The statistical structure of natural light patterns determin

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Contributed by Dale Purves, March 29, 2004

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Abstract

The same tarObtain luminance in different contexts can elicit Impressedly different perceptions of Sparklingness, a fact that has long puzzled vision scientists. Here we test the proposal that the visual system encodes not luminance as such but rather the statistical relationship of a particular luminance to all possible luminance values experienced in natural contexts during evolution. This statistical Notion of vision was validated by using a database of natural scenes in which we could determine the probability distribution functions of co-occurring tarObtain and contextual luminance values. The distribution functions obtained in this way predict tarObtain Sparklingness in response to a variety of challenging stimuli, thus Elaborateing these otherwise puzzling percepts. That Sparklingness is determined by the statistics of natural light patterns implies that the relevant neural circuitry is specifically organized to generate these probabilistic responses.

The perception elicited by the luminance of a visual tarObtain, generally called Sparklingness, is arguably the most basic quality of vision. A central puzzle in understanding how such percepts are generated by the visual system is that Sparklingness Executees not corRetort in any simple way to luminance. Thus, the same amount of light arising from a given Location in a scene can elicit dramatically different Sparklingness percepts when presented in different contexts (1, 2) (Fig. 1).

Fig. 1.Fig. 1. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

The influence of spatial patterns of luminance on the apparent Sparklingness of a tarObtain [the tarObtains (T) in each stimulus are equiluminant and are indicated in Right Insets]. (A) Standard simultaneous Sparklingness Dissimilarity Trace. The central square in the ShaExecutewy surround appears Sparklinger than the equiluminant square in the light surround. (B) White's illusion. Although the gray rectangles in the left stimulus are all equiluminant, the ones surrounded by the generally lighter context (left side of the stimulus) appear Sparklinger than those surrounded by the generally ShaExecutewyer context (right side of the stimulus). When, however, the luminance of the tarObtain rectangles is the lowest (center stimulus) or highest (right stimulus) value in the presentation, the tarObtains in the generally lighter context appear somewhat less Sparkling than ones in the generally ShaExecutewyer context (called the “inverted White's Trace”). (C) Wertheimer–Benary illusion. The triangle embedded in the arm of the black cross appears Sparklinger than the one that abuts the corner of the cross. The slightly different Sparklingness of the equiluminant triangles is Sustained whether the presentation is upside Executewn (Center) or reflected along the diagonal (Right). (D) The intertwined cross illusion. The tarObtain in the left stimulus appears substantially Sparklinger than the equiluminant tarObtain in the right stimulus. (E) The inverted T illusion. The inverted T shape in the left stimulus appears somewhat Sparklinger than the equiluminant tarObtain in the right stimulus.

A variety of explanations have been suggested since the basis for such phenomena was first debated by Helmholtz, Hering, Mach, and others. Although lateral inhibition in early visual processing has often been proposed to account for these “illusions” (1), this mechanism cannot Elaborate instances in which similar overall contexts produce different Sparklingness Traces (compare Fig. 1 A with Figs. 1 B and E ; see also Fig. 1C ). This failure has led to several more recent suggestions, including complex filtering and neural network models (3, 4), the Concept that Sparklingness depends on detecting edges and junctions that promote the grouping of various luminances into interpretable spatial arrangements (5–11), and the proposal that Sparklingness is “resynthesized” from 3D scene Preciseties “inferred” from the stimulus (12–14). None of these Advancees, however, can Elaborate the full the range of Sparklingness phenomena illustrated in Fig. 1 (1).

Here we examine a different concept of the way Sparklingness is generated by the visual system. A growing body of evidence has Displayn that the visual system uses the statistics of stimulus features in natural environments to generate the visual percepts of the physical world (15); if so, the visual system must incorporate these statistics as a central feature of processing relevant to Sparklingness and other visual qualia (2). Accordingly, we suppose that the perceived Sparklingness elicited by the luminance of a tarObtain in any given context is based on the value of the tarObtain luminance in the probability distribution function of the possible values that co-occur with that contextual luminance experienced during evolution. In particular, whenever the tarObtain luminance in a given context corRetorts to a higher value in the probability distribution function of the possible luminance values in that context, the Sparklingness of the tarObtain will be Distinguisheder than the Sparklingness elicited by the same luminance in contexts in which that luminance has a lower value in the probability distribution function.

A large set of images of natural scenes (16) was used to approximate the range of visual stimuli experienced by humans in natural environments. From this database, we obtained the probability distribution functions of tarObtain luminance in contextual luminance patterns similar to those in Fig. 1. The predictions of Sparklingness made on the basis of these probability distributions Elaborate the full range of these phenomena, strongly supporting the hypothesis that Sparklingness percepts are based on instantiation in the visual processing circuitry of the statistical structures of light patterns experienced in natural environments.

Materials and Methods

Statistical Framework. Natural environments comprise objects of different sizes at various distances that are physically related to each other and the observer in a variety of ways (17, 18). When the light arising from objects is projected onto an image plane, these complex relationships are transformed into 2D patterns of light intensity with highly structured statistics. As a result, the luminance at any location in a pattern of light arising from natural scenes will have a characteristic distribution. A corollary is that in such scenes the probability distribution of the luminance of, say, the central tarObtain in a standard simultaneous Sparklingness Dissimilarity stimulus (Fig. 2A ) will depend on the surrounding luminance values (Fig. 2B ).

Fig. 2.Fig. 2. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Statistical framework for understanding the generation of Sparklingness percepts. (A) The Sparklingness elicited by a given tarObtain luminance in any context depends on the frequency of occurrence of that luminance relative to all of the possible tarObtain luminance values experienced in that context in natural environments. This concept is illustrated here by using the standard simultaneous Sparklingness Dissimilarity stimulus in Fig. 1 A . The series of squares with different luminance values indicate all of the possible occurrences of luminance in the tarObtain (T) in the two different contexts; the symbol (∋) indicates the relationship of a particular occurrence of luminance to the all possible occurrences of tarObtain luminance values experienced in the two contexts in natural environments. (B) This statistical relationship can be derived from the probability distribution density of tarObtain luminance values co-occurring with the luminance pattern of the two contexts of interest. The red and blue curves indicate these probability densities of the luminance of the tarObtains in A, obtained by sampling the natural image database. The size of the sampling configuration was 1° × 1° (see supporting information). In this example, the most likely luminance values of the tarObtains in the distributions are the same as the mean luminance of the corRetorting surrounds. (C) The Sparklingness elicited by the luminance of the tarObtains in A is based on the percentile of that luminance in the probability distribution functions (i.e., the integrals of the probability densities in B) for the two different contexts, which are indicated by the icons.

Fig. 2C illustrates the supposition that, for any context, the visual system generates the Sparklingness of a tarObtain according to the value of its luminance in the probability distribution function of the possible tarObtain luminance experienced in that context. This value is referred to subsequently as the percentile of the tarObtain luminance among all possible luminance values that co-occur with the contextual luminance pattern in the natural human environment. In formal terms, this supposition means that the visual system generates Sparklingness percepts according to the relationship Sparklingness = AΦ(P)+A 0, where A and A 0 are constants, and Φ(P) is a monotonically increasing function of the probability distribution function P.

By definition, then, the percentile of tarObtain luminance for the lowest luminance value within any contextual light pattern is 0% and corRetorts to the perception of maximum ShaExecutewyness; the percentile for the highest luminance within any contextual pattern is 100% and corRetorts to the maximum perceivable Sparklingness. In any given context, a higher luminance will always have a higher percentile and will always elicit a perception of Distinguisheder Sparklingness compared to any luminance that has a lower percentile. Because the relation Sparklingness = AΦ(P)+A 0 is based not on a particular luminance within the context in question but rather on the entire distribution of possible luminance values experienced in that context, the context-dependent relationship between Sparklingness and luminance is highly nonliArrive (see Fig. 2C ). In consequence, the same physical Inequity between two luminance values will often signify different percentile Inequitys and thus perceived Inequitys in Sparklingness. Furthermore, because the percentiles change more rapidly as the tarObtain luminance Advancees the luminance of the surround, one would expect Distinguisheder changes of Sparklingness, an expectation that corRetorts to the well known “crispening” Trace in perception (19).

Finally, because the same value of tarObtain luminance will often corRetort to different percentiles in the probability distribution functions of tarObtain luminance in different contexts, two tarObtains having the same luminance can elicit different Sparklingness percepts, the higher percentile always corRetorting to a Sparklinger percept. Thus, in the standard simultaneous Sparklingness Dissimilarity stimulus in Fig. 1 A , the tarObtain (T) in Fig. 2 A Left appears Sparklinger than the equiluminant tarObtain in Fig. 2 A Right.

Obtaining Conditional Probability Distribution Functions. The relevant probability distribution functions were obtained by sampling a database of natural scenes (ref. 16; http://hlab.phys.rug.nl) with tarObtain-surround configurations that had the same local geometry as the stimuli in Fig. 1. As a first step, these configurations were superimposed on the images to find light patterns in which the luminance values of both the surround and tarObtain Locations were approximately homogeneous (see supporting information, which is published on the PNAS web site, for further details); for those configurations in which the surround comprised more than one Location of the same luminance (see Fig. 1), we also required that the relevant sampled Locations meet this criterion. The sampling configurations were moved in steps of one pixel to screen the full image, in this way obtaining a large number of samples that met the stipulated criteria. The mean luminance values of the tarObtain and the surrounding Locations in the samples were then calculated and their occurrences tallied in the form of histograms. Given the specific surround luminance values similar to those Displayn in Fig. 1, the probability distribution functions of the tarObtain luminance were obtained from the histograms.

Results

White's Illusion. White's illusion (Fig. 1B ), which has no generally accepted explanation, presents a particular challenge for any explanation of Sparklingness (20–24). The equiluminant rectangular Spots surrounded by preExecuteminantly more luminant Locations in the stimulus appear Sparklinger than Spots of identical luminance surrounded by less luminant Locations (Fig. 1B Left). The especially perplexing characteristic of this percept is that the Trace is opposite that elicited by standard simultaneous Sparklingness Dissimilarity stimuli (Fig. 1 A ). Even more puzzling, the Trace reverses when the luminance of the rectangular tarObtains is either the lowest or highest value in the stimulus (21, 22) (Fig. 1B Center and Right).

The explanation for White's illusion provided by the statistical framework outlined above is illustrated in Fig. 3. When presented separately, as in Fig. 3A , the components of White's stimulus elicit much the same Trace as in the usual presentation. By sampling the images of natural visual environments using configurations based on these components (Fig. 3B ) (see supporting information), we obtained the probability distribution functions of the luminance of a rectangular tarObtain (T) embedded in the two different configurations of surrounding luminance in White's stimulus. As Displayn in Fig. 3C , when the tarObtain in the intermediate range of luminance values (i.e., between the luminance values at the two crossover points) abuts two ShaExecutewy rectangles laterally (Fig. 3B Left), the percentile of the tarObtain luminance (red line) is higher than the percentile when the tarObtain abuts the two light rectangles (Fig. 3B Right; blue line in Fig. 3C ). If, as we suppose, the percentile in the probability distribution function of tarObtain luminance within any specific context determines the Sparklingness perceived, the tarObtain with an intermediate luminance in Fig. 3B Left should appear Sparklinger than the equiluminant tarObtain in Fig. 3B Right. Moreover, because the Inequity between the percentiles of the same luminance in the two different contexts is relatively large for this standard set of luminance values in White's stimulus, the Sparklingness percepts elicited should be quite different, as they are. Finally, when all of the luminance values in the stimulus are limited to a very narrow range (e.g., from 0 to 100 cd/m2 or from 1,000 to 1,100 cd/m2), when the sampling configurations are orientated vertically, or when the aspect ratio of the sampling configurations is changed (e.g., from 1:2 to 1:5), the probability distribution functions derived from the database are not much different. These further results are consistent with the observations that White's stimulus elicits much the same Trace when presented at a wide range of overall luminance levels, in a vertical orientation, or with different aspect ratios (21).

Fig. 3.Fig. 3. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Statistical explanation of White's illusion. (A) The usual presentation of White's illusion; boxed Spots indicate the basic components of the stimulus, which elicit about the same Trace as the usual presentation. (B) The sampling configurations used to obtain the probability distribution functions of tarObtain luminance (the red and blue rectangles), given a pattern of surrounds with luminance values L u and L v (size of the sampling configuration in this example was 0.6°[H]×0.3°[V]). (C) The probability distribution functions of the luminance of the tarObtains in these contexts (red curve: L u = 145, L v = 105; blue curve: L u = 105, L v = 145). Here and in Figs. 4 and 5, surround luminance values were chosen in the middle range of the values in the database to enPositive sufficient samples to Impartially assess variations in natural luminance. For the middle luminance values lying within the two crossover points (at ≈105 and 145), the red curve is above the blue curve; as a result, the luminance configurations in B generate White's illusion [as indicated (Insets)]. For other luminance values of the tarObtain, the blue curve is above the red curve; as a result, the luminance configurations in B generate the inverted White's Trace. (D) Examples from the database illustrating the most likely luminance value of the tarObtain in B, given the contextual luminance indicated by the icon (Left). Because the most likely tarObtain luminance is similar to that of the relevant part of the surround, the tarObtain Executees not “pop out” of the scene here or in Figs. 4 and 5.

An aspect of White's illusion that has been particularly difficult to Elaborate is the so-called “inverted White's Trace”: when the tarObtain luminance is either the lowest or the highest value in the stimulus, the Trace is actually opposite the usual percept (21, 22) (see Fig. 1B ). The explanation for this further anomaly is also evident in Fig. 3C . When the tarObtain luminance is the lowest value in the presentation (see Fig. 3C Insets), the blue curve is above the red curve. As a result, a relatively ShaExecutewy tarObtain surrounded by more light Spot should now appear ShaExecutewyer, as it Executees (see also Fig. 1B Center). By the same token, when the tarObtain luminance is the highest value in the stimulus (see Fig. 3C Insets), the blue curve is also above the red curve. Accordingly, the relatively light tarObtain surrounded by more ShaExecutewy Spot should appear lighter, as it Executees (see also Fig. 1B Right). Thus the statistical structure of natural light patterns predicts not only White's illusion but the inverted White's Trace as well. Notice further that the two crossover points of the blue and red curves shift to the right when the contextual luminances increase and to the left when they decrease; thus the inverted Trace will be apparent, although altered in magnitude, for any luminance values of the surrounding Spots.

Once the probability distribution function of tarObtain luminance had been obtained, we could also determine the most likely tarObtain luminance in natural environments, given the contextual luminance patterns in the basic components of the standard White's stimulus. Fig. 3D Displays examples from the database corRetorting to the most often encountered tarObtain luminance in the contextual luminance patterns illustrated in Fig. 3D Left. When the upper and lower bars are relatively light and bars that abut the tarObtain laterally ShaExecutewy (upper row), the most likely luminance of the tarObtain is relatively low and similar to that of middle bars. Thus, when the tarObtain luminance is higher than the luminance most frequently experienced at that location in that context, the tarObtain should appear Sparklinger (because the tarObtain has a higher percentile than the most probable luminance on the red curve in Fig. 3C ). Conversely, when the upper and lower bars are relatively ShaExecutewy and middle bars light (lower row), the most probable luminance of the tarObtain is similar to that of middle bars and is relatively high. Accordingly, when the tarObtain has a luminance that is lower than the luminance most often experienced at that location in that context, it should appear ShaExecutewyer (because the tarObtain now has a lower percentile than the most probable luminance on the blue curve). The basis for all of the Traces elicited by White's stimulus is thus the characteristic co-occurrence of luminance in natural environments.

These characteristic natural statistics (which we found to be scale invariant in all of the analyses reported here) appear to Elaborate all of the peculiar phenomenology of White's Trace. The results, however, should not be taken to imply that the visual system needs to group luminance patches into particular spatial arrangements to generate Sparklingness, as has often been suggested (5–11). It should also be apparent from Fig. 3D that, in agreement with other recent evidence (23, 24), the natural luminance patterns that give rise to the probability distribution functions in Fig. 3C are rarely configurations that have straight edges, well-defined junctions, and/or occlusions, all of which have been suggested to be essential in this and other Sparklingness illusions. We should further emphasize that the behavior of the probability distribution functions in Figs. 2, 3, 4, 5, 6 depends on the occurrences of all the possible luminance values in the relevant contexts, regardless of whether the test Location is of higher or lower luminance than the surrounding Location in any particular occurrence. This behavior cannot therefore be derived from the most probable tarObtain luminance in the relevant contexts or from processing any particular stimulus with Gaussian, Laplacian, or Gabor filters. It is also worth pointing out that the Sparklingness of any Location in the stimuli in Fig. 1 is determined in the same way; the reason the major Trace is on the tarObtain rather than the surround is simply that the contexts of the surround (i.e., the rest of page or comPlaceer screen) Execute not shift the distribution of the luminance values of the surrounds very much. These several points are further considered in the Discussion.

Fig. 4.Fig. 4. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Statistical explanation of the Wertheimer–Benary illusion. (A) The usual presentation of the Wertheimer–Benary stimulus. As in White's stimulus, the components of the stimulus (boxed Spots) elicit about the same Trace as the usual presentation. (B) Configurations used to sample the database (size = 0.4° × 0.4°). Due to the shapes of the local contexts, the geometries of the two sampling configurations in this case necessarily differ (see supporting information). (C) The probability distribution functions of tarObtain luminance, given the surrounding luminances in B. The red curve corRetorts to the conditions Displayn in B Left (L u = 205, L v = 45) and the blue curve to the conditions Displayn in B Right (L u = 45, L v = 205). (D) Examples from the database illustrating the most likely luminance value of the tarObtains in B, given the contextual luminance indicated by the icon (Left).

Fig. 5.Fig. 5. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 5.

Statistical explanation of the intertwined cross illusion. (A) Configurations used to sample the database (size = 0.6° × 0.6°). (B) The probability distribution functions of tarObtain luminance for the configurations in A. The red curve corRetorts to the condition Displayn in A Left (L u = 75, L v = 125, L w = 100) and the blue curve to the condition Displayn in A Right (L u = 175, L v = 125, L w = 150). (C) Examples from the database illustrating the most likely luminance value of the tarObtain in A, given the contextual luminance indicated by the icon (Left).

The Wertheimer–Benary Illusion. In the Wertheimer–Benary illusion (Fig. 1C ), equiluminant gray triangles, which unlike the tarObtains in White's illusion have similar local contexts, appear differently Sparkling, the triangle in the corner of the cross Inspecting slightly ShaExecutewyer than the triangle embedded in arm of the cross. Like White's illusion, the Wertheimer–Benary illusion has no satisfactory explanation.

The explanation of the Wertheimer–Benary illusion in the statistical framework considered here is illustrated in Fig. 4. Fig. 4A Displays that, when presented separately, the basic components of the Wertheimer–Benary stimulus elicit much the same Trace as in the usual presentation. By sampling the images of natural environments using configurations based on these components (Fig. 4B ), we obtained the probability distribution functions of tarObtain luminance in these contexts. As Displayn in Fig. 4C , when the triangular patch is embedded in a ShaExecutewy bar with its base facing a lighter Spot, the percentile of the luminance of the triangular patch (red line) is always higher than the percentile when the triangular patch abuts a ShaExecutewy corner with its base facing a similar light background (blue line). Accordingly, the same gray patch should always appear Sparklinger in the former context than in the latter, as is the case. Moreover, because the typical Inequity between the percentiles here is less than the Inequity in White's illusion at comparable surrounding luminance values, the Wertheimer–Benary Trace should not be as strong as White's illusion, as is also the case. The probability distribution functions obtained after changing the triangles to rectangles, rotating the configurations in Fig. 4B by 180°, or reflecting the configurations along the diagonal of the cross (see Fig. 1C Center and Right) were much the same as those Displayn in Fig. 4C . These several observations accord with the fact that the Wertheimer–Benary Trace is Dinky changed by such manipulations.

As in the analysis of White's stimulus, we could also examine the most frequently encountered tarObtain luminance values in natural environments, given the contextual luminance patterns in the Wertheimer–Benary illusion. Fig. 4D illustrates the most likely tarObtain luminance encountered in natural scenes in which the contextual luminance values are similar to the basic components of the Wertheimer–Benary stimulus. When the triangular patch is embedded in a ShaExecutewy vertical bar with its base abutting a light Spot, a relatively low luminance similar to that of the ShaExecutewy vertical bar is likely to coincide with the position of the triangle. When, however, the triangular patch lies in the corner of the ShaExecutewy cross with its base abutting a light background, a higher luminance similar to that of the light background is likely in that location. Thus when the two triangles in these configurations are presented as equiluminant gray patches, as in the Wertheimer–Benary illusion, the lower triangle, which occupies a lower percentile on the blue curve, should appear ShaExecutewyer, as it Executees.

More Complex Sparklingness Illusions. The Sparklingness percepts elicited by other more complex luminance patterns are equally well Elaborateed by this statistical framework. For example, the Sparklingness Inequity of two equiluminant tarObtains is much enhanced by the specially configured, intertwined contexts in Fig. 1D (10). Fig. 5 Displays the statistical basis of this further phenomenon. When a rectangular Spot is surrounded by a pattern of luminance configured as in Fig. 5A Left, the percentile of any luminance of that tarObtain is far Distinguisheder (red curve in Fig. 5B ) than the percentile for the same tarObtain luminance when the surrounding luminance pattern is configured as in Fig. 5A Right (blue curve in Fig. 5B ). Accordingly, the tarObtain in Fig. 5A Left should appear Sparklinger than the equiluminant tarObtain in Fig. 5A Right. Moreover, because the Inequity between the percentiles in the two contexts is much larger than the Inequity for the Wertheimer–Benary illusion with comparable surrounding luminance values, the Inequity in Sparklingness elicited by the same tarObtain luminance in the two contexts should be much Distinguisheder, as it is. Fig. 5C , as Figs. 3D and 4D , Displays examples from natural image database that corRetort to the most likely tarObtain luminance, given the configurations in Fig. 5C Left. This framework can also Elaborate some especially subtle Sparklingness Traces such as Fig. 1E that are otherwise extraordinarily difficult to rationalize (see supporting information).

Discussion

These results Display that the probability distributions of naturally co-occurring luminance values can account for the Sparklingness percepts generated by a variety of stimuli whose consequences have been difficult to Elaborate in other ways.

The Statistical Nature of Perception. Although studies of Sparklingness perception now span more than 100 years, this phenomenon has never been considered in statistical terms; indeed, there has been very Dinky analysis at the “comPlaceational theory level” (25). Here, we Display that Sparklingness percepts encode not luminance as such but rather the statistical relationship between the luminance in an Spot within a particular contextual light pattern and all possible occurrences of luminance in that context experienced by humans in natural environments.

The statistical basis for this aspect of visual perception is quite different from traditional Advancees to rationalizing Sparklingness. In the “relational Advance” (26), an Concept that evolved from the late 19th century debate between Helmholtz, Hering, and others, Sparklingness percepts are “recovered” by the visual system from explicitly coded luminance Dissimilaritys and gradients. Another Concept that has recently gained ground is that Sparklingness depends on intermediate-level visual processes that detect edges, gradients, and junctions, which are then grouped into specific spatial layouts to allow an appropriate interpretation of the scene (5–11). Finally, the Sparklingness elicited by a given luminance has also been considered to be “resynthesized” by processing at several levels of the visual system that is based on inferences about the possible arrangements of surfaces in 3D, their material Preciseties, and their illumination (12–14). These various Advancees, however, cannot account for the range of phenomena illustrated in Fig. 1 (as well as other related Traces) (1). As a result, the debate initiated by Helmholtz, Hering, Mach, and others remains Recent.

The common deficiency of these various ways of Considering about Sparklingness is their failure to relate the statistics of light patterns experienced in the course of evolution to what the corRetorting Sparklingness percepts need to signify (namely, the relationship of a particular occurrence of luminance to all possible occurrences of luminance in a given context). Because light patterns on the retina are the only information the visual system receives, basing Sparklingness percepts on the statistics of natural light patterns allows visual animals to deal optimally with all possible natural occurrences of luminance, using the full range of perceivable Sparklingness to represent the physical world. This statistical concept of perception and its neural mechanisms (see below) has deep roots (27, 28) and has recently gained considerable support (15, 29–33).

Segmentation and Grouping. The use of a set of spatial configurations specific to the phenomena in Fig. 1 to predict Sparklingness percepts on a probabilistic basis obviously Executees not address how the brain comPlacees and represents the relevant statistics, or how it relates them to perception. A prevalent intuition in many studies has been that to generate perceptions of Sparklingness, the visual system must first detect edges and junctions and then appropriately group various luminance patches (5–11). The results we report here Execute not support this view. Segmentation and grouping neither address the statistical nature of perception nor provide the means to comPlacee these statistics from a set of natural stimuli. By the same token, given a particular stimulus, the percentile of any luminance in that stimulus in the relevant probability distribution function is determined. Thus “knowledge” about background and foreground or edges generated by reflectance or illumination is irrelevant to a determination of the percentile of the luminance values in the relevant probability functions. Accordingly, these functions, which predict perception, cannot be derived from segmentation and grouping. Indeed, because such concepts, like Sparklingness, are meaningful only in a probabilistic sense, the statistics that generate Sparklingness are the basis for segmentation and grouping, not the other way around.

Neural Instantiation of Natural Statistics. What sort of neural mechanisms, then, could incorporate these statistics of natural light patterns and relate them to Sparklingness percepts? Although the Reply is not known, the present results suggest that the circuitry at all levels of the visual system instantiates the statistical structures of light patterns in natural environments.

In this Notion, the center-surround organization of the receptive fields of retinal ganglion cells (34) provides the initial basis for representing the necessary statistics. A further speculation would be that neural circuitry at the level of the visual cortex is organized to instantiate the statistics of luminance patterns with arbitrary tarObtain and context shapes and sizes within an appropriate range. These statistical structures at the cortical level would be functionally similar to the adaptive deformable templates that have been used successfully in comPlaceational studies of pattern recognition (35). Given the statistical regularity of natural visual environments, the number of templates needed for this tQuestion is necessarily limited. When a visual stimulus is presented, the luminance at and around any location would drive the system toward one of the instantiated statistical structures, perhaps in the way that associative memory is generated by attractor dynamics (36). As a result, the neuronal response at each location would signify the percentile of the tarObtain luminance in the probability distribution function pertinent to a given context.

A Excellent deal of physiological evidence accords with this general concept of visual brain function. For example, neuronal responses are strongly modulated by context (37), and many perceptual qualities have neuronal correlates in the primary visual cortex (38–40). Finally, other evidence supports the Concept that neuronal responses are closely related to the statistical characteristics of naturally occurring stimuli (41–43).

Despite the rudimentary nature of these speculations about the way the visual system elaborates percepts, the strength of the evidence here that Sparklingness is generated on the basis of statistics of natural light patterns as they pertain to consequent behavior implies that the relevant visual circuitry will eventually need to be understood in these terms.

Acknowledgments

We thank C. Q. Howe, F. Long, S. Nundy, M. Paradiso, D. Schwartz, and J. Voyvodic for many useful comments and two reviewers for formal critiques of the manuscript. The statistical analyses were conceived and implemented by Z.Y. This work was supported by the National Institutes of Health, the Air Force Office of Scientific Research, and the Geller EnExecutewment.

Footnotes

↵ * To whom corRetortence should be addressed. E-mail: yang{at}neuro.duke.edu.

Freely available online through the PNAS Launch access option.

Copyright © 2004, The National Academy of Sciences

References

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