Fluctuating environmental light limits number of surfaces visually recognizable by colour

Small changes in daylight in the environment can produce large changes in reflected light, even over short intervals of time. Do these changes limit the visual recognition of surfaces by their colour? To address this question, information-theoretic methods were used to estimate computationally the maximum number of surfaces in a sample that can be identified as the same after an interval. Scene data were taken from successive hyperspectral radiance images. With no illumination change, the average number of surfaces distinguishable by colour was of the order of 10,000. But with an illumination change, the average number still identifiable declined rapidly with change duration. In one condition, the number after two minutes was around 600, after 10 min around 200, and after an hour around 70. These limits on identification are much lower than with spectral changes in daylight. No recoding of the colour signal is likely to recover surface identity lost in this uncertain environment.


Results
Amplifying variation by reflection. As a preliminary, to illustrate the physical differences in the variation of direct and reflected light, radiance data were sampled selectively from a scene containing both sky and a mixture of landcover types. The hyperspectral radiance images of the scene were acquired at 14:09, 14:11, and 15:16 in the course of a previous study 32 . The images in Fig. 1 show colour renderings of the radiance data. Sample areas were defined by a thin horizontal strip, size 896 × 30 pixels (leftmost image, white rectangle near top). Radiance values were transformed into long-, medium-, and short-wavelength-sensitive cone excitations. The standard deviation (SD) of the differences in excitations at 14:09 and 14:11 and separately at 14:11 and 15:16 were obtained as a function of the vertical position of the strip in the 1344 × 1024-pixel image. The size of the strip was a compromise between making reliable estimates of the SD and avoiding bias.
The plots in Fig. 1 show the SD of the magnitude of the differences in cone excitations relative to the mean over the sample at each vertical sample position, plotted on the left and right axes. Data from regions of the scene with mainly sky, mountains, trees, or buildings are demarcated by horizontal grey lines. The left plot is for differences between cone excitations at 14:09 and 14:11. For direct light from the sky, the relative SD varies between 0.22% and 0.27%. These values for a 2-min interval are of the same order as those from independent pyrheliometer recordings from other scenes. For light reflected from distant mountains, the relative SD increases to about 1.1%, but from the nearer trees and buildings it is between 2.7% and 12.7%, which should be detectable by a normal trichromatic observer with sensitivity characterized by the Weber-Fechner fraction 7 or rather larger values 33 or by colorimetric measures 34,35 .
The right plot is for differences between cone excitations at 14:11 and 15:16. For direct light from the sky, the relative SD increases little across this larger, 65-min interval, as expected, whereas for light from trees and buildings it is an order of magnitude larger (the horizontal scale is five-times larger in this plot).
Illumination fluctuations are to be expected with plant canopies 27,36 , which add to the spatial and spectral variance 12 . Even so, foliage movement seems to contribute little to the variance in Fig. 1 since the multiplicative increase in relative SD between the left and right plots is about the same for mountains and trees. In the remainder of this analysis, samples were not limited to strips and were drawn freely from the whole image. The sample area is a thin horizontal strip (leftmost image, white rectangle near top). Its vertical position is plotted on the leftmost axis in pixels and on the rightmost in degrees of visual angle. Variation is quantified by the standard deviation (SD) of the differences in cone excitations relative to the mean of the sample, plotted on the horizontal axis in per cent. Data are for a 2-min interval in the left plot and for a 65-min interval in the right plot, which has a larger horizontal scale. www.nature.com/scientificreports/ Representations of radiances by cone excitations are useful for quantifying the physical effects of illumination changes, but they are poorly suited to quantifying observer responses 7,25 . Equally different cone excitations do not generally imply equally distinguishable radiances.
Numbers of distinguishable surfaces. A colour space standardized by the Commission Internationale de l'Eclairage (CIE) was used to represent radiances in a perceptually relevant way 37 . This space CIECAM02 38 has axes corresponding to lightness, redness-greenness, and yellowness-blueness and is approximately uniform in the sense that equal Euclidean distances correspond to approximately equal perceived colour differences 39,40 . As a control, another colour space S-CIELAB 41 was also tested, which though less uniform than CIECAM02 space, simulates the spatial-frequency filtering of the whole image by the eye 42 and the resulting spectral mixing 43 .
To provide a reference level for similarities in surface appearance, estimates of the number of surfaces distinguishable by colour were obtained for single radiance images from each of the 18 scenes in Fig. 2. Although population estimates of these numbers have been made previously 20 , sample estimates are needed for the scenes used in this analysis. Estimates depend both on scene composition and on illumination. They also depend on an observer threshold, without which the number of surfaces may not be well defined 43 .
The first data row in Table 1 shows the estimated number of distinguishable surfaces averaged over the 18 scenes, with confidence limits in Supplementary Table S1 online. Values are for two models of observer internal noise, one a Gaussian distribution and the other a uniform distribution. The width of each distribution was referred to a hard discrimination threshold ΔE thr of 0.5, equivalent to a just perceptible colour difference in CIECAM02 space 44 .   20 . Notice that these estimates refer to the underlying radiance image, not the discrete hyperspectral sample that approximates it 21 .
With S-CIELAB space, the corresponding estimates are much smaller, about 760 and 1200, that is, about 6% of those with CIECAM02 space, for both models of observer internal noise (Supplementary Table S2 online). The reduction seems less to do with spatial-frequency filtering and more to do with the properties of CIELAB space itself, which gives much smaller estimates than CIECAM02 space (not shown here).
Doubling ΔE thr reduced the average estimated number of distinguishable surfaces to about 1600 and 2600 with CIECAM02 space and the two models of observer internal noise (Supplementary Table S3).
Recall that these estimates take no account of illumination changes.

Numbers of surfaces identifiable over short time intervals.
What, then, are the effects of an illumination change? Estimates of the number of surfaces identifiable by their colour over intervals of about 1-15 min were obtained for single pairs of radiance images from each of the scenes in Fig. 2. Over these short intervals, the spectrum of the solar beam did not measurably change according to recordings from a neutral reference surface in the field of view 21 . The second data row in Table 1 shows the estimates. With CIECAM02 space, the average estimated number of identifiable surfaces per scene is about 270 with both models of observer internal noise and a reference discrimination threshold ΔE thr of 0.5. This average estimate is almost two orders of magnitude smaller than that for the number of distinguishable surfaces. Doubling ΔE thr reduced the average estimate from about 270 to about 180 (Supplementary Table S3).
With S-CIELAB space, the corresponding average estimates differ from those with CIECAM02 space by about a factor of two (Supplementary Tables S2). There was no reliable correlation between the number identifiable and the length of the time interval with this range of intervals.

Long time intervals.
How does increasing the interval between images beyond 15 min affect the number of surfaces identifiable by their colour? Estimates of this number for intervals t ranging from about 1 min to at least 4.6 h were obtained from the four scenes in the top row of Fig. 2. For each scene, at least 100 pairs of images with different intervals were available. Colour images of the main sequences are shown elsewhere 32 . This analysis used the same methods as in the preceding section. Again to provide a reference level, estimates of the number of distinguishable surfaces were also obtained.
The third data row of Table 1 shows the estimated number of distinguishable surfaces averaged over the multiple images from each of the four scenes, with confidence limits in Supplementary Table S1 online. The average estimates of about 9500 and 15,000 for the two models of observer noise are somewhat smaller than with the set of 18 scenes in the first data row, but they come from images recorded later in the day. Figure 3 shows the logarithm of the estimated number of identifiable surfaces plotted against the logarithm of the interval t between images from each scene represented in CIECAM02 colour space with Gaussian internal noise and a reference discrimination threshold ΔE thr of 0.5. The sample values of log Δt are distributed nonuniformly because of the linear timing regime used in the original image acquisitions 32 . The dashed lines are linear regressions. Similar plots were obtained with the assumption of uniform internal noise and with images represented in S-CIELAB space.
If the magnitude of the illumination changes were constant with increasing interval, then the linear regressions would be flat, whereas the logarithm of the estimated number identifiable declines rapidly with log Δt. The regressions account for between 63% and 94% of the variance over the approximately 4.6 h range. Still, as an explanatory variable, Δt is only a proxy measure for the unspecified change in the spectral and geometric properties of the illumination. The actual change and the resulting variance about the regression line depend Table 1. Numbers of distinguishable surfaces and surfaces identifiable over time intervals. Entries are logarithmic inverses of mutual information estimates averaged over images, image pairs, and regression estimates. Estimated 95% confidence limits are in Supplementary Table S1 online. Entries to 2 significant figures. a Gaussian and uniform models of observer internal noise were referred to a hard discrimination threshold ΔE thr = 0.5 b Number of images from each scene acquired at different times. c All scenes in Fig. 2  www.nature.com/scientificreports/ on the reflecting surfaces in the scene, the level of illumination, the time of day, and the differential effects of changing solar altitude and azimuth on the distribution of shadows. Nonetheless, the regression fits can be used to estimate the number identifiable for representative values of Δt, say 2 min, 10 min, and 1 h. The bottom three data rows in Table 1 summarize these estimates averaged over the four scenes, with confidence limits in Supplementary Table S1 online. With CIECAM02 space and Gaussian internal noise, the average estimated number identifiable at 2 min is about 580, falling to about 210 at 10 min, and 69 at 1 h. The same values were obtained with uniform internal noise. The value of 210 at 10 min is compatible with the average of 270 for the 18 pairs of images with intervals of 1-15 min (see confidence limits, Supplementary Table S1 online). With S-CIELAB space, average estimates varied from being smaller than with CIECAM02 space at short intervals to being larger at long intervals, due presumably to spatial-frequency filtering.
As noted earlier, these illumination changes were mainly geometric, with little or no change in spectrum.

Spectral changes in illumination.
Are the effects of changes in illumination of the kind considered here similar to those with purely spectral changes in illumination on a scene? Spectral changes are usually simulated 18,45 since they are difficult to record naturally. To answer this question, estimates of the number of surfaces identifiable by colour were obtained under a change in a global illuminant that was equivalent to a shift in daylight spectrum from a correlated colour temperature of 6500 K, corresponding to typical daylight, to one of 4000 K, corresponding to the setting sun. With CIECAM02 space and Gaussian internal noise with a reference discrimination threshold ΔE thr of 0.5, the estimated number of surfaces identifiable under this spectral illuminant change was about 4400 per scene averaged over the four scenes in the top row of Fig. 2. With uniform internal noise instead of Gaussian noise, it was about 5500 per scene. Both values are manifestly greater than the corresponding values of 580 obtained with real-world changes in illumination over 2 min (Table 1).

Discussion
The reflecting properties of materials in a natural environment vary randomly from point to point owing to variations in their composition, texture, orientation, weathering, and other factors 10,21 . The light within this environment also varies randomly from point to point, with mutual reflection, occlusion, and transilluminance producing chromatic variation extending beyond the daylight locus 12,46 . The effect of this diversity on vision is, however, moderated by the differing abundances of surface colours 20,47 . Thus the average number of surfaces in a scene that can be distinguished by their colour is of the order of 10,000, much less than the number of colours that can be distinguished within the scene 20,47 .
Even then, the number of distinguishable surfaces does not represent the number that retain their visual identity over time. Illumination and surface reflection together determine the image presented to the eye. And because natural illumination varies, even over intervals as short as a few minutes, there can be large physical changes in reflected light from some or all of a scene. The number of surfaces that can therefore be identified by their colour after an interval is much less than the number that can be distinguished. In one condition of this study, the average number that can be identified is around 600 after two minutes, equivalent to about 5% of the number distinguishable, and it falls to around 200 after 10 min, and to around 70 after an hour. Crucially, though, it is not these particular values that are significant, but the order of magnitude of the effects they represent. www.nature.com/scientificreports/ These estimates may be the best possible for a normal trichromatic observer, yet they do depend on the observer model. Most obviously, increasing observer internal noise decreases both the number of distinguishable surfaces and the number identifiable after an interval. Similarly, including spatial-frequency filtering of the image by the eye with S-CIELAB colour space reduces the number of distinguishable surfaces but also reduces the rate at which the number of identifiable surfaces declines with the length of the interval. These reductions are attributable partly to the use of CIELAB colour space instead of the more uniform CIECAM02 colour space and partly to the reduction in uncorrelated variance between images.
The present findings on real-world illumination changes appear to confirm an earlier speculation 20 that colour constancy, or the lack of it, does not generally determine the extent to which surfaces can be identified by their colour in natural scenes under different illuminants. To be clear, this speculation was based on other phenomena: the effect of relative frequency of different colours on the distinguishability of surface colours and the effect of simulated spectral changes in daylight. In fact, as shown here, real-world illumination changes have an even greater impact than relative frequency.
Still, it might reasonably be argued that the contribution of higher-level cognitive mechanisms has not been considered. There is a long history of the study of observers' ability to separate the appearance of surfaces from judgements about them 45,[48][49][50][51] , specifically, to be aware of a difference in illumination and, at the same time, of the stability of surface reflectance. Yet it is one thing to be aware of this stability and another to correctly identify individual surfaces by their colour. These two competencies are distinct, and the one does not necessarily imply the other.
There are several qualifications to this analysis. First, the information-theoretic estimates, despite providing a least upper bound on the number identifiable, do not actually indicate which surfaces are identifiable. To find those surfaces, a specific mapping from one image to the other needs to be defined, and its performance is usually imperfect 29 . Illustrations of some errors in identification with mappings defined by standard chromatic adaptation transformations are given elsewhere 21,29 .
Second, observers were assumed to behave optimally. Procedural factors were not taken into account, for example, how search for a particular surface might be implemented 52 or affected by peripheral colour awareness 53 , attention 54 , or memory 55,56 . Observers' search strategies can turn out to be far from optimal, with local scene colour 57 , context 58 , and salience 59 all influencing performance. Global image properties can also affect appearance judgements 13,60,61 . As a consequence, observers presented with a possible match may accept colour differences that exceed conventional threshold values 16,18,62 . In short, the numerical limits reported here are likely to be overestimates.
Third, these limits are contingent on the chosen sample of 18 scenes. They included near, middle, and distance views drawn from the main land-cover classes 30,31 , containing shrubs, ferns, flowers, rock, stone, urban buildings, and farm outbuildings. Larger data sets might reveal different limits, though the control measurements with simulated spectral changes in daylight on the 18 scenes were consistent with those previously reported with 50 scenes 20 .
Fourth, and last, the limits are also contingent on the characteristics of the illumination variations. In the presence of cloud, changes in solar altitude and azimuth may produce changes in the pattern of reflected light qualitatively different from those considered in this analysis.
Throughout this analysis, the concern has been only with the spectral properties of the light reflected from individual surfaces in samples drawn from a scene. If, instead, observers had access to more than just spectral properties, for example, local spatial features such as texture 63 and shape 64 , a more robust response might be achieved. But spatial features remain defined by the light they reflect, which, in turn, depends on the fluctuating incident beam. They are therefore subject to the same information-theoretic limits that affect recognition by colour. By the nature of these limits, any recoding of the colour signal, including the usual transformations associated with colour constancy, is unlikely to retrieve surface identity lost in this uncertain environment.

Methods
Irradiance fluctuations. An independent estimate of the minimum level of irradiance fluctuations was obtained from pyrheliometer recordings archived by the World Radiation Monitoring Center (WRMC). The station nearest to the site of the hyperspectral recordings used in this study was Cener in Sarriguren, Navarra, Spain 8,9 . Normal incidence recordings of surface irradiance were extracted for days in June and October containing fewest interruptions of the solar beam 36 . The standard deviation (SD) of the mean at 1-min intervals was derived by a method proposed by Rice for nonparametric residual variance estimates 65 . Its value divided by the mean, i.e. the relative SD, varied through the day. On 3 June 2010, it had a minimum of 0.13% at 13:00 and on 19 October 2010 a minimum of 0.09% at 13:00. On both days it remained less than 0.5% between 7:00 h and 16:00 but increased outside this interval.
Hyperspectral radiance data. Eighteen pairs of unaveraged hyperspectral radiance images of outdoor vegetated and nonvegetated stationary scenes were extracted from sets of hyperspectral data collected from the Minho region of Portugal in 2002 and 2003. One consisted of 14 scenes from which single pairs of images were available separated by intervals of about 1 min to 15 min 12,19 . The other set consisted of four scenes from which multiple pairs of images were available separated by intervals of about 1 min up to 4.6 h 32 . Pairs of images were excluded if significant movement in the scene was detected during the acquisition or became obvious during subsequent image registration operations. Each image had dimensions 1344 × 1024 pixels and spectral range 400-720 nm sampled at 10-nm intervals. The angular subtense of each scene at the hyperspectral camera was approximately 6.9° × 5.3°, so that each pixel in the image represented the integrated image radiance over approximately 0.3 × 0.3 arcmin 32 . www.nature.com/scientificreports/ The contribution of noise in the imaging system to differences in successive hyperspectral images was negligible in comparison with the effects of illumination change, even over 2 min, as illustrated by the plots in Fig. 1.
Colour renderings of one member of each image pair are shown in Fig. 2. Telespectroradiometer recordings of the correlated colour temperature of the direct illumination on a neutral reference surface in the field of view did not differ reliably between acquisitions up to 15 min apart. Reliable changes in correlated colour temperature, e.g. from 5949 K to 3014 K, were, however, recorded across much larger intervals of 4.6 h with the scene at the top right in Fig. 2.
Each hyperspectral image was registered over wavelength by uniform scaling and translation to compensate for variations in optical image size, especially at the ends of the spectrum. Each pair or sequence of hyperspectral images for each scene was then registered over acquisition time by translation to compensate for any residual differences in optical image position. All image registrations were performed to subpixel accuracy with in-house software. For some scenes, padding artefacts a few pixels wide were visible at the edges of the images, and were subsequently trimmed. Images were calibrated for spectral radiance against independent spectral radiance data recorded from a neutral reference surface or surfaces embedded in the scene or in the field of view 21 . Data from these image pairs has not been previously reported.

Simulated illumination changes.
As a control, a reflected radiance image L(u, v; ) , indexed by spatial coordinates u, v, and wavelength λ, was represented as the product of an effective spectral reflectance R(u, v; ) and a global illuminant E 0 ( ) , defined by a daylight with the same correlated colour temperature as the direct beam; that is, L(u, v; ) = E 0 ( )R(u, v; ) . Notation follows previous use 21,38 . Given R(u, v; ) and two fixed daylight illuminants, E 1 ( ) and E 2 ( ) , corresponding radiance images were then obtained as ) . The fixed daylight illuminants were drawn from around noon and towards the evening, with respective correlated colour temperatures of 6500 K and 4000 K 4,66 .

Cone excitations.
For demonstration only, the spectral radiance L(u, v; ) at time t, was converted to long-, medium-, and short-wavelength-sensitive cone excitations q L (u, v, t), q M (u, v, t), q S (u, v, t) in a standard way 38 . Integrals were evaluated numerically over the spectral range 400-720 nm in 10-nm steps. For each k = L, M, S, cone excitations q k (u, v, t) were subjected to von Kries scaling 7 by the corresponding spatial mean q k (t) of the sample points; that is, q ′ k (u, v, t) = q k (u, v, t) q k (t) . Sample areas were defined by a thin horizontal strip, size 896 × 30 pixels. At each point (u, v) in the sample, the magnitude of the physical difference in cone excitations at times t 1 and t 2 , was summarized by the unweighted Euclidean norm �e(u, v) = k �q ′ k (u, v) 2 1/2 . The SD of �e(u, v) was then evaluated over (u, v) and the result recorded as a function of the vertical position of the strip in the 1344 × 1024-pixel image. Because of von Kries scaling, the SD was defined relative to the mean of the sample.
Uniform colour spaces. Hyperspectral radiance images were represented in the approximately uniform colour space CIECAM02 38 and, for comparison, S-CIELAB 41 , where S-CIELAB is an extension of CIELAB that incorporates pattern-separable spatial filtering (https ://githu b.com/wande ll/SCIEL AB-1996/). The spectral radiance L(u, v; ) was converted to normalized tristimulus values and then into CIECAM02 coordinates and into CIELAB coordinates for S-CIELAB space 39,40 . The coordinates of CIECAM02 are J, a C , b C , where J correlates with lightness, ranging from 0 to 100, and a C and b C correlate with redness-greenness and yellowness-blueness, respectively. The corresponding coordinates of CIELAB are L * , a * , b * . There are, however, differences in the degree of uniformity of CIECAM02 and CIELAB spaces 67 . Their physiological plausibility has been evaluated with electroencephalographic and magnetoencephalographic methods 68 .
Observer uncertainty. The effect of uncertainty in the observer was modelled in CIECAM02 and S-CIELAB spaces as internal additive noise 20,69 . The underlying probability density function or pdf was assumed to be either Gaussian or uniform, with the latter providing a link to the deterministic or hard discrimination thresholds ΔE thr used in colorimetry 7 . A just perceptible colour difference corresponds to a value for ΔE thr of 0.5 in CIECAM02 space, which is approximately equivalent 44 to a value of 1.0 in CIELAB space 40,70,71 , though larger values may be defined by acceptability criteria 62 and in categorization tasks 16 . Memory effects are not considered here 55,56 .
The Gaussian and uniform distributions were each parameterized by a nominal width w, which was referred 47 to values of ΔE thr . For a Gaussian distribution with SD σ , say, w was defined as 12 1/2 σ . For a uniform distribution, w was defined as the width of the support of the distribution. Since the SD of the uniform distribution is 12 −1/2 w , Gaussian and uniform distributions with the same w then have the same variance. Values of ΔE thr were set to 0.5 and 1.0 in CIECAM02 space and to 1.0 in S-CIELAB space.
Mutual information and distinguishable points. The method used to estimate the number of surfaces distinguishable by their colour follows previous studies 20,21,47 . Scenes were not segmented into regions, except for the trivial limit defined by pixel resolution. Critically, points are assumed to be drawn randomly from each scene 29 . At each instant, the triplets J, a C , b C in CIECAM02 space or L * , a * , b * in S-CIELAB space can be treated as instances a , say, of a three-dimensional continuous random variable A with pdf f (a) , which underlies the observed distribution of colours in the scene. Notice that the spatial filtering associated with S-CIELAB is applied before the random draw rather than afterwards.
The uncertainty in the random variable A is quantified 28 by the Shannon differential entropy h(A) given by www.nature.com/scientificreports/ which is measured in bits if the logarithm is to the base 2 (the symbols h and a should not be confused with colorimetric quantities). When f is the uniform function, that is, when the colours are equally probable, the entropy coincides with the logarithm of the conventional volume of the colour gamut. Observer responses can also be treated as instances of a three-dimensional continuous random variable, B say. The amount of information that B provides about A is given by the mutual information 28 , written I (A; B) . Its inverse logarithm may be interpreted as the approximate number of points N in the scene that can be distinguished in the presence observer uncertainty; that is, To evaluate I (A; B) , it can be expressed as a combination of the differential entropies h (A) , h(B) , and h(A, B) , where h (A, B) is the differential entropy of A and B taken jointly; that is, Suppose that observer internal noise is represented by a three-dimensional continuous random variable W , so that B = A + W . If W is obtained by drawing pseudorandom values from the assumed noise distribution, the right hand side of (2) can be estimated numerically. But using histograms in place of the unknown pdf f in (1) can lead to biases in estimates. Instead, the more accurate Kozachenko-Leonenko kth-nearest-neighbour estimator 72,73 was used in conjunction with an offset method 29 (https ://githu b.com/imari nfr/klo). Though this calculation sets a limit on the number of distinguishable points, the number of distinguishable surfaces cannot exceed this limit 43 .

Mutual information and identifiable points.
The method used to estimate the number of surfaces identifiable by their colour after an interval is similar. At times t 1 and t 2 , the triplets in CIECAM02 space or S-CIELAB space are treated as instances of three-dimensional continuous random variables A 1 and A 2 . If observer responses are treated as instances of a three-dimensional continuous random variable B = A 2 + W , then the amount of information that B provides about A 1 is given by the mutual information I(A 1 ; B) = I(A 1 ; A 2 + W) , which can be estimated as before. Its inverse logarithm may be interpreted as the approximate number of points N in the scene that can be identified between times t 1 and t 2 in the presence observer uncertainty.
For the special case in which the time interval is zero, so that t 1 = t 2 and A 1 = A 2 = A , say, the inverse logarithm of the mutual information I(A; B) = I(A; A + W) reduces to the number of distinguishable points. An intuitive rationale for this interpretation is provided elsewhere 20,21 . This relationship between distinguishability and identification across time does not imply that the same processes necessarily mediate observer judgements 74 .
Although it might seem counterintuitive, N is not presented as a proportion of the total number of points in the scene, defined in some way, since N is independent of sample size providing that the sample is sufficiently large. This independence can be confirmed empirically 18 by plotting the variation in the number of points identified by nearest-neighbour matching 29 as sample size is progressively increased: the number of matched points asymptotes below what is theoretically possible.
Because of the linearizing effect of a logarithmic scale on estimates of N, means and 95% BCa confidence limits 75 over scenes were calculated for the corresponding values of mutual information and then inverse logarithms taken.