A multi-channel approach to brightness coding

Towards an image-based brightness model for self-luminous stimuli

Brightness is one of the most important perceptual correlates of color appearance models (CAMs) when self-luminous stimuli are targeted. However, the vast majority of existing CAMs adopt the presence of a uniform background surrounding the stimulus, which severely limits their practical application in lighting. In this paper, a study on the brightness perception of a neutral circular stimulus surrounded by a non-uniform background consisting of a neutral ring-shaped luminous area and a dark surround is presented. The ring-shaped luminous area is presented with 3 thicknesses (0.33 cm, 0.67 cm and 1.00 cm), at 4 angular distances to the edge of the central stimulus (1.2°, 6.4°, 11.3° and 16.1°) and at 3 luminance levels (90 cd/m², 335 cd/m², 1200 cd/m²). In line with the literature, the results of the visual matching experiments show that the perceived brightness decreases in presence of a ring and the effect is maximal at the highest luminance of the ring, for the largest thickness and at the closest distance. Based on the observed results, an image-based model inspired by the physiology of the retina is proposed. The model includes the calculation of cone-fundamental weighted spectral radiance, scattering in the eye, cone compression and receptive field post-receptor organization. The wide receptive field assures an adaptive shift determined by both the adaptation to the stimulus and to the background. It is shown that the model performs well in predicting the matching experiments, including the impact of the thickness, the distance and the intensity of the ring, showing its potential to become the basic framework of a Lighting Appearance Model.

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.

The perception threshold of the panda illusion, a particular form of 2D pulse-width-modulated halftone, correlates with visual acuity

To call attention to the danger of extinction of the panda bear, the Lithuanian artist Ilja Klemencov created the artwork “They can disappear”. The illustration is composed of black-and-white zigzagged lines, which form the famous panda logo of the World Wild Fund For Nature (WWF) when seen from a distance. If one is too close to the artwork, it is difficult to spot the bear, however, if one steps back or takes off one’s glasses the panda suddenly appears. This led us to ask if the ability to see the panda is related to the visual acuity of the observer and if therefore, the panda illusion can be used to assess the spatial resolution of the eye. Here we present the results of the comparison between visual acuity determined using the Landolt C and that predicted from the panda illusion in 23 healthy volunteers with artificially reduced visual acuity. Furthermore, we demonstrate that the panda illusion is based on a 2D pulse-width modulation, explain its technical history, and provide the equations required to create the illusion. Finally, we explain why the illusion indeed can be used to predict visual acuity and discuss the neural causes of its perception with best-corrected visual acuity.

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.

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.

An Illumination Representation Approach to the Chevreul Effect

Within cognitive science of brightness and color perception, the argument has repeatedly been brought forward that it is necessary to consider mental representations for illuminations as well as mental representations for surfaces as integral elements of the functional architecture of the perceptual system. Here, we show that such an approach of dual semantic categories for perceptual representations can fruitfully be applied to the Chevreul effect, a brightness phenomenon of enhanced contrast at borders that played a prototypical role for a very different type of approaches. In these approaches, mechanisms processing retinal intensities are postulated that result in just one brightness dimension without explicitly referring to semantic categories of the perceptual system (surface vs. illumination representation). We argue that the Chevreul effect arises as a result of an interpretation by the visual system that the Chevreul stimulus is covered by a gradual illumination. Our first experiment shows that the Chevreul effect diminishes substantially when this interpretation is prevented by separating the elements of the Chevreul stimulus in depth. In the second experiment, we show that the strength of the Chevreul effect is strongly affected by embedding the Chevreul stimulus into three-dimensional scenes that either support or conflict with the interpretation of an illumination gradient across the stimulus.

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.

Modelling the Mach bands illusion by means of a diffusion model

First, we criticize the validity of the principle of lateral inhibition. Second, on the basis of illusory phenomena and stabilized retinal images, we point out that the retina does not code the absolute luminance; the retina forwards a relative luminance sketch towards higher levels of the visual system. However, at the level of conscious processing the perceptual counterpart of absolute luminance, brightness, is available. Therefore, it is reasonable to assume that a reconstruction process is carried out by the visual system, which recovers the inner representation that corresponds to the retinal light distribution from the coded relative luminance sketch. We provide an illustrative description of a computational model of this reconstruction process. The basis of the reconstruction is a mathematically provable theorem, according to which if image P is produced from image I by Laplacian filtering, and then P is used as the sources and sinks of a homogeneous linear diffusion process, then the equilibrium of the diffusion will be identical to the original image I. We have illustrated this by a one-dimensional heat diffusion example, and by a series of test tubes connected to each other, also in one dimension. Brightness illusions are considered as a side effect of this diffusion-based reconstruction process. If the diffusion process deviates from the principle of homogeneous linearity, then the result of the reconstruction will deviate from the original image I. We showed a concrete illustration of this with regards to the Mach bands illusion: here we violated the principle of homogeneous linearity by means of inserting a small vertical tube serving as a serial resistance between each test tube and the horizontal connecting tube. This violation resulted in a change of water level in the source and the sink test tubes corresponding to the Mach bands illusion.

Mach bands explained by response normalization

Mach bands are the illusory dark and bright bars seen at the foot and knee of a luminance trapezoid. First demonstrated by Ernst Mach in the latter part of the 19th century, Mach bands are a test bed not only for models of brightness illusions but of spatial vision in general. Up until 50 years ago the dominant explanation of Mach Bands was that they were caused by lateral inhibition among retinal neurons. More recently, the dominant idea has been that Mach bands are a consequence of a visual process that generates a sparse, binary description of the image in terms of "edges" and "bars". Another recent explanation is that Mach bands result from learned expectations about the pattern of light typically found on sharply curved surfaces. In keeping with recent multi-scale filtering accounts of brightness illusions as well as current physiology, I show however that Mach bands are most simply explained by response normalization, whereby the gains of early visual channels are adjusted on a local basis to make their responses more equal. I show that a simple one-dimensional model of response normalization explains the range of conditions under which Mach bands occur, and as importantly, the conditions under which they do not occur.

Perceived contrast in complex images

To understand how different spatial frequencies contribute to the overall perceived contrast of complex, broadband photographic images, we adapted the classification image paradigm. Using natural images as stimuli, we randomly varied relative contrast amplitude at different spatial frequencies and had human subjects determine which images had higher contrast. Then, we determined how the random variations corresponded with the human judgments. We found that the overall contrast of an image is disproportionately determined by how much contrast is between 1 and 6 c/°, around the peak of the contrast sensitivity function (CSF). We then employed the basic components of contrast psychophysics modeling to show that the CSF alone is not enough to account for our results and that an increase in gain control strength toward low spatial frequencies is necessary. One important consequence of this is that contrast constancy, the apparent independence of suprathreshold perceived contrast and spatial frequency, will not hold during viewing of natural images. We also found that images with darker low-luminance regions tended to be judged as having higher overall contrast, which we interpret as the consequence of darker local backgrounds resulting in higher band-limited contrast response in the visual system.

Depth effect on lightness revisited: The role of articulation, proximity and fields of illumination

The coplanar ratio principle proposes that when the luminance range in an image is larger than the canonical reflectance range of 30:1, the lightness of a target surface depends on the luminance ratio between that target and its adjacent coplanar neighbor (Gilchrist, 1980). This conclusion is based on experiments in which changes in the perceived target depth produced large changes in its perceived lightness without significantly altering the observers' retinal image. Using the same paradigm, we explored how this depth effect on lightness depends on display complexity (articulation), proximity of the target to its highest coplanar luminance and spatial distribution of fields of illumination. Importantly, our experiments allowed us to test differing predictions made by the anchoring theory (Gilchrist et al., 1999), the coplanar ratio principle, as well as other models. We report three main findings, generally consistent with anchoring theory predictions: (1) Articulation can substantially increase the depth effect. (2) Target lightness depends not on the adjacent luminance but on the highest coplanar luminance, irrespective of its position relative to the target. (3) When a plane contains multiple fields of illumination, target lightness depends on the highest luminance in its field of illumination, not on the highest coplanar luminance.

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.

A neurodynamical model of brightness induction in v1

Brightness induction is the modulation of the perceived intensity of an area by the luminance of surrounding areas. Recent neurophysiological evidence suggests that brightness information might be explicitly represented in V1, in contrast to the more common assumption that the striate cortex is an area mostly responsive to sensory information. Here we investigate possible neural mechanisms that offer a plausible explanation for such phenomenon. To this end, a neurodynamical model which is based on neurophysiological evidence and focuses on the part of V1 responsible for contextual influences is presented. The proposed computational model successfully accounts for well known psychophysical effects for static contexts and also for brightness induction in dynamic contexts defined by modulating the luminance of surrounding areas. This work suggests that intra-cortical interactions in V1 could, at least partially, explain brightness induction effects and reveals how a common general architecture may account for several different fundamental processes, such as visual saliency and brightness induction, which emerge early in the visual processing pathway.

A possible role and basis of visual pathway selection in brightness induction

It is a well-known fact that the perceived brightness of any surface depends on the brightness of the surfaces that surround it. This phenomenon is termed as brightness induction. Isotropic arrays of multi-scale DoG (Difference of Gaussians) as well as cortical Oriented DoG (ODOG) and extensions thereof, like the Frequency-specific Locally Normalized ODOG (FLODOG) functions have been employed towards prediction of the direction of brightness induction in many brightness perception effects. But the neural basis of such spatial filters is seldom obvious. For instance, the visual information from retinal ganglion cells to such spatial filters, which have been generally speculated to appear at the early stage of cortical processing, are fed by at least three parallel channels viz. Parvocellular (P), Magnocellular (M) and Koniocellular (K) in the subcortical pathway, but the role of such pathways in brightness induction is generally not implicit. In this work, three different spatial filters based on an extended classical receptive field (ECRF) model of retinal ganglion cells, have been approximately related to the spatial contrast sensitivity functions of these three parallel channels. Based on our analysis involving different brightness perception effects, we propose that the M channel, with maximum conduction velocity, may have a special role for an initial sensorial perception. As a result, brightness assimilation may be the consequence of vision at a glance through the M pathway; contrast effect may be the consequence of a subsequent vision with scrutiny through the P channel; and the K pathway response may represent an intermediate situation resulting in ambiguity in brightness perception. The present work attempts to correlate this phenomenon of pathway selection with the complementary nature of these channels in terms of spatial frequency as well as contrast.

Variability in constancy of the perceived surface reflectance across different illumination statistics

In contrast to the classical findings of lightness constancy, recent psychophysical studies show the strong dependency of the perceived reflectance of a surface on the structure of the natural illumination. The present study examined this inconstancy for systematic variations in the light field and an image-based explanation for it. Observers matched the specular and diffuse reflectance of a three-dimensional object in a complex scene under a fixed light field to that in the scene under different light fields with variable mean, contrast, and gamma. For the both specular and diffuse components, the matched reflectance was relatively constant against changes in the mean illuminance but varied extensively with changes in the contrast and gamma of the light field. We found that the matching data were well predicted by the similarity of the subband histograms of the images. The results support the notion that early spatial filtering can provide a unified account of both the constancy in the perceived surface reflectance against mean illuminance and the inconstancy for higher-order illumination statistics.

Changing the Chevreul illusion by a background luminance ramp: lateral inhibition fails at its traditional stronghold--a psychophysical refutation

The Chevreul illusion is a well-known 19^th century brightness illusion, comprising adjacent homogeneous grey bands of different luminance, which are perceived as inhomogeneous. It is generally explained by lateral inhibition, according to which brighter areas projected to the retina inhibit the sensitivity of neighbouring retinal areas. Lateral inhibition has been considered the foundation-stone of early vision for a century, upon which several computational models of brightness perception are built. One of the last strongholds of lateral inhibition is the Chevreul illusion, which is often illustrated even in current textbooks. Here we prove that lateral inhibition is insufficient to explain the Chevreul illusion. For this aim, we placed the Chevreul staircase in a luminance ramp background, which noticeably changed the illusion. In our psychophysical experiments, all 23 observers reported a strong illusion, when the direction of the ramp was identical to that of the staircase, and all reported homogeneous steps (no illusion) when its direction was the opposite. When the background of the staircase was uniform, 14 saw the illusion, and 9 saw no illusion. To see whether the change of the entire background area or that of the staircase boundary edges were more important, we placed another ramp around the staircase, whose direction was opposite to that of the original, larger ramp. The result is that though the inner ramp is rather narrow (mean = 0.51 deg, SD = 0.48 deg, N = 23), it still dominates perception. Since all conditions of the lateral inhibition account were untouched within the staircase, lateral inhibition fails to model these perceptual changes. Area ratios seem insignificant; the role of boundary edges seems crucial. We suggest that long range interactions between boundary edges and areas enclosed by them, such that diffusion-based models describe, provide a much more plausible account for these brightness phenomena, and local models are insufficient.

Spatiotemporal analysis of brightness induction

Brightness induction refers to a class of visual illusions in which 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 of the visual system. A novel quadrature-phase motion cancelation technique was developed to measure the magnitude of the grating induction brightness illusion across a wide range of spatial frequencies, temporal frequencies and test field heights. Canceling contrast is greatest at low frequencies and declines with increasing frequency in both dimensions, and with increasing test field height. Canceling contrast scales as the product of inducing grating spatial frequency and test field height (the number of inducing grating cycles per test field height). When plotted using a spatial axis which indexes this product, the spatiotemporal induction surfaces for four test field heights can be described as four partially overlapping sections of a single larger surface. These properties of brightness induction are explained in the context of multiscale spatial filtering. The present study is the first to measure the magnitude of grating induction as a function of temporal frequency. Taken in conjunction with several other studies (Blakeslee & McCourt, 2008; Magnussen & Glad, 1975; Robinson & de Sa, 2008) the results of this study illustrate that at least one form of brightness induction is very much faster than that reported by DeValois, Webster, DeValois, and Lingelbach (1986) and Rossi and Paradiso (1996), and are inconsistent with the proposition that brightness induction results from a slow "filling in" process.

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 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.

Spatial filtering versus anchoring accounts of brightness/lightness perception in staircase and simultaneous brightness/lightness contrast stimuli

J. Cataliotti and A. Gilchrist (1995) reported that, consistent with anchoring theory, the lightness of a black step in a reflectance staircase was not altered by moving a white step from a remote to an adjacent location. Recently, E. Economou, S. Zdravkovic, and A. Gilchrist (2007) reported data supporting three additional predictions of the anchoring model (A. Gilchrist et al., 1999): 1) equiluminant incremental targets in staircase simultaneous lightness contrast stimuli appeared equally light; 2) the simultaneous lightness contrast effect was due mainly to the lightening of the target on the black surround; and 3) the strength of lightness induction was greatest for darker targets. We investigated similar stimuli using brightness/lightness matching and found, contrary to these reports, that: 1) the relative position of the steps in a luminance staircase significantly influenced their brightness/lightness; 2) equiluminant incremental targets in staircase simultaneous brightness/lightness contrast stimuli did not all appear equally bright/light; 3) an asymmetry due to a greater brightening/lightening of the target on the black surround was not general; and 4) darker targets produced larger effects only when plotted on a log scale. In addition, the ODOG model (B. Blakeslee & M. E. McCourt, 1999) did an excellent job of accounting for brightness/lightness matching in these stimuli.

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.

Multiresolution wavelet framework models brightness induction effects

A new multiresolution wavelet model is presented here, which accounts for brightness assimilation and contrast effects in a unified framework, and includes known psychophysical and physiological attributes of the primate visual system (such as spatial frequency channels, oriented receptive fields, contrast sensitivity function, contrast non-linearities, and a unified set of parameters). Like other low-level models, such as the ODOG model [Blakeslee, B., & McCourt, M. E. (1999). A multiscale spatial filtering account of the white effect, simultaneous brightness contrast and grating induction. Vision Research, 39, 4361-4377], this formulation reproduces visual effects such as simultaneous contrast, the White effect, grating induction, the Todorović effect, Mach bands, the Chevreul effect and the Adelson-Logvinenko tile effects, but it also reproduces other previously unexplained effects such as the dungeon illusion, all using a single set of parameters.

The role of features in structuring visual images

Edges and lines carry much information about images and many models have been developed to explain how the human visual system may process them. One recent approach is the local energy model of Morrone and Burr. This model detects and locates both lines and edges simultaneously, by taking the Pythagorean sum of the output of pairs of matched filters (even- and odd-symmetric operators) to produce the all-positive local energy function. Maxima of this function signal the presence of all image features that are then classified as lines or edges (or both) and as positive or negative, depending on the strength of response of the even- and odd-symmetric operators. If the feature is an edge, it carries with it a brightness description that extends over space to the next edge. The model successfully explains many visual illusions, such as the Craik-O'Brien, Mach bands and a modified version of the Chevreul. Features can structure the visual image, often creating appearances quite contrary to the physical luminance distributions. In some examples the features dictate totally the image structure, 'capturing' all other information; in others the features are seen in transparence together with an alternate image. All cases can be predicted from the rules for combination of local energy at different scales.

The lowest spatial frequency channel determines brightness perception

This study investigates the role played by individual spatial scales in determining the apparent brightness of greyscale patterns. We measured the perceived difference in brightness across an edge in the presence of notch filtering and high-pass filtering for two stimulus configurations, one that elicits the perception of transparency and one that appears opaque. For both stimulus configurations, the apparent brightness of the surfaces delimited by the border decreased monotonically with progressive (ideal) high-pass filtering, with a critical cut-off at 1 c/deg. Using two octave ideal notch filtering, the maximum detrimental effect on apparent brightness was observed at about 1c/deg. Critical frequencies for apparent brightness did not vary with contrast, viewing distance, or surface size, suggesting that apparent brightness is determined by the channel tuned at 1 c/deg. Modelling the data with the local energy model [Morrone, M. C., & Burr, D. C. (1988). Feature detection in human vision: a phase dependent energy model. Proceedings of the Royal Society (London), B235, 221-245] at 1c/deg confirmed the suggestion that this channel mediates apparent brightness for both opaque and transparent borders, with no need for pooling or integration across spatial channels.

Added luminance ramp alters perceived edge blur and contrast: a critical test for derivative-based models of edge coding

In many models of edge analysis in biological vision, the initial stage is a linear 2nd derivative operation. Such models predict that adding a linear luminance ramp to an edge will have no effect on the edge's appearance, since the ramp has no effect on the 2nd derivative. Our experiments did not support this prediction: adding a negative-going ramp to a positive-going edge (or vice-versa) greatly reduced the perceived blur and contrast of the edge. The effects on a fairly sharp edge were accurately predicted by a nonlinear multi-scale model of edge processing [Georgeson, M. A., May, K. A., Freeman, T. C. A., & Hesse, G. S. (in press). From filters to features: Scale-space analysis of edge and blur coding in human vision. Journal of Vision], in which a half-wave rectifier comes after the 1st derivative filter. But we also found that the ramp affected perceived blur more profoundly when the edge blur was large, and this greater effect was not predicted by the existing model. The model's fit to these data was much improved when the simple half-wave rectifier was replaced by a threshold-like transducer [May, K. A. & Georgeson, M. A. (2007). Blurred edges look faint, and faint edges look sharp: The effect of a gradient threshold in a multi-scale edge coding model. Vision Research, 47, 1705-1720.]. This modified model correctly predicted that the interaction between ramp gradient and edge scale would be much larger for blur perception than for contrast perception. In our model, the ramp narrows an internal representation of the gradient profile, leading to a reduction in perceived blur. This in turn reduces perceived contrast because estimated blur plays a role in the model's estimation of contrast. Interestingly, the model predicts that analogous effects should occur when the width of the window containing the edge is made narrower. This has already been confirmed for blur perception; here, we further support the model by showing a similar effect for contrast perception.

Spatial frequency difference between textures interferes with brightness perception

Abrupt changes in luminance trigger and restrict brightness filling-in. If brightness was actively filled-in and mediated by cells signaling both luminance borders and surface brightness, then brightness spreading could also get disrupted by changes in texture. We measured psychophysically the brightness of a uniform luminance disk, which was segmented into two parts by different textures. The brightness of the central part of the disk was substantially reduced, and the reduction depended on spatial frequency, but not on the orientation difference between the textures. The results show that texture borders are able to block brightness filling-in. The bandwidth of brightness spreading was estimated to be approximately 1.5 octaves. This suggests that brightness information spreads only between neurons of similar spatial frequency characteristics.

Only two phase mechanisms, ±cosine, in human vision

We evaluated the proposal that there exist detectors of the following four cardinal phases in human vision: +cosine, -cosine, +sine, and -sine. First, we assessed whether there was evidence that these cardinal phases were processed by independent 'labeled lines,' using a discrimination at detection threshold paradigm. Second, we assessed whether suprathreshold phase discrimination was best at phases intermediate between these cardinal values. Third, we tried to replicate previous evidence showing that an absence of facilitation occurs only between cosine pedestals and sine tests (or vice-versa). In all three experimental approaches we found no compelling evidence for four cardinal phase groupings. We did however find evidence for independent detectors for pure increments and decrements (+/-cosine). We suggest that phase discrimination, whether at threshold or suprathreshold, is mediated by mechanisms that encode the relative positions and contrasts of local increments and decrements within the stimulus.

Gradient representation and perception in the early visual system--a novel account of Mach band formation

Recent evidence suggests that object surfaces and their properties are represented at early stages in the visual system of primates. Most likely invariant surface properties are extracted to endow primates with robust object recognition capabilities. In real-world scenes, luminance gradients are often superimposed on surfaces. We argue that gradients should also be represented in the visual system, since they encode highly variable information, such as shading, focal blur, and penumbral blur. We present a neuronal architecture which was designed and optimized for segregating and representing luminance gradients in real-world images. Our architecture in addition provides a novel theory for Mach bands, whereby corresponding psychophysical data are predicted consistently.

Smooth Gradient Representations as a Unifying Account of Chevreul's Illusion, Mach Bands, and a Variant of the Ehrenstein Disk

Recent evidence suggests that the primate visual system generates representations for object surfaces (where we consider representations for the surface attribute brightness). Object recognition can be expected to perform robustly if those representations are invariant despite environmental changes (e.g., in illumination). In real-world scenes, it happens, however, that surfaces are often overlaid by luminance gradients, which we define as smooth variations in intensity. Luminance gradients encode highly variable information, which may represent surface properties (curvature), nonsurface properties (e.g., specular highlights, cast shadows, illumination inhomogeneities), or information about depth relationships (cast shadows, blur). We argue, on grounds of the unpredictable nature of luminance gradients, that the visual system should establish corresponding representations, in addition to surface representations. We accordingly present a neuronal architecture, the so-called gradient system, which clarifies how spatially accurate gradient representations can be obtained by relying on only high-resolution retinal responses. Although the gradient system was designed and optimized for segregating, and generating, representations of luminance gradients with real-world luminance images, it is capable of quantitatively predicting psychophysical data on both Mach bands and Chevreul's illusion. It furthermore accounts qualitatively for a modified Ehrenstein disk.

Neuronal mechanisms for illusory brightness perception in humans

Biological visual systems are extraordinarily capable of recovering the shape and brightness of objects from sparse and fragmentary information. Using functional magnetic imaging, we show that two associative areas of the dorsal pathway--in the caudal region of the intrapariatal sulcus and in the lateral occipital sulcus--respond specifically to the Craik-O'Brien-Cornsweet illusion generated by high-pass filtered edges. Other visual areas, including primary visual cortex, also respond strongly to the retinotopic location of the edge, but these areas respond equally well to a line of matched contrast and detectability, rather than specifically to the brightness illusion. The reconstruction of surface and/or its brightness seems to be achieved by associative areas from the information about visual features provided by the primary visual cortices, even where there is no physical difference in luminance.

Spatial frequency tuning of brightness polarity identification

Recent studies have shown that cells in the primary visual cortex can, in addition to borders, also encode surface brightness. Whether the brightness is encoded by a large extraclassical receptive field or by a filling-in type mechanism activated by the luminance border is not known. These explanations imply different spatial frequency tunings for the underlying mechanism. In a psychophysical masking paradigm we measured spatial frequency tuning functions for identification of both luminance polarity (bright/dark) and luminance border orientation of oval and circular luminance patches with variable diameters (0.2-10 deg). For both tasks we obtained nearly overlapping narrow (1.5 octave) bandpass masking tuning functions centered at 1.5-5.0 c/deg. Stimulus size and shape had only minimal effect on the tuning functions. The results favor the idea of brightness filling-in and suggest that the cells activated by the luminance border modulate the activity of the cells signaling surface brightness. Further, the brightness processing mechanism is spatial frequency selective.

Mechanisms of contrast induction in heterogeneous displays

This study examines how judgments of a region's contrast are influenced by components of a heterogeneous surround. Each stimulus comprised a 5x5 grid of squares in a homogeneous background of fixed mean luminance, with the central square the target. On a given trial, the task was to judge (with feedback) whether the (Weber) contrast of the target was 0.04 or -0.04 (relative to the background); the contrasts assigned (in random order) to the 24 surrounding squares were drawn from the values -0.98, -0.33, 0.33, 0.98 in conformity to one of nine pre-chosen histograms. Presentations were brief (80 ms) in one condition and long (800 ms) in another. A novel psychophysical method was used to estimate the impact exerted on judged target contrast (JTC) by a given contrast in a given grid position. Results were similar for four observers. For both display durations, the four squares sharing an edge with the target influenced JTC 2.4-9 times more than any other surrounding squares. In long presentations, abutting squares of extreme contrast repelled target contrast: squares of contrast -0.98 (0.98) increased (decreased) JTC. However, lower contrast abutting squares attracted target contrast: squares of contrast -0.33 (0.33) decreased (increased) JTC. This central finding can be explained by supposing that: (a) JTC is strongly correlated with the average boundary contrast from surround to target, as registered by linear, edge-selective neurons, and, crucially, (b) the responses of these neurons are themselves subject to lateral inhibition from the rectified responses of other similarly tuned neurons. Finally, in brief presentations, a polarity-specific asymmetry was observed: the two positive abutting-square contrasts continued to influence JTC as they did in long presentations, but contrasts -0.33 and -0.98 ceased to exert much impact, suggesting that lateral influences on target appearance propagate more quickly from positive than from negative contrast abutting regions.

Separation of edge detection and brightness perception

When a low spatial frequency noise mask is superimposed onto a luminance staircase, the perceived brightness pattern is dramatically altered although the edges remain visible. We measured contrast thresholds for the edges and for the illusory scalloping (Chevreul-illusion), as a function of noise center spatial frequency. The masking tuning functions overlapped, but peaked at different spatial frequencies and contrast levels. The results suggest that perceived brightness is triggered only by the low spatial frequency components of the edges--the high spatial frequency components are not able to produce a brightness pattern.

Brightness assimilation in bullseye displays

In simultaneous brightness contrast displays, a gray target square G(B) bordered by black appears brighter than an identical gray target square G(W) bordered by white. Here we demonstrate that this effect can be reversed if G(B) is surrounded by bands that alternate outward from black to white, while G(W) is surrounded by bands that alternate outward from white to black. With these simple "bullseye" displays assimilation generally occurs--G(B) appears darker than G(W). Experiments 1 and 2 used a 2AFC design with a 2.2 s display duration. The results of these experiments indicate that (i) substantial assimilation occurs for target Weber contrasts (relative to the gray background) of -0.25, 0, and 0.25, but assimilation was maximal when target contrast was -0.25 and decreased as target contrast increased, (ii) assimilation effects were the same whether the width of the four surround bands was 20% of the target or 40% of the target, and (iii) assimilation occurs with as few as 2 surround-bands and the magnitude of the effect increases slightly as the number of bands increase. When experiment 1 was re-run using the method of matching (experiment 3), however, the results changed dramatically: (moderate) assimilation effects were found only when target contrast was -0.25; when target contrast was 0.25, there was a brightness contrast effect; when target contrast was 0, there was no illusion. Assimilation effects in bullseye displays are not predicted by the CSF model described in DeValois and DeValois [Spatial Vision, Oxford University Press, New York, 1988], the anchoring model of Gilchrist et al. [Psychological Review, 106(4) (1999) 795], or Blakeslee and McCourt's [Vision Research 39 (1999) 4361] ODOG model. We propose that this assimilation effect is the result of a contrast inhibition mechanism similar to that proposed by Chubb et al. [Proceedings for the National Academy of Science, vol. 86, 1989, p. 9631] to underlie contrast effects.

A multiscale spatial filtering account of the Wertheimer-Benary effect and the corrugated Mondrian

Blakeslee and McCourt [Blakeslee, B., & McCourt, M.E. (1997). Similar mechanisms underlie simultaneous brightness contrast and grating induction. Vision Research, 37, 2849-2869] demonstrated that a multiscale array of two-dimensional difference-of-Gaussian (DOG) filters provided a simple but powerful model for explaining a number of seemingly complex features of grating induction (GI), while simultaneously encompassing salient features of brightness induction in simultaneous brightness contrast (SBC), brightness assimilation and Hermann Grid stimuli. The DOG model (and isotropic contrast models in general) cannot, however, account for another important group of brightness effects including the White effect [White, M. (1997). A new effect of pattern on perceived lightness. Perception, 8, 413-416] and a variant of SBC [Todorovic, D. (1997). Lightness and junctions. Perception, 26, 379-395]. Blakeslee and McCourt [Blakeslee, B., McCourt, M.E. (1999). A multiscale spatial filtering account of the White effect, simultaneous brightness contrast and grating induction. Vision Research, 39, 4361-4377] developed a modified version of the model, an oriented (ODOG) model, which differed from the DOG model in that the filters were anisotropic and their outputs were pooled nonlinearly. Using this model, they were able to account for both groups of induction effects. The present paper examines two additional sets of brightness illusions that cannot be explained by isotropic contrast models. Psychophysical brightness matching is employed to quantitatively measure the size of the brightness effect for two Wertheimer-Benary stimuli [Benary, W. (1924). Beobachtungen zu einem experiment uber helligkeitskontrast. Psychologische Forschung, 5, 131-142; Todorovic, D. (1997). Lightness and junctions. Perception, 26, 379-395] and for low- and high-contrast versions of corrugated Mondrian stimuli [Adelson, E.H. (1993). Perceptual organization and the jugdement of brightness. Science, 262, 2042-2044; Todorovic, D. (1997). Lightness and junctions. Perception, 26, 379-395]. Brightness matches are obtained on both homogeneous and checkerboard matching backgrounds. The ODOG model qualitatively predicts the appearance of the test patches in the Wertheimer-Benary stimuli and corrugated Mondrian stimuli. In addition, it quantitatively predicts the relative magnitudes of the corrugated Mondrian effects in the various conditions. In general, the psychophysical results and ODOG modeling argue strongly that like SBC, GI, the White effect and Todorovic's SBC demonstration, induced brightness in Wertheimer-Benary stimuli and in the corrugated Mondrian primarily reflects early-stage filtering operations in the visual system.

Detection of incremental and decremental bars at different locations across Mach bands and related stimuli

Two-alternative forced-choice procedures were used to measure the detectability of bright and dark bars at various locations across luminance patterns that produced Mach bands. Detection performance was significantly affected by both dark and bright Mach bands: poor detection performance was observed at locations near, but not in, the Mach bands; relatively good detection performance at locations within the Mach bands was caused by reliable changes in the width, depth, or symmetry of the bands produced by the signal bars. The changes were apparent with signals of lower luminance than that needed for detection in the plateau regions far from the bands, but, because the cues were not sufficiently reliable to allow errorless performance, unusually shaped psychometric functions were obtained.

Lightness induction revisited

Lightness induction is the classical visual phenomenon whereby the lightness of an object is shown to depend on its immediate surround. Despite the long history of its study, lightness induction has not yet been coherently and satisfactorily explained in all its variety. The two main theories that compete to explain it descend (i) from H von Helmholtz, who believed that lightness induction originates from some central mechanisms that take into account the whole viewing situation, with particular stress upon the apparent illumination of the object; and (ii) E Hering who argued in favour of more peripheral sensory mechanisms based on local luminance contrast. The balance between these theories has recently been shifted towards Helmholtz's position by E H Adelson who has provided additional evidence that lightness induction depends on perceptual interpretation and, particularly, on apparent transparency. I challenge Adelson's conclusions by introducing modified versions of his tile pattern that use luminance gradients. In the first of these new demonstrations there is a strong lightness induction even though no apparent transparency is experienced. In the second there is a clear impression of transparent strips, yet no lightness induction is present. And the third shows that breaking up the Adelson tile pattern, while it affects neither the impression of transparency nor the type of grey-level junctions, makes the lightness-induction effect vanish. This implies that Adelson's illusion can be accounted for by neither local contrast, nor the apparent transparency, nor the type of grey-level junctions. Presented here is an alternative look at lightness induction as a phenomenon of the pictorial (as contrasted to natural) vision, which rests on the lightness-shadow invariance, much as Gregory's 'inappropriate constancy scaling' theory of geometrical illusions rests on the apparent size-distance invariance.

Visual neuroscience: illuminating the dark corners

Recent experiments suggest that our perception of lightness involves a sophisticated interpretation of illumination and shadow. This finding challenges common notions about hierarchical processing and the neural basis of perception.

Neural dynamics of binocular brightness perception

How does the visual cortex combine information from both eyes to generate perceptual representations of object surfaces? Important clues about this process may be derived from data about the perceived brightness of surface regions under binocular viewing conditions, including data about binocular brightness summation in response to Ganzfelds, the U-shaped data of Fechner's paradox that violates binocular brightness summation, and the effects of different combinations of monocular and binocular contours and surface luminance differences on threshold sensitivity to monocular flashes of light. How to reconcile these apparently contradictory data properties has been a severe challenge to previous models, and none has explained them all. The present article quantitatively simulates them all by further developing the FACADE vision model. Key model processes discount the illuminant and compute image contrasts in each monocular channel using shunting on-center off-surround networks; binocularly fuse these discounted monocular signals using shunting on-center off-surround networks with nonlinear excitatory and inhibitory signals; and use these binocularly fused activities to trigger filling-in of a binocular surface representation that represents perceived surface brightness. Previous models that have suggested explanations of subsets of these data are discussed.

The missing-fundamental illusion at isoluminance

The missing-fundamental illusion describes how a square wave with its fundamental Fourier component removed appears as a square wave. This illusion is normally explained with reference to the bandpass nature of the luminance-contrast-sensitivity function, together with a 'default-to-square-wave' rule. Since the chromatic-contrast-sensitivity function is low-pass, we should not expect a missing-fundamental illusion at isoluminance. Using a simultaneous-detection-and-identification paradigm to eliminate contrast as a cue to discrimination, we nevertheless found that chromatic missing fundamentals and square waves could not be separately identified at detection threshold: just under twice the contrast required to detect the stimuli was needed to identify them. To test whether this was due to insufficiently narrow chromatic-channel bandwidths, we measured detection and identification thresholds for chromatic F and 3F sine-wave gratings. In this case identification was possible almost at detection threshold, suggesting that channel bandwidth limitations were not the critical factor. It is suggested that the weak missing-fundamental illusion observed at isoluminance probably reflects the operation of mechanisms similar to those that are responsible for the chromatic Craik-Cornsweet illusion.

A multiscale spatial filtering account of the White effect, simultaneous brightness contrast and grating induction

Blakeslee and McCourt ((1997) Vision Research, 37, 2849-2869) demonstrated that a multiscale array of two-dimensional difference-of-Gaussian (DOG) filters provided a simple but powerful model for explaining a number of seemingly complex features of grating induction (GI), while simultaneously encompassing salient features of brightness induction in simultaneous brightness contrast (SBC), brightness assimilation and Hermann Grid stimuli. The DOG model (and isotropic contrast models in general) cannot, however, account for another important group of brightness effects which includes the White effect (White (1979) Perception, 8, 413-416) and the demonstrations of Todorovic ((1997) Perception, 26, 379-395). This paper introduces an oriented DOG (ODOG) model which differs from the DOG model in that the filters are anisotropic and their outputs are pooled nonlinearly. The ODOG model qualitatively predicts the appearance of the test patches in the White effect, the Todorovic demonstration, GI and SBC, while quantitatively predicting the relative magnitudes of these brightness effects as measured psychophysically using brightness matching. The model also accounts for both the smooth transition in test patch brightness seen in the White effect (White & White (1985) Vision Research, 25, 1331-1335) when the relative phase of the test patch is varied relative to the inducing grating, and for the spatial variation of brightness across the test patch as measured using point-by-point brightness matching. Finally, the model predicts intensive aspects of brightness induction measured in a series of Todorovic stimuli as the arms of the test crosses are lengthened (Pessoa, Baratoff, Neumann & Todorokov (1998) Investigative Ophthalmology and Visual Science, Supplement, 39, S159), but fails in one condition. Although it is concluded that higher-level perceptual grouping factors may play a role in determining brightness in this instance, in general the psychophysical results and ODOG modeling argue strongly that the induced brightness phenomena of SBC, GI, the White effect and the Todorovic demonstration, primarily reflect early-stage cortical filtering operations in the visual system.

A two-dimensional model of brightness perception based on spatial filtering consistent with retinal processing

We have applied a multiple scale, 2-D model of brightness perception to a broad range of brightness phenomena. The filters encapsulate only processing that is well established to occur in retinal ganglion cells. Their outputs are then combined in the simplest way compatible with the earliest levels of cortical processing. Not only essential features of a number of the phenomena but also more subtle shading effects are reproduced. Because of the retinal nature of this model, these results would appear to support previous speculation that much of the ground work for brightness perception is performed at the retinal level.

The Craik-O'Brien-Cornsweet illusion in colour: quantitative characterisation and comparison with luminance

The strength of the Craik-O'Brien-Cornsweet illusion was measured for different values of spatial and temporal stimulus parameters, in the traditional achromatic version, and in an isoluminant colour version. It was found that the illusion is much weaker with isoluminant colour stimuli than with achromatic luminance stimuli. The illusion depends on the spatial parameters of the stimulus in a way that yields an approximate scale invariance: The strength of the illusion is similar for different stimulus sizes, as long as the ratio of the width of the transition region around the edge, where luminance or colour change, to the total stimulus width is preserved. In both the achromatic and the chromatic case, the strength of the illusion decreases with increasing presentation time. The similarity of the differences between brightness and colour effects on one hand and the differences in sensitivity for colour and luminance changes in humans on the other suggests that a lack of gradient detection underlies the Craik-O'Brien-Cornsweet illusion.

The combination of filters in early spatial vision: a retrospective analysis of the MIRAGE model

Since the discovery of spatial-frequency-tuned channels in the visual system, most theories attempting to account for pattern encoding have assumed that the filters can be independently accessed and flexibly combined. We review here an alternative model, 'MIRAGE', in which the filters are inflexibly combined before pattern analysis. In the MIRAGE model the half-wave rectified outputs of all spatial-frequency channels are combined before locating spatial zero-bounded regions in the neural image, which serve as the spatial primitives for pattern analysis. We describe the evidence that led to this model, and review recent evidence on the rules of filter combination.

Brightness with and without perceived transparency: when does it make a difference?

Subjects matched the brightness of test patches whose inner (adjacent) surrounds appeared either as transparent overlays on a wider background that included the test patch or as regions differing in reflectance from the test patch and the outer surround. In the above configurations the luminance and spatial extent of the inner surround was identical, thus controlling for the effects of surround luminance. Configuration condition had a significant effect on test-patch brightness. In general, test-patch brightness was significantly elevated under conditions favouring the interpretation of the stimulus as including a transparent overlay. The largest effect occurred for the configuration in which the perception of transparency was supported by stereo depth cues. The brightness effect was mediated by the virtual transmittance of the transparent overlay, increasing in magnitude with decreasing transmittance. Further, the effect of transparency on brightness was greatest for test-patch luminances near to those of their immediate surrounds.

Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes

A number of researchers have suggested that in order to understand the response properties of cells in the visual pathway, we must consider the statistical structure of the natural environment. In this paper, we focus on one aspect of that structure, namely, the correlational structure which is described by the amplitude or power spectra of natural scenes. We propose that the principle insight one gains from considering the image spectra is in understanding the relative sensitivity of cells tuned to different spatial frequencies. This study employs a model in which the peak sensitivity is constant as a function of frequency with linear bandwith increasing (i.e., approximately constant in octaves). In such a model, the "response magnitude" (i.e., vector length) of cells increases as a function of their optimal (or central) spatial frequency out to about 20 cyc/deg. The result is a code in which the response to natural scenes, whose amplitude spectra typically fall as 1/f, is roughly constant out to 20 cyc/deg. An important consideration in evaluating this model of sensitivity is the fact that natural scenes show considerable variability in their amplitude spectra, with individual scenes showing falloffs which are often steeper or shallower than 1/f. Using a new measure of image structure (the "rectified contrast spectrum" or "RCS") on a set of calibrated natural images, it is shown that a large part of the variability in the spectra is due to differences in the sparseness of local structure at different scales. That is, an image which is "in focus" will have structure (e.g., edges) which has roughly the same magnitude across scale. That is, the loss of high frequency energy in some images is due to the reduction of the number of regions that contain structure rather than the amplitude of that structure. An "in focus" image will have structure (e.g., edges) across scale that have roughly equal magnitude but may vary in the area covered by structure. The slope of the RCS was found to provide a reasonable prediction of physical blur across a variety of scenes in spite of the variability in their amplitude spectra. It was also found to produce a good prediction of perceived blur as judged by human subjects.