the lightness phenomena observed in human perception. Instead we think that our findings support the idea that low-level contributions to perceived lightness are primarily determined by the luminance contrast at surface boundaries.

Standard deviation of luminance distribution affects lightness and pupillary response

We examined whether the standard deviation (SD) of luminance distribution serves as information of illumination. We measured the lightness of a patch presented in the center of a scrambled-dot pattern while manipulating the SD of the luminance distribution. Results showed that lightness decreased as the SD of the surround stimulus increased. We also measured pupil diameter while viewing a similar stimulus. The pupil diameter decreased as the SD of luminance distribution of the stimuli increased. We confirmed that these results were not obtained because of the increase of the highest luminance in the stimulus. Furthermore, results of field measurements revealed a correlation between the SD of luminance distribution and illuminance in natural scenes. These results indicated that the visual system refers to the SD of the luminance distribution in the visual stimulus to estimate the scene illumination.

A unified account of perceptual layering and surface appearance in terms of gamut relativity

When we look at the world--or a graphical depiction of the world--we perceive surface materials (e.g. a ceramic black and white checkerboard) independently of variations in illumination (e.g. shading or shadow) and atmospheric media (e.g. clouds or smoke). Such percepts are partly based on the way physical surfaces and media reflect and transmit light and partly on the way the human visual system processes the complex patterns of light reaching the eye. One way to understand how these percepts arise is to assume that the visual system parses patterns of light into layered perceptual representations of surfaces, illumination and atmospheric media, one seen through another. Despite a great deal of previous experimental and modelling work on layered representation, however, a unified computational model of key perceptual demonstrations is still lacking. Here we present the first general computational model of perceptual layering and surface appearance--based on a boarder theoretical framework called gamut relativity--that is consistent with these demonstrations. The model (a) qualitatively explains striking effects of perceptual transparency, figure-ground separation and lightness, (b) quantitatively accounts for the role of stimulus- and task-driven constraints on perceptual matching performance, and (c) unifies two prominent theoretical frameworks for understanding surface appearance. The model thereby provides novel insights into the remarkable capacity of the human visual system to represent and identify surface materials, illumination and atmospheric media, which can be exploited in computer graphics applications.

Complex cells decrease errors for the Müller-Lyer illusion in a model of the visual ventral stream

To improve robustness in object recognition, many artificial visual systems imitate the way in which the human visual cortex encodes object information as a hierarchical set of features. These systems are usually evaluated in terms of their ability to accurately categorize well-defined, unambiguous objects and scenes. In the real world, however, not all objects and scenes are presented clearly, with well-defined labels and interpretations. Visual illusions demonstrate a disparity between perception and objective reality, allowing psychophysicists to methodically manipulate stimuli and study our interpretation of the environment. One prominent effect, the Müller-Lyer illusion, is demonstrated when the perceived length of a line is contracted (or expanded) by the addition of arrowheads (or arrow-tails) to its ends. HMAX, a benchmark object recognition system, consistently produces a bias when classifying Müller-Lyer images. HMAX is a hierarchical, artificial neural network that imitates the “simple” and “complex” cell layers found in the visual ventral stream. In this study, we perform two experiments to explore the Müller-Lyer illusion in HMAX, asking: (1) How do simple vs. complex cell operations within HMAX affect illusory bias and precision? (2) How does varying the position of the figures in the input image affect classification using HMAX? In our first experiment, we assessed classification after traversing each layer of HMAX and found that in general, kernel operations performed by simple cells increase bias and uncertainty while max-pooling operations executed by complex cells decrease bias and uncertainty. In our second experiment, we increased variation in the positions of figures in the input images that reduced bias and uncertainty in HMAX. Our findings suggest that the Müller-Lyer illusion is exacerbated by the vulnerability of simple cell operations to positional fluctuations, but ameliorated by the robustness of complex cell responses to such variance.

The spinning dancer illusion and spontaneous brain fluctuations: an fMRI study

The brain activation associated with the Spinning Dancer Illusion, a cognitive visual illusion, is not entirely known. Inferences from other study modalities point to the involvement of the dorso-parieto-occipital areas in the spontaneous switchings of perception in other bistable non-kinetic illusions. fMRI is a mature technique used to investigate the brain responses associated with mental changes. Resting-state fMRI is a novel technique that may help ascertain the effects of spontaneous brain changes in the top-down regulation of visual perception. The purpose of this report is to describe the brain activation associated with the subjective illusory changes of perception of a kinetic bistable stimulus. We hypothesize that there is a relationship between the perception phases with the very slow cortical spontaneous fluctuations, recently described. A single normal subject who was trained to produce voluntarily perception phase switches underwent a series of fMRI studies whose blocks were either defined post-hoc or accordingly with a predefined timeline to assess spontaneous and voluntarily evoked visual perception switches, respectively. Correlation of findings with resting-state fMRI and independent component analysis of the task series was sought. Phases of the rotation direction were found associated with right parietal activity. Independent component analysis of the task series and their comparison with basal resting-state components suggest that this activity is related to one of the very slow spontaneous brain fluctuations. The spontaneous fluctuations of the cortical activity may explain the subjective changes in perception of direction of the Spinning Dancer Illusion. This observation is a proof-of-principle, suggesting that the spontaneous brain oscillations may influence top-down sensory regulation.

The Müller-Lyer Illusion in a computational model of biological object recognition

Studying illusions provides insight into the way the brain processes information. The Müller-Lyer Illusion (MLI) is a classical geometrical illusion of size, in which perceived line length is decreased by arrowheads and increased by arrowtails. Many theories have been put forward to explain the MLI, such as misapplied size constancy scaling, the statistics of image-source relationships and the filtering properties of signal processing in primary visual areas. Artificial models of the ventral visual processing stream allow us to isolate factors hypothesised to cause the illusion and test how these affect classification performance. We trained a feed-forward feature hierarchical model, HMAX, to perform a dual category line length judgment task (short versus long) with over 90% accuracy. We then tested the system in its ability to judge relative line lengths for images in a control set versus images that induce the MLI in humans. Results from the computational model show an overall illusory effect similar to that experienced by human subjects. No natural images were used for training, implying that misapplied size constancy and image-source statistics are not necessary factors for generating the illusion. A post-hoc analysis of response weights within a representative trained network ruled out the possibility that the illusion is caused by a reliance on information at low spatial frequencies. Our results suggest that the MLI can be produced using only feed-forward, neurophysiological connections.

The Adaptive Nature of Memory and Its Illusions

In this article I discuss how false memories do not always have to be associated with negative outcomes. Indeed, under some circumstances, memory illusions, like other illusions more generally, can have positive consequences. I discuss these consequences in the context of the adaptive function of memory, including how false memories can have fitness-relevant benefits for subsequent behavior and problem solving. My hope is that this article changes how illusions are conceptualized, especially those arising from memory. Rather than being a “demon” that vexes our theories of memory, illusions can be thought of as sometimes having positive consequences much in the same way as many of the other outputs of a very powerful, adaptive memory system.

Exact feature probabilities in images with occlusion

To understand the computations of our visual system, it is important to understand also the natural environment it evolved to interpret. Unfortunately, existing models of the visual environment are either unrealistic or too complex for mathematical description. Here we describe a naturalistic image model and present a mathematical solution for the statistical relationships between the image features and model variables. The world described by this model is composed of independent, opaque, textured objects, which occlude each other. This simple structure allows us to calculate the joint probability distribution of image values sampled at multiple arbitrarily located points, without approximation. This result can be converted into probabilistic relationships between observable image features as well as between the unobservable properties that caused these features, including object boundaries and relative depth. We show that the image model is sufficient to explain a wide range of natural scene properties. Finally, we discuss the implications of this description of natural scenes for the study of vision.

Lightness, brightness and transparency: a quarter century of new ideas, captivating demonstrations and unrelenting controversy

The past quarter century has witnessed considerable advances in our understanding of Lightness (perceived reflectance), Brightness (perceived luminance) and perceived Transparency (LBT). This review poses eight major conceptual questions that have engaged researchers during this period, and considers to what extent they have been answered. The questions concern 1. the relationship between lightness, brightness and perceived non-uniform illumination, 2. the brain site for lightness and brightness perception, 3 the effects of context on lightness and brightness, 4. the relationship between brightness and contrast for simple patch-background stimuli, 5. brightness "filling-in", 6. lightness anchoring, 7. the conditions for perceptual transparency, and 8. the perceptual representation of transparency. The discussion of progress on major conceptual questions inevitably requires an evaluation of which approaches to LBT are likely and which are unlikely to bear fruit in the long term, and which issues remain unresolved. It is concluded that the most promising developments in LBT are (a) models of brightness coding based on multi-scale filtering combined with contrast normalization, (b) the idea that the visual system decomposes the image into "layers" of reflectance, illumination and transparency, (c) that an understanding of image statistics is important to an understanding of lightness errors, (d) Whittle's logW metric for contrast-brightness, (e) the idea that "filling-in" is mediated by low spatial frequencies rather than neural spreading, and (f) that there exist multiple cues for identifying non-uniform illumination and transparency. Unresolved issues include how relative lightness values are anchored to produce absolute lightness values, and the perceptual representation of transparency. Bridging the gap between multi-scale filtering and layer decomposition approaches to LBT is a major task for future research.

The brightness of colour

Background

The perception of brightness depends on spatial context: the same stimulus can appear light or dark depending on what surrounds it. A less well-known but equally important contextual phenomenon is that the colour of a stimulus can also alter its brightness. Specifically, stimuli that are more saturated (i.e. purer in colour) appear brighter than stimuli that are less saturated at the same luminance. Similarly, stimuli that are red or blue appear brighter than equiluminant yellow and green stimuli. This non-linear relationship between stimulus intensity and brightness, called the Helmholtz-Kohlrausch (HK) effect, was first described in the nineteenth century but has never been explained. Here, we take advantage of the relative simplicity of this ‘illusion’ to explain it and contextual effects more generally, by using a simple Bayesian ideal observer model of the human visual ecology. We also use fMRI brain scans to identify the neural correlates of brightness without changing the spatial context of the stimulus, which has complicated the interpretation of related fMRI studies.

Results

Rather than modelling human vision directly, we use a Bayesian ideal observer to model human visual ecology. We show that the HK effect is a result of encoding the non-linear statistical relationship between retinal images and natural scenes that would have been experienced by the human visual system in the past. We further show that the complexity of this relationship is due to the response functions of the cone photoreceptors, which themselves are thought to represent an efficient solution to encoding the statistics of images. Finally, we show that the locus of the response to the relationship between images and scenes lies in the primary visual cortex (V1), if not earlier in the visual system, since the brightness of colours (as opposed to their luminance) accords with activity in V1 as measured with fMRI.

Conclusions

The data suggest that perceptions of brightness represent a robust visual response to the likely sources of stimuli, as determined, in this instance, by the known statistical relationship between scenes and their retinal responses. While the responses of the early visual system (receptors in this case) may represent specifically the statistics of images, post receptor responses are more likely represent the statistical relationship between images and scenes. A corollary of this suggestion is that the visual cortex is adapted to relate the retinal image to behaviour given the statistics of its past interactions with the sources of retinal images: the visual cortex is adapted to the signals it receives from the eyes, and not directly to the world beyond.

[The Hermann grid illusion: the classic textbook interpretation is obsolete]

The Hermann grid is an optical illusion in which the crossings of white grid lines appear darker than the grid lines outside the crossings. The illusion disappears when one fixates the crossings. The discoverer, Ludimar Hermann (1838-1914), interpreted the illusion as evidence for lateral connections in the retina. In most textbooks on sensory physiology and ophthalmology, the Hermann grid illusion serves to illustrate "lateral inhibition." This paper summarises new findings that show that the classic explanation is incomplete. In 2004, a seemingly subtle modification, a small undulation of the grid lines, was shown to demolish the illusion. In 2007, a more convincing explanation appeared: An artificial neural network was trained for "lightness constancy"- the ability of our visual system to interpret luminance in the interest of object recognition, independent of illumination. After having learned lightness constancy, the network was subjected to a number of lightness illusions, among them the Hermann grid illusion. An analysis of the coupling constants of this neural network promises to further our understanding of the Hermann grid illusion.