The place of white in a world of grays: a double-anchoring theory of lightness perception

Iconic logic: the visual art of drawing the right conclusion

Most people, evidence suggests, have a hard time thinking straight. Symbolic logic is a tool that can help remedy this problem. Unfortunately, it is highly abstract and uses symbols whose meanings rely on unintuitive arbitrary conventions. Without sacrificing rigor, iconic logic is more concrete and uses icons that resemble what they stand for and whose meanings are thus easier to picture, process, and remember. Here I review and critique iconic existential graphs and concept diagrams-the former link iconic logic to iconic mathematics; the latter expand popular Euler or Venn diagrams and have, to some degree, been empirically investigated for user-friendliness. I lay out how expertise in perception, cognition, and genetics can inform and improve such empirical research to help make iconic logic more ergonomic. After all, logic is a tool, and tools should not only suit their use but also their user.

Empirical evaluation of computational models of lightness perception

Lightness of a surface depends not only on its physical characteristics, but also on the properties of the surrounding context. As a result, varying the context can significantly alter surface lightness, an effect exploited in many lightness illusions. Computational models can produce outcomes similar to human illusory percepts, allowing for demonstrable assessment of the applied mechanisms and principles. We tested 8 computational models on 13 typical displays used in lightness research (11 Illusions and 2 Mondrians), and compared them with results from human participants (N = 85). Results show that HighPass and MIR models predict empirical results for simultaneous lightness contrast (SLC) and its close variations. ODOG and its newer variants (ODOG-2 and L-ODOG) in addition to SLC displays were able to predict effect of White's illusion. RETINEX was able to predict effects of both SLC displays and Dungeon illusion. Dynamic decorrelation model was able to predict obtained effects for all tested stimuli except two SLC variations. Finally, FL-ODOG model was best at simulating human data, as it was able to predict empirical results for all displays, bar the Reversed contrast illusion. Finally, most models underperform on the Mondrian displays that represent most natural stimuli for the human visual system.

Simple Assumptions to Improve Markov Illuminance and Reflectance

Murray recently introduced a novel computational lightness model, Markov illuminance and reflectance (MIR). MIR is a promising new approach that simulates human lightness processing using a conditional random field (CRF) where natural-scene statistics of reflectance and illumination are implemented. Although MIR can account for various lightness illusions and phenomena, it has limitations, such as the inability to predict reverse-contrast phenomena. In this study, we improved MIR performance by modifying its inference process, the prior on X-junctions, and that on general illumination changes. Our modified model improved predictions for Checkerboard assimilation, the simplified Checkershadow and its control figure, the influence of luminance noise, and White's effect and its several variants. In particular, White's effect is a partial reverse contrast that is challenging for computational models, so this improvement is a significant advance for the MIR framework. This study showed the high extensibility and potential of MIR, which shows the promise for further sophistication.

Lightness contrast & assimilation: testing the hypotheses

Lightness contrast alters lightness of a target decreasing its similarity with neighbouring surfaces (inducers), while lightness assimilation has an opposite effect, similarity is increased. Previous studies emphasized some aspects of stimulation that favour occurrence of one or both of these two phenomena: spatial frequency of the inducers, magnitude and direction of the reflectance difference between the target and the inducers. More importantly, based on previous studies three precise hypotheses can be formulated that predict occurrence of the two phenomena: spatial frequency, differential stimulation and assimilation asymmetry. We manipulated target and inducers’ reflectance, and inducers’ spatial frequency. This enabled us not only to test the importance of these factors, but to predict lightness for each stimulus, according to all three hypotheses. Our results confirmed the importance of tested factors for both lightness contrast and assimilation. Unfortunately, the proposed hypotheses were poor in predicting the obtained data. Differential stimulation hypothesis correctly predicted obtained effect in less than half situations, since small reflectance differences produced contrast, and large differences produced assimilation. Spatial frequency hypothesis did not correctly predict the strength of obtained effects, and we obtained largest assimilation effects with low spatial frequency inducers. Finally, assimilation asymmetry hypothesis did not predict a single obtained effect. Contrary to this hypothesis predictions, we obtained contrast with decrement, and assimilation with increment inducers.

Why Does Rubin's Vase Differ Radically From Optical Illusions? Framing Effects Contra Cognitive Illusions

Many researchers use the term "context" loosely to denote diverse kinds of reference points. The issue is not about terminology but rather about the common conflation of one kind of reference points, such as rules of perception, which is responsible for optical illusions, with another kind, known as "context" or "frame," as exemplified in Rubin's vase. Many researchers regard Rubin's vase as a special kind of optical illusions. This paper rather argues that the two phenomena are radically different. Optical illusions are occasional mistakes that people quickly recognize and eagerly correct, while the different figures of Rubin's vase are not mistakes but, rather, the outcomes of different perspectives that do not need correction. The competing figures in Rubin's vase can, at best, in light of more information, be more warranted or unwarranted. This paper discusses at length one ramification of the proposed distinction. The framing effects, such as loss/gain frame, are the products of contexts and, hence, resemble greatly the figures in Rubin's vase. In contrast, cognitive illusions generated occasionally by the rules of thumb (heuristics) are mistakes and, hence, resemble optical illusions. The proposed distinction carries other ramifications regarding, e.g., happiness studies, moral judgments, and the new philosophy of science.

Most Findings Obtained With Untimed Visual Illusions Are Confounded

Visual illusions have been studied extensively, but their time course has not. Here we show, in a sample of more than 550 people, that unrestricted presentation times-as opposed to presentations lasting only a single second-weaken the Ebbinghaus illusion, strengthen lightness contrast with double increments, and do not alter lightness contrast with double decrements. When presentation time is unrestricted, these illusions are affected in the same way (decrease, increase, no change) by how long observers look at them. Our results imply that differences in illusion magnitude between individuals or groups are confounded with differences in inspection time, no matter whether stimuli are evaluated in matching, adjustment, or untimed comparison tasks. We offer an explanation for why these three illusions progress differently, and we spell out how our findings challenge theories of lightness, theories of global-local processing, and the interpretation of all research that has investigated visual illusions, or used them as tools, without considering inspection time.

Task-driven and flexible mean judgment for heterogeneous luminance ensembles

Spatial averaging of luminances over a variegated region has been assumed in visual processes such as light adaptation, texture segmentation, and lightness scaling. Despite the importance of these processes, how mean brightness can be computed remains largely unknown. We investigated how accurately and precisely mean brightness can be compared for two briefly presented heterogeneous luminance arrays composed of different numbers of disks. The results demonstrated that mean brightness judgments can be made in a task-dependent and flexible fashion. Mean brightness judgments measured via the point of subjective equality (PSE) exhibited a consistent bias, suggesting that observers relied strongly on a subset of the disks (e.g., the highest- or lowest-luminance disks) in making their judgments. Moreover, the direction of the bias flexibly changed with the task requirements, even when the stimuli were completely the same. When asked to choose the brighter array, observers relied more on the highest-luminance disks. However, when asked to choose the darker array, observers relied more on the lowest-luminance disks. In contrast, when the task was the same, observers' judgments were almost immune to substantial changes in apparent contrast caused by changing the background luminance. Despite the bias in PSE, the mean brightness judgments were precise. The just-noticeable differences measured for multiple disks were similar to or even smaller than those for single disks, which suggested a benefit of averaging. These findings implicated flexible weighted averaging; that is, mean brightness can be judged efficiently by flexibly relying more on a few items that are relevant to the task.

Layer and framework theories of lightness

Lightness (the perceived dimension running from black to white) represents a problem for vision science because the light coming to the eye from an object totally fails to specify the shade of gray of the object, due to the confounding of surface gray and illumination intensity. The two leading approaches, decomposition theories and anchoring theories, split the retinal image into overlapping layers and adjacent frameworks, respectively. Because each approach has important strengths and some weaknesses, an integration of them would mark an important step forward for the lightness theory. But the problem remains how this integration can actually be realized.

The Influence of Physical Illumination on Lightness Perception in Simultaneous Contrast Displays

Three experiments investigated the role of physical illumination on lightness perception in simultaneous lightness contrast (SLC). Four configurations were employed: the classic textbook version of the illusion and three configurations that produced either enhanced or reduced SLC. Experiment 1 tested the effect of ambient illumination on lightness perception. It simulated very dark environmental conditions that nevertheless still allowed perception of different shades of gray. Experiment 2 tested the effect of the intensity of Gelb lighting on lightness perception. Experiment 3 presented two conditions that integrated illumination conditions from Experiments 1 and 2. Our results demonstrated an illumination effect on both lightness matching and perceived SLC contrast: As the intensity of illumination increased, the target on the black background appeared lighter, while the target on the white background was little affected. We hypothesize the existence of two illumination ranges that affect lightness perception differently: low and normal. In the low range, the SLC contrast was reduced and targets appeared darker. In the normal range, the SLC contrast and lightness matchings for each background were little changed across illumination intensities.

Bioplausible multiscale filtering in retino-cortical processing as a mechanism in perceptual grouping

Why does our visual system fail to reconstruct reality, when we look at certain patterns? Where do Geometrical illusions start to emerge in the visual pathway? How far should we take computational models of vision with the same visual ability to detect illusions as we do? This study addresses these questions, by focusing on a specific underlying neural mechanism involved in our visual experiences that affects our final perception. Among many types of visual illusion, 'Geometrical' and, in particular, 'Tilt Illusions' are rather important, being characterized by misperception of geometric patterns involving lines and tiles in combination with contrasting orientation, size or position. Over the last decade, many new neurophysiological experiments have led to new insights as to how, when and where retinal processing takes place, and the encoding nature of the retinal representation that is sent to the cortex for further processing. Based on these neurobiological discoveries, we provide computer simulation evidence from modelling retinal ganglion cells responses to some complex Tilt Illusions, suggesting that the emergence of tilt in these illusions is partially related to the interaction of multiscale visual processing performed in the retina. The output of our low-level filtering model is presented for several types of Tilt Illusion, predicting that the final tilt percept arises from multiple-scale processing of the Differences of Gaussians and the perceptual interaction of foreground and background elements. The model is a variation of classical receptive field implementation for simple cells in early stages of vision with the scales tuned to the object/texture sizes in the pattern. Our results suggest that this model has a high potential in revealing the underlying mechanism connecting low-level filtering approaches to mid- and high-level explanations such as 'Anchoring theory' and 'Perceptual grouping'.

Lightness Constancy in Surface Visualization

Color is a common channel for displaying data in surface visualization, but is affected by the shadows and shading used to convey surface depth and shape. Understanding encoded data in the context of surface structure is critical for effective analysis in a variety of domains, such as in molecular biology. In the physical world, lightness constancy allows people to accurately perceive shadowed colors; however, its effectiveness in complex synthetic environments such as surface visualizations is not well understood. We report a series of crowdsourced and laboratory studies that confirm the existence of lightness constancy effects for molecular surface visualizations using ambient occlusion. We provide empirical evidence of how common visualization design decisions can impact viewers' abilities to accurately identify encoded surface colors. These findings suggest that lightness constancy aids in understanding color encodings in surface visualization and reveal a correlation between visualization techniques that improve color interpretation in shadow and those that enhance perceptions of surface depth. These results collectively suggest that understanding constancy in practice can inform effective visualization design.

Grouping Factors and the Reverse Contrast Illusion

In simultaneous lightness contrast, two identical gray target squares lying on backgrounds of different intensities appear different in lightness. Traditionally, this illusion was explained by lateral inhibitory mechanisms operating retinotopically. More recently, spatial filtering models have been preferred. We report tests of an anchoring theory account in which the illusion is attributed to grouping rules used by the visual system to compute lightness. We parametrically varied the belongingness of two gray target bars to their respective backgrounds so that they either appeared to group with a set of bars flanking them, or they appeared to group with their respective backgrounds. In all variations, the retinal adjacency of the gray squares and their backgrounds was essentially unchanged. We report data from seven experiments showing that manipulation of the grouping rules governs the size and direction of the simultaneous lightness contrast illusion. These results support the idea that simultaneous lightness contrast is the product of anchoring within perceptual groups.

What visual illusions tell us about underlying neural mechanisms and observer strategies for tackling the inverse problem of achromatic perception

Research in lightness perception centers on understanding the prior assumptions and processing strategies the visual system uses to parse the retinal intensity distribution (the proximal stimulus) into the surface reflectance and illumination components of the scene (the distal stimulus—ground truth). It is agreed that the visual system must compare different regions of the visual image to solve this inverse problem; however, the nature of the comparisons and the mechanisms underlying them are topics of intense debate. Perceptual illusions are of value because they reveal important information about these visual processing mechanisms. We propose a framework for lightness research that resolves confusions and paradoxes in the literature, and provides insight into the mechanisms the visual system employs to tackle the inverse problem. The main idea is that much of the debate and confusion in the literature stems from the fact that lightness, defined as apparent reflectance, is underspecified and refers to three different types of judgments that are not comparable. Under stimulus conditions containing a visible illumination component, such as a shadow boundary, observers can distinguish and match three independent dimensions of achromatic experience: apparent intensity (brightness), apparent local intensity ratio (brightness-contrast), and apparent reflectance (lightness). In the absence of a visible illumination boundary, however, achromatic vision reduces to two dimensions and, depending on stimulus conditions and observer instructions, judgments of lightness are identical to judgments of brightness or brightness-contrast. Furthermore, because lightness judgments are based on different information under different conditions, they can differ greatly in their degree of difficulty and in their accuracy. This may, in part, explain the large variability in lightness constancy across studies.

A Neurocomputational account of the role of contour facilitation in brightness perception

A new filling-in model is proposed in order to account for challenging brightness illusions, where inducing background elements are spatially separated from the gray target such as dungeon, cube and grating illusions, bullseye display and ring patterns. This model implements the simple idea that neural response to low-contrast contour is enhanced (facilitated) by the presence of collinear or parallel high-contrast contours in its wider neighborhood. Contour facilitation is achieved via dendritic inhibition, which enables the computation of maximum function among inputs to the node. Recurrent application of maximum function leads to the propagation of the neural signal along collinear or parallel contour segments. When a strong global-contour signal is accompanied with a weak local-contour signal at the same location, conditions are met to produce brightness assimilation within the Filling-in Layer. Computer simulations showed that the model correctly predicts brightness appearance in all of the aforementioned illusions as well as in White's effect, Benary's cross, Todorović's illusion, checkerboard contrast, contrast-contrast illusion and various variations of the White's effect. The proposed model offers new insights on how geometric factors (contour colinearity or parallelism), together with contrast magnitude contribute to the brightness perception.

Luminance gradient configuration determines perceived lightness in a simple geometric illusion

Accurate perception of surface reflectance poses a significant computational problem for the visual system. The amount of light reflected by a surface is affected by a combination of factors including the surface's reflectance properties and illumination conditions. The latter are not limited by the strength of the illuminant but also include the relative placement of the light illuminating the surface, the orientation of the surface and its 3d shape, all of which result in a pattern of luminance gradients across the surface. In this study we explore how luminance gradients contribute to lightness perception. We introduce a novel, simple lightness illusion. It consists of six separate checks, organized in rows of two. Each check has a negative luminance gradient across it. The top and the bottom rows are the same: with the darker check on the left, and the lighter check on the right. Two checks in the middle row are identical; however, the check on the right appears darker than the check on the left. As there are no shared borders between the checks, simultaneous contrast cannot explain the effect. However, there are multiple possible explanations including spatial filtering (Blakeslee and McCourt, 2004) or some higher-order mechanism such as perceptual grouping or amodal completion. Here, we explore these possibilities by manipulating the luminance configurations and the gradient slopes of the checks.

Brightness/darkness induction and the genesis of a contour

Visual contours often result from the integration or interpolation of fragmented edges. The strength of the completion increases when the edges share the same contrast polarity (CP). Here we demonstrate that the appearance in the perceptual field of this integrated unit, or contour of invariant CP, is concomitant with a vivid brightness alteration of the surfaces at its opposite sides. To observe this effect requires some stratagems because the formation in the visual field of a contour of invariant CP normally engenders the formation of a second contour and then the rise of two streams of induction signals that interfere in different ways. Particular configurations have been introduced that allow us to observe the induction effects of one contour taken in isolation. I documented these effects by phenomenological observations and psychophysical measurement of the brightness alteration in relation to luminance contrast. When the edges of the same CP complete to form a contour, the background of homogeneous luminance appears to dim at one side and to brighten at the opposite side (in accord with the CP). The strength of the phenomenon is proportional to the local luminance contrast. This effect weakens or nulls when the contour of the invariant CP separates surfaces filled with different gray shades. These conflicting results stimulate a deeper exploration of the induction phenomena and their role in the computation of brightness contrast. An alternative perspective is offered to account for some brightness illusions and their relation to the phenomenal transparency. The main assumption asserts that, when in the same region induction signals of opposite CP overlap, the filling-in is blocked unless the image is stratified into different layers, one for each signal of the same polarity. Phenomenological observations document this “solution” by the visual system.

A Gestalt Account of Lightness Illusions

Illusions of lightness offer valuable clues to how lightness values are computed by the visual system. The traditional domain of lightness illusions must be expanded to include failures of constancy, as there is no distinction between these categories. Just as lightness is (relatively) constant in the face of changes in illumination level, so it is equally constant in the face of changes in background reflectance. Simultaneous lightness contrast, the most familiar lightness illusion, is fairly weak, and represents a failure of background-independent lightness constancy. It is argued that a combination of the highest-luminance rule of anchoring plus the Kardos idea of codetermination can account for most lightness illusions. Kardos suggested that the lightness value of a target surface is partly determined relative to the field of illumination (or framework) in which it is embedded, and partly relative to the neighboring field of illumination. Although Kardos did not apply his principle of codetermination to failures of background-independent constancy such as the simultaneous contrast illusion, this can be done rather easily by defining a framework as a perceptual group instead of identifying it strictly with an objective field of illumination.

A cortical edge-integration model of object-based lightness computation that explains effects of spatial context and individual differences

Previous work has demonstrated that perceived surface reflectance (lightness) can be modeled in simple contexts in a quantitatively exact way by assuming that the visual system first extracts information about local, directed steps in log luminance, then spatially integrates these steps along paths through the image to compute lightness (Rudd and Zemach, 2004, 2005, 2007). This method of computing lightness is called edge integration. Recent evidence (Rudd, 2013) suggests that human vision employs a default strategy to integrate luminance steps only along paths from a common background region to the targets whose lightness is computed. This implies a role for gestalt grouping in edge-based lightness computation. Rudd (2010) further showed the perceptual weights applied to edges in lightness computation can be influenced by the observer's interpretation of luminance steps as resulting from either spatial variation in surface reflectance or illumination. This implies a role for top-down factors in any edge-based model of lightness (Rudd and Zemach, 2005). Here, I show how the separate influences of grouping and attention on lightness can be modeled in tandem by a cortical mechanism that first employs top-down signals to spatially select regions of interest for lightness computation. An object-based network computation, involving neurons that code for border-ownership, then automatically sets the neural gains applied to edge signals surviving the earlier spatial selection stage. Only the borders that survive both processing stages are spatially integrated to compute lightness. The model assumptions are consistent with those of the cortical lightness model presented earlier by Rudd (2010, 2013), and with neurophysiological data indicating extraction of local edge information in V1, network computations to establish figure-ground relations and border ownership in V2, and edge integration to encode lightness and darkness signals in V4.

A theory divided: current representations of the anchoring theory of lightness contradict the original's core claims

The anchoring theory of lightness perception (Gilchrist et al., Psychological Review 106 (1999) 795-834) has been described as one of the most successful approaches to lightness perception. Yet, not only does the original proposal contain serious gaps and inconsistencies, later expressions of the theory, which was never formally revised, seem to contradict the original claims while leaving the gaps unresolved. These problems call into question the theory's viability.

The roles of image decomposition and edge curvature in the 'snake' lightness illusion

The snake illusion is an effect in which the lightness of target patches is strongly affected by the luminance of remote patches. One explanation is that such images are decomposed into a pattern of illumination and a pattern of reflectance, involving a classification of luminance edges into illumination and reflectance edges. Based on this decomposition, perceived reflectance is determined by discounting the illumination. A problem for this account is that image decomposition is not unique, and that different decompositions may lead to different lightness predictions. One way to rule out alternative decompositions and ensure correct predictions is to postulate that the visual system tends to classify curved luminance edges as reflectance edges rather than illumination edges. We have constructed several variations of the basic snake display in order to test the proposed curvature constraint and the more general image decomposition hypothesis. Although the results from some displays have confirmed previous findings of the effect of curvature, the general pattern of data questions the relevance of the shape of luminance edges for the determination of lightness in this class of displays. The data also argue against an image decomposition mechanism as an explanation of this effect. As an alternative, a tentative neurally based account is sketched.

The effects of belongingness on the Simultaneous Lightness Contrast: a virtual reality study

Simultaneous Lightness Contrast (SLC) is the phenomenon whereby a grey patch on a dark background appears lighter than an equal patch on a light background. Interestingly, the lightness difference between these patches undergoes substantial augmentation when the two backgrounds are patterned, thereby forming the articulated-SLC display. There are two main interpretations of these phenomena: The mid-level interpretation maintains that the visual system groups the luminance within a set of contiguous frameworks, whilst the high-level one claims that the visual system splits the luminance into separate overlapping layers corresponding to separate physical contributions. This research aimed to test these two interpretations by systematically manipulating the viewing distance and the horizontal distance between the backgrounds of both the articulated and plain SLC displays. An immersive 3D Virtual Reality system was employed to reproduce identical alignment and distances, as well as isolating participants from interfering luminance. Results showed that reducing the viewing distance resulted in increased contrast in both the plain- and articulated-SLC displays and that, increasing the horizontal distance between the backgrounds resulted in decreased contrast in the articulated condition but increased contrast in the plain condition. These results suggest that a comprehensive lightness theory should combine the two interpretations.

Background, an important factor in visual search

The ability to detect an object depends on the contrast between the object and its background. Despite this, many models of visual search rely solely on the properties of target and distractors, and do not take the background into account. Yet, both target and distractors have their individual contrasts with the background. These contrasts generally differ, because the target and distractors are different in at least one feature. Therefore, background is likely to play an important role in visual search. In three experiments we manipulated the properties of the background (luminance, orientation and spatial frequency, respectively) while keeping the target and distractors constant. In the first experiment, in which target and distractors had a different luminance, changing the background luminance had an extensive effect on search times. When background luminance was in between that of the target and distractors, search times were always short. Interestingly, when the background was darker than both the target and the distractors, search times were much longer than when the background was lighter. Manipulating orientation and spatial frequency of the background, on the other hand, resulted in search times that were longest for small target-background differences. Thus, background plays an important role in search. This role depends on the individual contrast of both target and distractors with the background and the type of feature contrast (luminance, orientation or spatial frequency).

The relation between cognitive-perceptual schizotypal traits and the Ebbinghaus size-illusion is mediated by judgment time

In the Ebbinghaus illusion, a circle surrounded by smaller circles is perceived as larger than an identical one surrounded by larger circles. The illusion is reportedly weaker in individuals with (disorganized) schizophrenia or schizotypy than in controls, a finding that has been interpreted as evidence that both schizophrenia and schizotypy involve reduced contextual integration. In support of this view, we show that the Ebbinghaus illusion also decreases, in the general population, with cognitive-perceptual schizotypal traits (measured with both the cognitive-perceptual subscale of the Schizotypal Personality Questionnaire-Brief and the Magical Ideation scale). Our results were strong and separately replicable in different within-subjects and between-subjects conditions. However, a mediation analysis revealed that the reduction of the Ebbinghaus illusion was (statistically, hence without implying a causal relationship) entirely due to increased judgment time, i.e., the time subjects took to complete size comparisons. Judgment time increased with the strength of cognitive-perceptual schizotypal traits, but subjects with longer judgment times had smaller illusions regardless of these traits. We argue that there are at least two possible accounts of our results. Reduced contextual integration might be due to a reduced ability to integrate context, as previously suggested; alternatively, it could be due to a reduced tendency to integrate context—that is, to a detail-oriented processing style. We offer predictions for future research, testable with a deadline experiment that pits these two accounts against one another. Regardless of which account proves to be best, our results show that contextual integration decreases with cognitive-perceptual schizotypal traits, and that this relationship is mediated by judgment time. Future studies should thus consider either manipulating or measuring this time.

Reinterpreting behavioral receptive fields: lightness induction alters visually completed shape

BACKGROUND

A classification image (CI) technique has shown that static luminance noise near visually completed contours affects the discrimination of fat and thin Kanizsa shapes. These influential noise regions were proposed to reveal "behavioral receptive fields" of completed contours-the same regions to which early cortical cells respond in neurophysiological studies of contour completion. Here, we hypothesized that 1) influential noise regions correspond to the surfaces that distinguish fat and thin shapes (hereafter, key regions); and 2) key region noise biases a "fat" response to the extent that its contrast polarity (lighter or darker than background) matches the shape's filled-in surface color.

RESULTS

To test our hypothesis, we had observers discriminate fat and thin noise-embedded rectangles that were defined by either illusory or luminance-defined contours (Experiment 1). Surrounding elements ("inducers") caused the shapes to appear either lighter or darker than the background-a process sometimes referred to as lightness induction. For both illusory and luminance-defined rectangles, key region noise biased a fat response to the extent that its contrast polarity (light or dark) matched the induced surface color. When lightness induction was minimized, luminance noise had no consistent influence on shape discrimination. This pattern arose when pixels immediately adjacent to the discriminated boundaries were excluded from the analysis (Experiment 2) and also when the noise was restricted to the key regions so that the noise never overlapped with the physically visible edges (Experiment 3). The lightness effects did not occur in the absence of enclosing boundaries (Experiment 4).

CONCLUSIONS

Under noisy conditions, lightness induction alters visually completed shape. Moreover, behavioral receptive fields derived in CI studies do not correspond to contours per se but to filled-in surface regions contained by those contours. The relevance of lightness to two-dimensional shape completion supplies a new constraint for models of object perception.

Understanding transparency perception in architecture: presentation of the simplified perforated model

Issues of transparency perception are addressed from an architectural perspective, pointing out previously neglected factors that greatly influence this phenomenon in the scale of a building. The simplified perforated model of a transparent surface presented in the paper has been based on previously developed theories and involves the balance of light reflected versus light transmitted. Its aim is to facilitate an understanding of non-intuitive phenomena related to transparency (eg dynamically changing reflectance) for readers without advanced knowledge of molecular physics. A verification of the presented model has been based on the comparison of optical performance of the model with the results of Fresnel's equations for light-transmitting materials. The presented methodology is intended to be used both in the design and explanatory stages of architectural practice and vision research. Incorporation of architectural issues could enrich the perspective of scientists representing other disciplines.

Brightness induction magnitude declines with increasing distance from the inducing field edge

Brightness induction refers to a class of visual illusions where the perceived intensity of a region of space is influenced by the luminance of surrounding regions. These illusions are significant because they provide insight into the neural organization and processing strategies employed by the visual system. The nature of these processing strategies, however, has long been debated. Here we investigate the spatial characteristics of grating induction as a function of the distance from the inducing field edge to evaluate the viability of various competing models. In particular multiscale spatial filtering models and homogeneous filling-in models make very different predictions in regard to the magnitude of induction as a function of this distance. Filling-in explanations predict that the brightness/lightness of the filled-in region will be homogeneous, whereas multiscale filtering predicts a fall-off in induction magnitude with distance from the inducing field edge. Induction magnitude was measured using a narrow probe version of the quadrature-phase motion-cancellation paradigm (Blakeslee & McCourt, 2011) and a point-by-point brightness matching paradigm (Blakeslee & McCourt, 1997, 1999; McCourt, 1994). Both techniques reveal a decrease in the magnitude of induction with increasing distance from the inducing edge. A homogeneous filling-in mechanism cannot explain the induced structure in the test fields of these stimuli. The results argue strongly against filling-in mechanisms as well as against any mechanism that posits that induction is homogeneous. The structure of the induction is, however, well accounted for by the multiscale filtering (ODOG) model of Blakeslee and McCourt (1999). These results support models of brightness/lightness, such as filtering models, which preserve these gradients of induction.

Measuring the Breathing Light Illusion by means of induced simultaneous contrast

By blurring the margins of a surface, both its brightness and the perceived contrast against a superimposed figure with sharp boundaries increase. Also, if one approaches a blurred white spot on a grey background, this spot will appear wider and brighter: this phenomenon is known as the Breathing Light Illusion (BLI) (Gori and Stubbs, 2006 Perception 35 1573-1577). We studied the increment of the achromatic contrast of a grey sharp-boundary disk when it was superimposed on the BLI. This augmentation of the perceived contrast in the dynamic presentation of the BLI was significantly stronger than the effect that Agostini and Galmonte (2002a Psychonomic Bulletin and Review 9 264-269) obtained in static presentation. Our study leads to an indirect quantification of the BLI. Two control experiments showed that the increment of the achromatic contrast depends on the blurred spot and is independent of the dynamic increment in angular size. These results argue for a causal relationship between the increase in brightness due to the BLI and the darkening of the superimposed disk.

Relative Brightness in Natural Images Can Be Accounted for by Removing Blurry Content

One critical question regarding visual cognition concerns how the physical properties of the visual world are represented in early vision and then relayed to high-level vision. Here, we posit a simple theory: Processes that encode object appearance reduce their response to spatial content that is coarser than the size of the attended object. We show that a filtering procedure based on this theory can account for the relative brightness levels of test patches placed in images of natural scenes and for many hard-to-explain brightness illusions. The implication is that the perception of brightness differences in most brightness illusions actually corresponds to physical differences present in the images. Portions of the visual system may encode these physical differences by means of neural processes that adaptively reduce their response to low-spatial-frequency content.

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.

Linking depth to lightness and anchoring within the differentiation-integration formalism

Recently we developed a model that reproduces the Kanizsa square illusion based on two principles: (1) a spatial 2-D integration of luminance ratio and differentiated depth signals creates a "primary" lightness map and a depth map, respectively, which is then followed by (2) a modification of the primary lightness values under influence of the perceived depth (Kogo, Strecha, Van Gool, & Wagemans, 2010). Within this model, the process of the spatial integration inevitably introduced an arbitrary offset. In order to obtain absolute values of depth and lightness, the offset values needed to be determined by other constraints. This is the anchoring problem of the depth and lightness measurements. Here we report the anchoring rules that were established by investigating the model's responses to the Kanizsa square and its wide range of variations. For the primary lightness map, the highest value rule was applied, while the area rule appeared most plausible for the depth map. By applying the same principles to simple figures consisting of black and white areas of different size ratios, the model succeeded in reproducing published empirical results on lightness anchoring (Li & Gilchrist, 1999).

Von Bezold Assimilation Effect Reverses in Stereoscopic Conditions

Lightness contrast and lightness assimilation are opposite phenomena: in contrast, grey targets appear darker when bordering bright surfaces (inducers) rather than dark ones; in assimilation, the opposite occurs. The question is: which visual process favours the occurrence of one phenomenon over the other? Researchers provided three answers to this question. The first asserts that both phenomena are caused by peripheral processes; the second attributes their occurrence to central processes; and the third claims that contrast involves central processes, whilst assimilation involves peripheral ones. To test these hypotheses, an experiment on an IT system equipped with goggles for stereo vision was run. Observers were asked to evaluate the lightness of a grey target, and two variables were systematically manipulated: (i) the apparent distance of the inducers; and (ii) brightness of the inducers. The retinal stimulation was kept constant throughout, so that the peripheral processes remained the same. The results show that the lightness of the target depends on both variables. As the retinal stimulation was kept constant, we conclude that central mechanisms are involved in both lightness contrast and lightness assimilation.

The luminance misattribution in lightness perception

The Simultaneous Lightness Contrast is the condition whereby a grey patch on a dark background appears lighter than a physically identical patch on a light background. This is probably the most studied phenomenon in lightness perception. Although this phenomenon has been explained in terms of low-level mechanisms, convincing evidences supporting a high-level interpretation have been presented over the last decades. Two are the main highlevel interpretations. On one side, the layer approach claims that the visual system splits the luminance into separate overlapping layers, corresponding to separate physical contributions; whilst on the other side, the framework approach maintains that the visual system groups the luminance within a set of contiguous frameworks. One of the biggest weaknesses of the layer approach is that it cannot account properly for errors in lightness perception (Gilchrist, 2005 Current Biology, 15(9), 330-332). To extend the multiple layers interpretation to errors in lightness perception, in this study we show that the perceptual lightness difference among equal patches on different backgrounds increases even when the luminance contrast with their backgrounds shrinks. Specifically, it is shown that the perceptual lightness difference among equal patches on different backgrounds intensifies when a small-sized semi-transparent surface is interposed between the patches and the backgrounds. This result indicates that in these conditions the visual system besides decomposing the luminance into separate layers also becomes liable for a luminance misattribution. It is proposed that the photometric and geometric relationships among the luminance edges in the image might account for this misattribution.

Paradoxical lightness contrast

The visual system's computation of lightness (perceived reflectance) leads to contrast effects in which a gray target region appears lighter on a black background than on a white one. Here we show a paradoxical contrast effect in which targets look lighter after adding regions that increase the scene's average luminance, and darker after adding regions that decrease this luminance. The paradoxical effect emerges if the target sits either on a black local background surrounded by a white remote background, or on a white local background surrounded by a black remote background. It does not occur if both backgrounds have the same luminance. The effect is consistent with Bressan's double-anchoring theory, and likely also with those edge-integration theories that assume gain control, but differs from previously reported effects of assimilation, articulation, reverse contrast, and remote contrast.

Multiplicative and additive Adelson's snake illusions

Two different versions of Adelson's snake lightness illusion are quantitatively investigated. In one experiment an additive version of the illusion is investigated by varying the additive component of the atmosphere transfer function (ATF) introduced by Adelson [2000, in The New Cognitive Neuroscience Ed. M Gazzaniga (Cambridge, MA: MIT Press) pp 339-351]. In the other, a multiplicative version of the illusion is examined by varying the multiplicative component of the ATE In both experiments four observers matched the targets' lightness of the snake patterns with Munsell samples. Increasing the additive or the multiplicative component elicited an approximately equal increase in the magnitude of the lightness illusion. The results show that both components, in the absence of other kinds of information, can be used as heuristics by our visual system to anchor luminance of the object when converting it into lightness.

Brightness and darkness as perceptual dimensions

A common-sense assumption concerning visual perception states that brightness and darkness cannot coexist at a given spatial location. One corollary of this assumption is that achromatic colors, or perceived grey shades, are contained in a one-dimensional (1-D) space varying from bright to dark. The results of many previous psychophysical studies suggest, by contrast, that achromatic colors are represented as points in a color space composed of two or more perceptual dimensions. The nature of these perceptual dimensions, however, presently remains unclear. Here we provide direct evidence that brightness and darkness form the dimensions of a two-dimensional (2-D) achromatic color space. This color space may play a role in the representation of object surfaces viewed against natural backgrounds, which simultaneously induce both brightness and darkness signals. Our 2-D model generalizes to the chromatic dimensions of color perception, indicating that redness and greenness (blueness and yellowness) also form perceptual dimensions. Collectively, these findings suggest that human color space is composed of six dimensions, rather than the conventional three.

Vision scientists have long adhered to the classic opponent-coding theory of vision, which states that bright–dark, red–green, and blue–yellow form mutually exclusive color pairs. According to this theory, it is not possible to see both brightness and darkness at a single spatial location, or an extended set of locations, such as a uniform surface. One corollary of this statement is that all perceivable grey shades vary along a continuum from bright to dark. At first glance, the notion that brightness and darkness cannot coexist on a single surface accords with our common-sense notion that a given grey shade cannot be simultaneously both brighter and darker than any other grey shade. The results presented here suggest that this common-sense notion is not supported by experimental data. Our results imply that a given grey shade can indeed be simultaneously brighter and darker than another grey shade. This seemingly paradoxical conclusion arises naturally if one assumes that brightness and darkness constitute the dimensions of a two-dimensional perceptual space in which points represent grey shades. Our results may encourage scientists working in related fields to question the assumption that perceptual variables, rather than sensory variables, are encoded in opponent pairs.

Lightness constancy: Object identity and temporal integration

Studies of lightness constancy typically involve the comparison of two objects of the same shade that have been placed under different illuminations. In this study, we introduce factors such as object identity and immediate prior experience to measure the effect of these manipulations on constancy. In the first experiment, conditions sufficient to reproduce classical constancy failure (illumination difference, target values, articulation level) were determined. In the second experiment a lightness judgment was made for a gray target that was then seen to move into another illumination level for the second match. Motion was used in an attempt to stress the target?s identity. The shade was still judged significantly lighter when placed under the higher than under the lower illumination. Failure of constancy thus occurred even when object identity was not in question. In the third experiment a priming paradigm was used, to assess the strength of constancy: one shade would appear in one illumination level and another shade in the other illumination level. Motion was used to trick observers into thinking that only a single object was presented. The estimated shade varied as a function of the shade of the prime. In the last experiment, observers were asked to make another match when the object was removed from view: the match of its true color independent of illumination. The value of this match-from-memory was based on the value obtained in the higher illumination level. Taken together, the experiments show that through object identity, immediate prior experience can influence lightness in systematic fashion.

Occlusion, transparency, and lightness

The lightness of a visual surface is its perceived achromatic reflectance [Adelson, E. H., (2000). Lightness perception and lightness illusions. In M. Gazzaniga (Ed.), The new cognitive neuroscience (2nd ed.) (pp. 339-351) Berlin: Springer; Gilchrist, A. (1999). Lightness perception. In R. W. F. Keil (Ed.), MIT encyclopedia of cognitive science (pp. 471-472). Cambridge: MIT press]. Lightness ranges from black, through various shades of grey, up to white. Anderson and Winawer [Anderson, B., Winawer, J. (2005). Image segmentation and lightness perception. Nature, 434, 79-83] suggested that perceptual decomposition of image luminance into multiple sources in different layers (e.g., perceptual transparency) is critical to the their lightness illusions. However, I show that simple perceptual occlusion evoked by T-junctions will work as well, suggesting that perceptual scission of luminance into multiple layers is unnecessary for such effects. I argue that the lightness illusions presented by Anderson and Winawer involve fundamentally different mechanisms than previously studied lightness illusions, including those involving perceptual transparency.

Lightness of an object under two illumination levels

Anchoring theory (Gilchrist et al, 1999 Psychological Review 106 795-834) predicts a wide range of lightness errors, including failures of constancy in multi-illumination scenes and a long list of well-known lightness illusions seen under homogeneous illumination. Lightness values are computed both locally and globally and then averaged together. Local values are computed within a given region of homogeneous illumination. Thus, for an object that extends through two different illumination levels, anchoring theory produces two values, one for the patch in brighter illumination and one for the patch in dimmer illumination. Observers can give matches for these patches separately, but they can also give a single match for the whole object. Anchoring theory in its current form is unable to predict these object matches. We report eight experiments in which we studied the relationship between patch matches and object matches. The results show that the object match represents a compromise between the match for the patch in the field of highest illumination and the patch in the largest field of illumination. These two principles are parallel to the rules found for anchoring lightness: highest luminance rule and area rule.

The subjective duration of ramped and damped sounds

Two experiments demonstrate that the perceived durations of sounds as long as 1 sec are influenced by the sounds' amplitude envelopes, extending Schlauch, Ries, and DiGiovanni's (2001) observations on sounds of 200-msec duration. Sounds with a monotonic decay (i.e., damped sounds) are heard as substantially shorter than both steady sounds and those with a monotonic increase of level (i.e., ramped sounds). Neither a reaction time (Experiments 1 and 2) nor a staircase (Experiment 2) procedure supported a sensory explanation for these different subjective durations. The results are compatible with the suggestion of Stecker and Hafter (2000) that listeners exclude part of the tails of damped sounds in the computation of their subjective durations.