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A Bayesian observer model reveals a prior for natural daylights in hue perception
Equivalent electrical circuits (ECM) have proven to be effective in modeling the dynamic behavior of proton exchange membrane (PEM) electrolyzer voltage response. They are a valuable tool for studying the interactions between power electronics and PEM electrolyzers during dynamic operating conditions. Generally, the ECM takes into consideration the activation over-voltage that is present at both the anode and the cathode for the dynamic part of the model. Therefore, the monitoring of the ECM activation over-voltage is an important issue for the correct modeling of the PEM electrolyzer voltage. However, voltage sensors for this over-voltage are expensive and the reported observers of the PEM electrolyzer activation over-voltage are scarce and have not been validated over a sufficiently long time. This work aims at overcoming these drawbacks by proposing the use of a Luenberger observer to accurately estimate the activation over-voltage using an ECM. Based on this proposal, it is possible to build a device capable of emulating the electrolyzer voltage efficiently. Furthermore, a stability analysis of the observable system is provided to ensure its performance throughout the experiment period. Statistical results, based on experimental voltage data from a PEM electrolyzer QL–300, demonstrate the high accuracy and performance of the Luenberger observer under continuous changes in input currents, which demonstrates its robustness.
Neurons throughout the brain modulate their firing rate lawfully in response to sensory input. Theories of neural computation posit that these modulations reflect the outcome of a constrained optimization in which neurons aim to robustly and efficiently represent sensory information. Our understanding of how this optimization varies across different areas in the brain, however, is still in its infancy. Here, we show that neural sensory responses transform along the dorsal stream of the visual system in a manner consistent with a transition from optimizing for information preservation towards optimizing for perceptual discrimination. Focusing on the representation of binocular disparities—the slight differences in the retinal images of the two eyes—we re-analyze measurements characterizing neuronal tuning curves in brain areas V1, V2, and MT (middle temporal) in the macaque monkey. We compare these to measurements of the statistics of binocular disparity typically encountered during natural behaviors using a Fisher Information framework. The differences in tuning curve characteristics across areas are consistent with a shift in optimization goals: V1 and V2 population-level responses are more consistent with maximizing the information encoded about naturally occurring binocular disparities, while MT responses shift towards maximizing the ability to support disparity discrimination. We find that a change towards tuning curves preferring larger disparities is a key driver of this shift. These results provide new insight into previously-identified differences between disparity-selective areas of cortex and suggest these differences play an important role in supporting visually-guided behavior. Our findings emphasize the need to consider not just information preservation and neural resources, but also relevance to behavior, when assessing the optimality of neural codes.
How we perceive a visual stimulus can be influenced by its surrounding context. For example, the presence of a reference skews the perception of a similar feature in a stimulus, a phenomenon called reference repulsion. Ongoing research so far remains inconclusive regarding the stage of visual information processing where such repulsion occurs. We examined the influence of a reference on late visual processing. We measured the repulsion effect caused by an orientation reference presented after an orientation ensemble stimulus. The participants’ reported orientations were significantly biased away from the post-stimulus reference, displaying typical characteristics of reference repulsion. Moreover, explicit discrimination choices between the reference and the stimulus influenced the magnitudes of repulsion effects, which can be explained by an encoding-decoding model that differentiates the re-weighting of sensory representations in implicit and explicit processes. These results support the notion that reference repulsion may arise at a late decision-related stage of visual processing, where different sensory decoding strategies are employed depending on the specific task.
In conceptual spaces, the distance between concepts is represented by a metric that cannot usually be expressed as a function of a few, salient physical properties of the represented items. For example, the space of colours can be endowed with a metric capturing the degree to which two chromatic stimuli are perceived as different. But as many optical illusions have shown, the colour with which a stimulus is perceived depends, among other contextual factors, on the chromaticity of its surround, an effect called "chromatic induction". The surround pushes the colour of the stimulus away from its own chromaticity, increasing the salience of the boundary. Previous studies have described how the magnitude of the push depends on the chromaticity of both the stimulus and the surround, concluding that the space of colours contains anisotropies and inhomogeneities. The importance of contextuality has cast doubt on the practical or predictive utility of perceptual metrics, beyond a mathematical curiosity. Here we provide evidence that the metric structure of the space of colours is indeed useful and has predictive power. By using a notion of distance between colours emerging from a subjective metric, we show that the anisotropies and inhomogeneities reported in previous studies can be eliminated. The resulting symmetry allows us to derive a universal curve for the average chromatic induction that contains no fitting parameters and is confirmed by experimental data. The theory also predicts the magnitude of chromatic induction for every possible combination of stimulus and surround demonstrating that, at least in the case of colours, the metric captures the symmetries of perception, and augments the predictive power of theories.
The irreducible unique hues—red, green, blue, and yellow—remain one of the great mysteries of vision science. Attempts to create a physiologically parsimonious model that can predict the spectral locations of the unique hues all rely on at least one post hoc adjustment to produce appropriate loci for unique green and unique red, and struggle to explain the non-linearity of the Blue/Yellow system. We propose a neurobiological color vision model that overcomes these challenges by using physiological cone ratios, cone-opponent normalization to equal-energy white, and a simple adaptation mechanism to produce color-opponent mechanisms that accurately predict the spectral locations and variability of the unique hues.
Studies of color perception have led to mechanistic models of how cone-opponent signals from retinal ganglion cells are integrated to generate color appearance. But it is unknown how this hypothesized integration occurs in the brain. Here we show that cone-opponent signals transmitted from retina to primary visual cortex (V1) are integrated through highly organized circuits within V1 to implement the color opponent interactions required for color appearance. Combining intrinsic signal optical imaging (ISI) and 2-photon calcium imaging (2PCI) at single cell resolution, we demonstrate cone-opponent functional domains (COFDs) that combine L/M cone-opponent and S/L + M cone-opponent signals following the rules predicted from psychophysical studies of color perception. These give rise to an orderly organization of hue preferences of the neurons within the COFDs and the generation of hue “pinwheels”. Thus, spatially organized neural circuits mediate an orderly transition from cone-opponency to color appearance that begins in V1. Psychophysical studies predict that retinal cone-opponent mechanisms interact in specific combinations to generate color perception. Here, the authors show that the predicted interactions are implemented by organized circuits in primary visual cortex.
Perception of magnitudes such as duration or distance is often found to be systematically biased. The biases, which result from incorporating prior knowledge in the perceptual process, can vary considerably between individuals. The variations are commonly attributed to differences in sensory precision and reliance on priors. However, another factor not considered so far is the implicit belief about how successive sensory stimuli are generated: independently from each other or with certain temporal continuity. The main types of explanatory models proposed so far—static or iterative—mirror this distinction but cannot adequately explain individual biases. Here we propose a new unifying model that explains individual variation as combination of sensory precision and beliefs about temporal continuity and predicts the experimentally found changes in biases when altering temporal continuity. Thus, according to the model, individual differences in perception depend on beliefs about how stimuli are generated in the world.
Our sensory systems transform external signals into neural activity, thereby producing percepts. We are endowed with an intuitive notion of similarity between percepts, that need not reflect the proximity of the physical properties of the corresponding external stimuli. The quantitative characterization of the geometry of percepts is therefore an endeavour that must be accomplished behaviorally. Here we characterized the geometry of color space using discrimination and matching experiments. We proposed an individually tailored metric defined in terms of the minimal chromatic difference required for each observer to differentiate a stimulus from its surround. Next, we showed that this perceptual metric was particularly adequate to describe two additional experiments, since it revealed the natural symmetry of perceptual computations. In one of the experiments, observers were required to discriminate two stimuli surrounded by a chromaticity that differed from that of the tested stimuli. In the perceptual coordinates, the change in discrimination thresholds induced by the surround followed a simple law that only depended on the perceptual distance between the surround and each of the two compared stimuli. In the other experiment, subjects were asked to match the color of two stimuli surrounded by two different chromaticities. Again, in the perceptual coordinates the induction effect produced by surrounds followed a simple, symmetric law. We conclude that the individually-tailored notion of perceptual distance reveals the symmetry of the laws governing perceptual computations.
Comment: 42 pages, 9 figures, 1 appendix. (v2) 47 pages, 10 figures, 1 appendix. (v3) Text modified after peer-review process. (v4) 34 pages, 1 appendix, 10 figures. Article accepted to be published at Mathematical Neuroscience and Applications
According to the efficient coding hypothesis, sensory systems are adapted to maximize their ability to encode information about the environment. Sensory neurons play a key role in encoding by selectively modulating their firing rate for a subset of all possible stimuli. This pattern of modulation is often summarized via a tuning curve. The optimally efficient distribution of tuning curves has been calculated in variety of ways for one-dimensional (1-D) stimuli. However, many sensory neurons encode multiple stimulus dimensions simultaneously. It remains unclear how applicable existing models of 1-D tuning curves are for neurons tuned across multiple dimensions. We describe a mathematical generalization that builds on prior work in 1-D to predict optimally efficient multidimensional tuning curves. Our results have implications for interpreting observed properties of neuronal populations. For example, our results suggest that not all tuning curve attributes (such as gain and bandwidth) are equally useful for evaluating the encoding efficiency of a population.
Colors are represented in the cone-opponent signals, L-M vs S cones, at least up to the level of inputs to the primary visual cortex. We explored the hue selective responses in early cortical visual areas through recordings of steady-state visual evoked potentials (SSVEPs), elicited by a flickering checkerboard whose color smoothly swept around the hue circle defined in a cone-opponent color space. If cone-opponency dominates hue representation in the source of SSVEP signals, SSVEP amplitudes as a function of hue should form a profile that is line-symmetric along the cardinal axes of the cone-opponent color space. Observed SSVEP responses were clearly chromatic ones with increased SSVEP amplitudes and reduced response latencies for higher contrast conditions. The overall elliptic amplitude profile was significantly tilted away from the cardinal axes to have the highest amplitudes in the “lime-magenta” direction, indicating that the hue representation in question is not dominated by cone-opponency. The observed SSVEP amplitude hue profile was better described as a summation of a perceptual response and cone-opponent responses with a larger weight to the former. These results indicate that hue representations in the early visual cortex, measured by the SSVEP technique, are possibly related to perceptual color contrast.
Color serves both to segment a scene into objects and background and to identify objects. Although objects and surfaces usually contain multiple colors, humans can readily extract a representative color description, for instance, that tomatoes are red and bananas yellow. The study of color discrimination and identification has a long history, yet we know little about the formation of summary representations of multicolored stimuli. Here, we characterize the human ability to integrate hue information over space for simple color stimuli varying in the amount of information, stimulus size, and spatial configuration of stimulus elements. We show that humans are efficient at integrating hue information over space beyond what has been shown before for color stimuli. Integration depends only on the amount of information in the display and not on spatial factors such as element size or spatial configuration in the range measured. Finally, we find that observers spontaneously prefer a simple averaging strategy even with skewed color distributions. These results shed light on how human observers form summary representations of color and make a link between the perception of polychromatic surfaces and the broader literature of ensemble perception.
Conventional models of color vision assume that blue and yellow (along with red and green) are the fundamental building blocks of color appearance, yet how these hues are represented in the brain and whether and why they might be special are questions that remain shrouded in mystery. Many studies have explored the visual encoding of color categories, from the statistics of the environment to neural processing to perceptual experience. Blue and yellow are tied to salient features of the natural color world, and these features have likely shaped several important aspects of color vision. However, it remains less certain that these dimensions are encoded as primary or “unique” in the visual representation of color. There are also striking differences between blue and yellow percepts that may reflect high-level inferences about the world, specifically about the colors of light and surfaces. Moreover, while the stimuli labeled as blue or yellow or other basic categories show a remarkable degree of constancy within the observer, they all vary independently of one another across observers. This pattern of variation again suggests that blue and yellow and red and green are not a primary or unitary dimension of color appearance, and instead suggests a representation in which different hues reflect qualitatively different categories rather than quantitative differences within an underlying low-dimensional “color space.”
We measured discrimination thresholds for illumination changes along different chromatic directions starting from chromatically biased reference illuminations. Participants viewed a Mondrian-papered scene illuminated by LED lamps. The scene was first illuminated by a reference illumination, followed by two comparisons. One comparison matched the reference (the target); the other (the test) varied from the reference, nominally either bluer, yellower, redder, or greener. The participant's task was to correctly select the target. A staircase procedure found thresholds for discrimination of an illumination change along each axis of chromatic change. Nine participants completed the task for five different reference illumination conditions (neutral, blue, yellow, red, and green). We find that relative discrimination thresholds for different chromatic directions of illumination change vary with the reference illumination. For the neutral reference, there is a trend for thresholds to be highest in the bluer illumination-change direction, replicating our previous reports of a "blue bias" for neutral reference illuminations. For the four chromatic references (blue, yellow, red, and green), the change in illumination toward the neutral reference is less well discriminated than changes in the other directions: a "neutral bias." The results have implications for color constancy: In considering the stability of surface appearance under changes in illumination, both the starting chromaticity of the illumination and direction of change must be considered, as well as the chromatic characteristics of the surface reflectance ensemble. They also suggest it will be worthwhile to explore whether and how the human visual system has internalized the statistics of natural illumination changes.
PsychoPy is an application for the creation of experiments in behavioral science (psychology, neuroscience, linguistics, etc.) with precise spatial control and timing of stimuli. It now provides a choice of interface; users can write scripts in Python if they choose, while those who prefer to construct experiments graphically can use the new Builder interface. Here we describe the features that have been added over the last 10 years of its development. The most notable addition has been that Builder interface, allowing users to create studies with minimal or no programming, while also allowing the insertion of Python code for maximal flexibility. We also present some of the other new features, including further stimulus options, asynchronous time-stamped hardware polling, and better support for open science and reproducibility. Tens of thousands of users now launch PsychoPy every month, and more than 90 people have contributed to the code. We discuss the current state of the project, as well as plans for the future.
We investigated several sensory and cognitive determinants of colour constancy across 40 illumination hues. In the first experiment, we measured colour naming for the illumination and for the colour induced by the illumination on the colorimetric grey. Results confirmed that the induced colours are approximately complementary to the colour of the illumination. In the second experiment, we measured colour constancy using achromatic adjustments. Average colour constancy was perfect under the blue daylight illumination and decreased in colour directions away from the blue daylight illumination due to undershooting and a strong blue bias. Apart from this blue bias, colour constancy was not related to illumination discrimination and to chromatic detection measured previously with the same setup and stimuli. We also observed a strong negative relationship between the degree of colour constancy and the consensus of naming the illumination colour. Constancy coincided with a low naming consensus, in particular because bluish illumination colours were sometimes seen as achromatic. Blue bias and category consensus alone explained >68%, and all determinants together explained >94% of the variance of achromatic adjustments. These findings suggest that colour constancy is optimised for blue daylight.
Significance
We present a law of human perception. The law expresses a mathematical relation between our ability to perceptually discriminate a stimulus from similar ones and our bias in the perceived stimulus value. We derived the relation based on theoretical assumptions about how the brain represents sensory information and how it interprets this information to create a percept. Our main assumption is that both encoding and decoding are optimized for the specific statistical structure of the sensory environment. We found large experimental support for the law in the literature, which includes biases and changes in discriminability induced by contextual modulation (e.g., adaptation). Our results imply that human perception generally relies on statistically optimized processes.
Characterizing humans' ability to discriminate changes in illumination provides information about the visual system's representation of the distal stimulus. We have previously shown that humans are able to discriminate illumination changes and that sensitivity to such changes depends on their chromatic direction. Probing illumination discrimination further would be facilitated by the use of computer-graphics simulations, which would, in practice, enable a wider range of stimulus manipulations. There is no a priori guarantee, however, that results obtained with simulated scenes generalize to real illuminated scenes. To investigate this question, we measured illumination discrimination in real and simulated scenes that were well-matched in mean chromaticity and scene geometry. Illumination discrimination thresholds were essentially identical for the two stimulus types. As in our previous work, these thresholds varied with illumination change direction. We exploited the flexibility offered by the use of graphics simulations to investigate whether the differences across direction are preserved when the surfaces in the scene are varied. We show that varying the scene's surface ensemble in a manner that also changes mean scene chromaticity modulates the relative sensitivity to illumination changes along different chromatic directions. Thus, any characterization of sensitivity to changes in illumination must be defined relative to the set of surfaces in the scene.
A chromatic surround can have a strong influence on the perceived hue of a stimulus. We investigated whether chromatic induction has similar effects on the perception of colors that appear pure and unmixed (unique red, green, blue, and yellow) as on other colors. Subjects performed unique hue settings of stimuli in isoluminant surrounds of different chromaticities. Compared with the settings in a neutral gray surround, unique hue settings altered systematically with chromatic surrounds. The amount of induced hue shift depended on the difference between stimulus and surround hues, and was similar for unique hue settings as for settings of nonunique hues. Intraindividual variability in unique hue settings was roughly twice as high as for settings obtained in asymmetric matching experiments, which may reflect the presence of a reference stimulus in the matching task. Variabilities were also larger with chromatic surrounds than with neutral gray surrounds, for both unique hue settings and matching of nonunique hues. The results suggest that the neural representations underlying unique hue percepts are influenced by the same neural processing mechanisms as the percepts of other colors.
To shed light on the perceptual basis of the color white, we measured settings of unique white in a dark surround. We find that settings reliably show more variability in an oblique (blue-yellow) direction in color space than along the cardinal axes of the cone-opponent mechanisms. This is against the idea that white perception arises at the null point of the cone-opponent mechanisms, but one alternative possibility is that it occurs through calibration to the visual environment. We found that the locus of maximum variability in settings lies close to the locus of natural daylights, suggesting that variability may result from uncertainty about the color of the illuminant. We tested this by manipulating uncertainty. First, we altered the extent to which the task was absolute (requiring knowledge of the illumination) or relative. We found no clear effect of this factor on the reduction in sensitivity in the blue-yellow direction. Second, we provided a white surround as a cue to the illumination or left the surround dark. Sensitivity was selectively worse in the blue-yellow direction when the surround was black than when it was white. Our results can be functionally related to the statistics of natural images, where a greater blue-yellow dispersion is characteristic of both reflectances (where anisotropy is weak) and illuminants (where it is very pronounced). Mechanistically, the results could suggest a neural signal responsive to deviations from the blue-yellow locus or an adaptively matched range of contrast response functions for signals that encode different directions in color space.
The variability of color-selective neurons in human visual cortex is considered more diverse than cone-opponent mechanisms.
We addressed this issue by deriving histograms of hue-selective voxels measured using fMRI with a novel stimulation paradigm,
where the stimulus hue changed continuously. Despite the large between-subject difference in hue-selective histograms, individual
voxels exhibited selectivity for intermediate hues, such as purple, cyan, and orange, in addition to those along cone-opponent
axes. In order to rule the possibility out that the selectivity for intermediate hues emerged through spatial summation of
activities of neurons selectively responding to cone-opponent signals, we further tested hue-selective adaptations in intermediate
directions of cone-opponent axes, by measuring responses to 4 diagonal hues during concurrent adaptation to 1 of the 4 hues.
The selective and unidirectional reduction in response to the adapted hue lends supports to our argument that cortical neurons
respond selectively to intermediate hues.
Bayesian observer models provide a principled account of the fact that our perception of the world rarely matches physical reality. The standard explanation is that our percepts are biased toward our prior beliefs. However, reported psychophysical data suggest that this view may be simplistic. We propose a new model formulation based on efficient coding that is fully specified for any given natural stimulus distribution. The model makes two new and seemingly anti-Bayesian predictions. First, it predicts that perception is often biased away from an observer's prior beliefs. Second, it predicts that stimulus uncertainty differentially affects perceptual bias depending on whether the uncertainty is induced by internal or external noise. We found that both model predictions match reported perceptual biases in perceived visual orientation and spatial frequency, and were able to explain data that have not been explained before. The model is general and should prove applicable to other perceptual variables and tasks.
The psychometric function relates an observer’s performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric functions, (2) assessing the goodness of fit, and (3) providing confidence intervals for the function’s parameters and other estimates derived from them, for the purposes of hypothesis testing. The present paper deals with the first two topics, describing a constrained maximum-likelihood method of parameter estimation and developing several goodness-of-fit tests. Using Monte Carlo simulations, we deal with two specific difficulties that arise when fitting functions to psychophysical data. First, we note that human observers are prone to stimulus-independent errors (orlapses). We show that failure to account for this can lead to serious biases in estimates of the psychometric function’s parameters and illustrate how the problem may be overcome. Second, we note that psychophysical data sets are usually rather small by the standards required by most of the commonly applied statistical tests. We demonstrate the potential errors of applying traditionalX
2 methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods.
'The dress' is a peculiar photograph: by themselves the dress' pixels are brown and blue, colors associated with natural illuminants [1], but popular accounts (#TheDress) suggest the dress appears either white/gold or blue/black [2]. Could the purported categorical perception arise because the original social-media question was an alternative-forced-choice? In a free-response survey (N = 1401), we found that most people, including those naïve to the image, reported white/gold or blue/black, but some said blue/brown. Reports of white/gold over blue/black were higher among older people and women. On re-test, some subjects reported a switch in perception, showing the image can be multistable. In a language-independent measure of perception, we asked subjects to identify the dress' colors from a complete color gamut. The results showed three peaks corresponding to the main descriptive categories, providing additional evidence that the brain resolves the image into one of three stable percepts. We hypothesize that these reflect different internal priors: some people favor a cool illuminant (blue sky), discount shorter wavelengths, and perceive white/gold; others favor a warm illuminant (incandescent light), discount longer wavelengths, and see blue/black. The remaining subjects may assume a neutral illuminant, and see blue/brown. We show that by introducing overt cues to the illumination, we can flip the dress color.
Copyright © 2015 Elsevier Ltd. All rights reserved.
This study investigated the perception of colorful ensembles and the effect of categories and perceptual similarity on their representation. We briefly presented ensembles of two hues and tested hue recognition with a range of seen and unseen hues. The average hue was familiar, even though it never appeared in the ensembles. Increasing the perceptual difference of ensemble hues inhibited this mean bias, and the categorical relationship of hues also affected the distribution of familiarity. The findings suggest there is an ensemble perception of hue, but this is affected by the categorical and metric relationships of the elements in the ensemble.
The average of a color distribution has special significance for color coding (e.g., to estimate the illuminant) but how it depends on the visual representation (e.g., perceptual versus cone-opponent) or nonlinearities (e.g., categorical coding) is unknown. We measured the perceived average of two colors shown alternated in spatial arrays. Observers adjusted the components until the average equaled a specified reference hue. Matches for red, blue–red, or yellow–green were consistent with the arithmetic mean chromaticity, while blue–green settings deviated toward blue. The settings show little evidence for categorical coding, and cannot be predicted from the scaled appearances of the individual components.
The phenomenon of colour constancy in human visual perception keeps surface colours constant, despite changes in their reflected light due to changing illumination. Although colour constancy has evolved under a constrained subset of illuminations, it is unknown whether its underlying mechanisms, thought to involve multiple components from retina to cortex, are optimised for particular environmental variations. Here we demonstrate a new method for investigating colour constancy using illumination matching in real scenes which, unlike previous methods using surface matching and simulated scenes, allows testing of multiple, real illuminations. We use real scenes consisting of solid familiar or unfamiliar objects against uniform or variegated backgrounds and compare discrimination performance for typical illuminations from the daylight chromaticity locus (approximately blue-yellow) and atypical spectra from an orthogonal locus (approximately red-green, at correlated colour temperature 6700 K), all produced in real time by a 10-channel LED illuminator. We find that discrimination of illumination changes is poorer along the daylight locus than the atypical locus, and is poorest particularly for bluer illumination changes, demonstrating conversely that surface colour constancy is best for blue daylight illuminations. Illumination discrimination is also enhanced, and therefore colour constancy diminished, for uniform backgrounds, irrespective of the object type. These results are not explained by statistical properties of the scene signal changes at the retinal level. We conclude that high-level mechanisms of colour constancy are biased for the blue daylight illuminations and variegated backgrounds to which the human visual system has typically been exposed.
In the retina of trichromatic primates, chromatic information is encoded in an opponent fashion and transmitted to the lateral geniculate nucleus (LGN) and visual cortex via parallel pathways. Chromatic selectivities of neurons in the LGN form two separate clusters, corresponding to two classes of cone opponency. In the visual cortex, however, the chromatic selectivities are more distributed, which is in accordance with a population code for color. Previous studies of cone signals in natural scenes typically found opponent codes with chromatic selectivities corresponding to two directions in color space. Here we investigated how the non-linear spatio-chromatic filtering in the retina influences the encoding of color signals. Cone signals were derived from hyper-spectral images of natural scenes and preprocessed by center-surround filtering and rectification, resulting in parallel ON and OFF channels. Independent Component Analysis (ICA) on these signals yielded a highly sparse code with basis functions that showed spatio-chromatic selectivities. In contrast to previous analyses of linear transformations of cone signals, chromatic selectivities were not restricted to two main chromatic axes, but were more continuously distributed in color space, similar to the population code of color in the early visual cortex. Our results indicate that spatio-chromatic processing in the retina leads to a more distributed and more efficient code for natural scenes.
Categorical perception provides a potential link between color perception and the linguistic categories that correspond to the basic color terms. We examined whether the sensory information of the second-stage chromatic mechanisms is further processed so that sensitivity for color differences yields categorical perception. In this case, sensitivity for color differences should be higher across than within category boundaries. We measured discrimination thresholds (JNDs) and color categories around an isoluminant hue circle in Derrington-Krauskopf-Lennie (DKL) color space at three levels of lightness. At isoluminant lightness, the global pattern of JNDs coarsely followed an ellipse. Deviations from the ellipse coincided with the orange-pink and the blue-green category borders, but these minima were also aligned with the second-stage cone-opponent mechanisms. No evidence for categorical perception of color was found for any other category borders. At lower lightness, categories changed substantially, but JNDs did not change accordingly. Our results point to a loose relationship between color categorization and discrimination. However, the coincidence of some boundaries with JND minima is not a general property of color categorical boundaries. Hence, our basic ability to discriminate colors cannot fully explain why we use the particular set of categories to communicate about colors. Moreover, these findings seriously challenge the idea that color naming forms the basis for the categorical perception of colors. With respect to previous studies that concentrated on the green-blue boundary, our results highlight the importance of controlling perceptual distances and examining the full set of categories when investigating category effects on color perception.
In this paper, we first prove that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent
property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder-Mead
algorithm becomes inefficient in high dimensions. We then propose an implementation of the Nelder-Mead method in which the
expansion, contraction, and shrink parameters depend on the dimension of the optimization problem. Our numerical experiments
show that the new implementation outperforms the standard Nelder-Mead method for high dimensional problems.
KeywordsNelder-Mead method–Simplex–Polytope–Adaptive parameter–Optimization
Colors defined by the two intermediate directions in color space, “orange–cyan” and “lime–magenta,” elicit the same spatiotemporal average response from the two cardinal chromatic channels in the lateral geniculate nucleus (LGN). While we found LGN functional magnetic resonance imaging (fMRI) responses to these pairs of colors were statistically indistinguishable, primary visual cortex (V1) fMRI responses were stronger to orange–cyan. Moreover, linear combinations of single-cell responses to cone-isolating stimuli of V1 cone-opponent cells also yielded stronger predicted responses to orange–cyan over lime–magenta, suggesting these neurons underlie the fMRI result. These observations are consistent with the hypothesis that V1 recombines LGN signals into “higher-order” mechanisms tuned to noncardinal color directions. In light of work showing that natural images and daylight samples are biased toward orange–cyan, our findings further suggest that V1 is adapted to daylight. V1, especially double-opponent cells, may function to extract spatial information from color boundaries correlated with scene-structure cues, such as shadows lit by ambient blue sky juxtaposed with surfaces reflecting sunshine.
Inferences about mechanisms at one particular stage of a visual pathway may be made from psychophysical thresholds only if the noise at the stage in question dominates that in the others. Spectral sensitivities, measured under bright conditions, for di-, tri-, and tetrachromatic eyes from a range of animals can be modelled by assuming that thresholds are set by colour opponency mechanisms whose performance is limited by photoreceptor noise, the achromatic signal being disregarded. Noise in the opponency channels themselves is therefore not statistically independent, and it is not possible to infer anything more about the channels from psychophysical thresholds. As well as giving insight into mechanisms of vision, the model predicts the performance of colour vision in animals where physiological and anatomical data on the eye are available, but there are no direct measurements of perceptual thresholds. The model, therefore, is widely applicable to comparative studies of eye design and visual ecology.
Humans are good at performing visual tasks, but experimental measurements have revealed substantial biases in the perception of basic visual attributes. An appealing hypothesis is that these biases arise through a process of statistical inference, in which information from noisy measurements is fused with a probabilistic model of the environment. However, such inference is optimal only if the observer's internal model matches the environment. We found this to be the case. We measured performance in an orientation-estimation task and found that orientation judgments were more accurate at cardinal (horizontal and vertical) orientations. Judgments made under conditions of uncertainty were strongly biased toward cardinal orientations. We estimated observers' internal models for orientation and found that they matched the local orientation distribution measured in photographs. In addition, we determined how a neural population could embed probabilistic information responsible for such biases.
Are boundaries between color categories associated with enhanced discrimination? In the present experiments, chromatic thresholds were obtained for discriminations along lines orthogonal to the yellow-blue axis of color space. The targets were parafoveal and thresholds were measured with a spatial two-alternative forced choice. In interleaved experimental runs, we also obtained empirical estimates of the subjective yellow-blue line by asking observers to categorize colors as reddish or greenish. Both types of measurement were made in the presence of a steady background that was metameric to equal-energy white. In a limited region from desaturated yellow to desaturated blue, an enhanced discrimination is found near the subjective transition between reddish and greenish hues. This line of optimal discrimination is not aligned with either of the cardinal axes of color space: In a MacLeod-Boynton chromaticity diagram, it runs obliquely with negative slope.
We have measured color discrimination in the isoluminant plane under rigorously controlled adaptation conditions. Two regimes were studied. Under the first regime the observer was adapted to the region of color space in which the discriminations were made. Thresholds for detecting changes along the S-(L + M) axis are a linearly increasing function of the excitation of the S cones. Thresholds for detecting changes along the L-M axis are independent of the locus of adaptation along this axis. The straightness of these functions is inconsistent with the theory that second stage mechanisms are more sensitive in the middle of their operating ranges. No convincing evidence of interactions in the effects of adaptation locus or test stimuli was observed. Under the second regime the observer was adapted to one point in color space and the stimuli to be discriminated were located in other places in color space. Discrimination seems to be limited primarily by mechanisms maximally sensitive to modulation along the isoluminant cardinal axes but evidence suggestive of the operation of higher order mechanisms was also found.
We measured the responses of 305 neurons in striate cortex to moving sinusoidal gratings modulated in chromaticity and luminance about a fixed white point. Stimuli were represented in a 3-dimensional color space defined by 2 chromatic axes and a third along which luminance varied. With rare exceptions the chromatic properties of cortical neurons were well described by a linear model in which the response of a cell is proportional to the sum (for complex cells, the rectified sum) of the signals from the 3 classes of cones. For each cell there is a vector passing through the white point along which modulation gives rise to a maximal response. The elevation (theta m) and azimuth (phi m) of this vector fully describe the chromatic properties of the cell. The linear model also describes neurons in l.g.n. (Derrington et al., 1984), so most neurons in striate cortex have the same chromatic selectivity as do neurons in l.g.n. However, the distributions of preferred vectors differed in cortex and l.g.n.: Most cortical neurons preferred modulation along vectors lying close to the achromatic axis and those showing overt chromatic opponency did not fall into the clearly defined chromatic groups seen in l.g.n. The neurons most responsive to chromatic modulation (found mainly in layers IVA, IVC beta, and VI) had poor orientation selectivity, and responded to chromatic modulation of a spatially uniform field at least as well as they did to any grating. We encountered neurons with band-pass spatial selectivity for chromatically modulated stimuli in layers II/III and VI. Most had complex receptive fields. Neurons in layer II/III did not fall into distinct groups according to their chromatic sensitivities, and the chromatic properties of neurons known to lie within regions rich in cytochrome oxidase appeared no different from those of neurons in the interstices. Six neurons, all of which resembled simple cells, showed unusually sharp chromatic selectivity.
The sense of time is foundational for perception and action, yet it frequently departs significantly from physical time. In the paper we review recent progress on temporal contextual effects, multisensory temporal integration, temporal recalibration, and related computational models. We suggest that subjective time arises from minimizing prediction errors and adaptive recalibration, which can be unified in the framework of predictive coding, a framework rooted in Helmholtz's ‘perception as inference’.
The perceived color of a chromatic stimulus is influenced by the chromaticity of its surround. To investigate these influences along the dimension of hue, we measured hue changes induced in stimuli of different hues by isoluminant chromatic surrounds. Generally, induced hue changes were directed in color space away from the hue of the inducing surround and depended on the magnitude on the hue difference between stimulus and surround. With increasing difference in hue between stimulus and surround, induced hue changes increased up to a maximum and then decreased for larger differences. This qualitative pattern was similar for different inducers, but quantitatively, induction was weaker along some directions in cone-opponent color space than along other directions. The strongest induction effects were found along an oblique, blue-yellow axis that corresponds to the daylight axis. The overall pattern of the induction effect shows similarities to the well-known tilt effect, where shifts in perceived angle of oriented stimuli are induced by oriented surrounds. This suggests analogous neural representations and similar mechanisms of contextual processing for different visual features such as orientation and color.
Full text available: http://jov.arvojournals.org/article.aspx?articleid=2363074
The ability to extract the mean of features from a rapidly viewed, heterogeneous array of objects has been demonstrated for a number of different visual properties. Few studies have previously investigated the rapid averaging of color; those that did had insufficient stimulus control or inappropriate methods. This study reports three experiments that directly test observers' ability to extract the mean hue from a rapidly presented, multielement color ensemble. In Experiment 1, ensembles varied in number of elements and number of colors. It was found that averaging was harder for ensembles with more colors but that changing the number of elements had no effect on accuracy, supportive of a distributed-attention account of rapid color averaging. Experiment 2a manipulated the hue range present in any single ensemble (varying the perceptual difference between ensemble elements) while still varying the number of colors. Range had a strong effect on ability to pick the mean hue. Experiment 2b found no effect of color categories on the accuracy or speed of mean selection. The results indicate that perceptual difference of elements is the dominant factor affecting ability to average rapidly seen color ensembles. Findings are discussed both in the context of perception and memory of multiple colors and ensemble perception generally.
The perception of color poses daunting challenges, because the light spectrum reaching the eye depends on both the reflectance of objects and the spectrum of the illuminating light source. Solving this problem requires sophisticated inferences about the properties of lighting and surfaces, and many striking examples of 'color constancy' illustrate how our vision compensates for variations in illumination to estimate the color of objects (for example [1-3]). We discovered a novel property of color perception and constancy, involving how we experience shades of blue versus yellow. We found that surfaces are much more likely to be perceived as white or gray when their color is varied along bluish directions, compared with equivalent variations along yellowish (or reddish or greenish) directions. This selective bias may reflect a tendency to attribute bluish tints to the illuminant rather than the object, consistent with an inference that indirect lighting from the sky and in shadows tends to be bluish [4]. The blue-yellow asymmetry has striking effects on the appearance of images when their colors are reversed, turning white to yellow and silver to gold, and helps account for the variation among observers in the colors experienced in 'the dress' image that recently consumed the internet. Observers variously describe the dress as blue-black or white-gold, and this has been explained by whether the dress appears to be in direct lighting or shade (for example [5]). We show that these individual differences and potential lighting interpretations also depend on the special ambiguity of blue, for simply reversing the image colors causes almost all observers to report the lighter stripes as yellowish.
Copyright © 2015 Elsevier Ltd. All rights reserved.
There has been an intense discussion among the public about the colour of a dress, shown in a picture posted originally on Tumblr (http://swiked.tumblr.com/post/112073818575/guys-please-help-me-is-this-dress-white-and; accessed on 10:56 am GMT on Tue 24 Mar 2015). Some people argue that they see a white dress with golden lace, while others describe the dress as blue with black lace. Here we show that the question "what colour is the dress?" has more than two answers. In fact, there is a continuum of colour percepts across different observers. We measured colour matches on a calibrated screen for two groups of observers who had reported different percepts of the dress. Surprisingly, differences between the two groups arose mainly from differences in lightness, rather than chromaticity of the colours they adjusted to match the dress. We speculate that the ambiguity arises in the case of this particular image because the distribution of colours within the dress closely matches the distribution of natural daylights. This makes it more difficult to disambiguate illumination changes from those in reflectance.
Copyright © 2015 Elsevier Ltd. All rights reserved.
Precise timing is crucial to decision-making and behavioral control, yet subjective time can be easily distorted by various temporal contexts. Application of a Bayesian framework to various forms of contextual calibration reveals that, contrary to popular belief, contextual biases in timing help to optimize overall performance under noisy conditions. Here, we review recent progress in understanding these forms of temporal calibration, and integrate a Bayesian framework with information-processing models of timing. We show that the essential components of a Bayesian framework are closely related to the clock, memory, and decision stages used by these models, and that such an integrated framework offers a new perspective on distortions in timing and time perception that are otherwise difficult to explain.
We gathered hyperspectral images of natural, foliage-dominated scenes and converted them to human cone quantal catches to characterize the second-order redundancy present within the retinal photoreceptor array under natural conditions. The data are expressed most simply in a logarithmic response space, wherein an orthogonal decorrelation robustly produces three principal axes, one corresponding to simple changes in radiance and two that are reminiscent of the blue–yellow and red–green chromatic-opponent mechanisms found in the primate visual system. Further inclusion of spatial stimulus dimensions demonstrates a complete spatial decorrelation of these three cone-space axes in natural cone responses.
consider some characteristics of the perception and representation of colors that, although not universal in animal vision, do appear to be universal in the normal color vision of humans, prevalent in other primates, and common in a number of other quite different but also highly visual species, including the birds and the bees
questions raised are (a) whether these characteristics of color perception and representation are merely arbitrary design features of these particular species, (b) whether these characteristics arose as specific adaptations to the particular environmental niches in which these species evolved, or (c) whether they may have emerged as advanced adaptations to some properties that prevail throughout the terrestrial environment (PsycINFO Database Record (c) 2012 APA, all rights reserved)
The influence of prejudice on perception should be greatest when certainty about stimulus identity is least We exploited this relationship to reveal Visual biases for the cardinal orientations vertical and horizontal Specifically. when we increased the variance of orientations in all array of grating patches, estimates of the mean became less oblique. This result is consistent with a stable prior. or prejudice, for those orientations most prevalent in natural scenes (C) 2009 Elsevier Ltd All rights reserved
In a space where Cartesian coordinates represent the excitations of the three cone types involved in color vision, a plane of constant luminance provides a chromaticity diagram in which excitation of each cone type (at constant luminance) is represented by a linear scale (horizontal or vertical), and in which the center-of-gravity rule applies with weights proportional to luminance.
Discrimination steps were measured for three subjects, along oblique axes passing through nine points in a 25 td constant-luminance chromaticity plane. When plotted in a normalized cone-excitation chromaticity diagram, the best-fitting discrimination ellipses for a given subject have approximately the same shape and orientation regardless of the reference chromaticity. Their orientation is consistent with the hypothesis that excitation of B-cones affects the red-green opponent balance, otherwise determined by R- and G-cone excitations, in a manner independent of initial cone-excitation levels. The CIELAB formula predicts an orientation for normalized ellipses in agreement with the data, but it also predicts systematic changes in the ratio of minor to major axes which are not observed experimentally.
This paper introduces a new technique for the analysis of the chromatic properties of neurones, and applies it to cells in the lateral geniculate nucleus (l.g.n.) of macaque. The method exploits the fact that for any cell that combines linearly the signals from cones there is a restricted set of lights to which it is equally sensitive, and whose members can be exchanged for one another without evoking a response. Stimuli are represented in a three-dimensional space defined by an axis along which only luminance varies, without change in chromaticity, a 'constant B' axis along which chromaticity varies without changing the excitation of blue-sensitive (B) cones, a 'constant R & G' axis along which chromaticity varies without change in the excitation of red-sensitive (R) or green-sensitive (G) cones. The orthogonal axes intersect at a white point. The isoluminant plane defined by the intersection of the 'constant B' and 'constant R & G' axes contains lights that vary only in chromaticity. In polar coordinates the constant B axis is assigned the azimuth 0-180 deg, and the constant R & G axis the azimuth 90-270 deg. Luminance is expressed as elevation above or below the isoluminant plane (-90 to +90 deg). For any cell that combines cone signals linearly, there is one plane in this space, passing through the white point, that contains all lights that can be exchanged silently. The position of this 'null plane' provides the 'signature' of the cell, and is specified by its azimuth (the direction in which it intersects the isoluminant plane of the stimulus space) and its elevation (its angle of inclination to the isoluminant plane). A colour television receiver was used to produce sinusoidal gratings whose chromaticity and luminance could be modulated along any vector passing through the white point in the space described. The spatial and temporal frequencies of modulation could be varied over a large range. When stimulated by patterns of low spatial and low temporal frequency, two groups of cells in the parvocellular laminae of the l.g.n. were distinguished by the locations of their null planes. The null planes of the larger group were narrowly distributed about an azimuth of 92.6 deg and more broadly about an elevation of 51.5 deg, which suggests that they receive opposed, but not equally balanced, inputs from only R and G cones. These we call R-G cells.(ABSTRACT TRUNCATED AT 400 WORDS)