Color changes in objects in natural scenesas a function of observation distance
and weather conditions
Javier Romero,* Raúl Luzón-González, Juan L. Nieves, and Javier Hernández-AndrésOptics Department, University of Granada, Campus Universitario Fuentenueva,
Natural scenes contain a great diversity of chroma-ticities coming from different natural objects (moun-tains, terrains, forests, etc.), from artificial objects(buildings, factories, etc.), and from the sky itself.Hues such as ochre, red, and brown deriving from ter-rains, green and yellow from the vegetation, and blueand white from the sky are very common. Othercolors belonging to fundamental hues, such as blue,green, yellow, red, and purple can be seen in flowerpetals, bird feathers, and insect wings and also inartificial objects.
Several authors [1–4] have studied the color gamutpresent in natural scenes. Nascimento et al. [1] de-scribed the distribution of colors measured in both
natural and urban scenes with reference to theCIE 1931 chromaticity diagram. In urban scenesthe color gamut is somewhat wider due to artificialobjects. In general, the natural scenes measuredby Nascimento et al. [1] included no objects very farfrom the camera, and the visibility conditions weregood. Hendley and Hecht [2] concluded that colorsin nature show low excitation purity values, meaningthat their chromaticity coordinates do not fall close tothe spectrum locus and they are far from the line ofthe purples in the chromaticity diagram. This mag-nitude of purity is related to the perceptual attributeof color saturation, that is, its pure-color content inthe sense of spectral color. A color becomes more sa-turated as its chromaticity coordinates plot nearer tothe spectrum locus and less saturated as they plotcloser to the area representing the white colors inthe chromaticity diagram. These authors point outthat saturation decreases as the distance between
the object and the observer grows, even on days withgood visibility.
It is well known that the atmosphere influencesour perception of the color of distant objects in nat-ural scenes [5]. The change in color of an objectobserved at a distance is a consequence of the inter-action between light and the different sized particlesin the atmosphere, known as absorption and scatter-ing processes. There are two ways of explaining thescattering process, depending on the size of the domi-nant particles present in the atmosphere. When thesize of the particles is less than 10% of the wave-length of the incident light, the scattering processcan be explained according to the Rayleigh theory, ac-cording to which the short wavelengths of light com-ing from a distant object undergo higher loss. Forparticle sizes of about the same size or larger than10% of the wavelength, such as those in water vapor,the scattering process is explained using theMie the-ory, according to which the dependence between lightscattering and wavelength decreases [5].
When an observer looks at a distant object, wehave to consider not only the direct light from the ob-ject to the observer, which undergoes scattering andabsorption processes, but also the light added in thecone of vision coming from light scattered by parti-cles in the atmosphere [5]. This component is knownas airlight, which is predominantly white or bluishdepending on the size of the particles in the atmo-sphere, and its presence leads to a loss in contrast inthe perception of objects at a distance [6,7]. As a con-sequence of airlight, objects appear to be whitish,brighter, and have less color saturation. As the dis-tance between the observer and the object increases,airlight becomes more important and objects appearto be less and less color-saturated, eventually ap-proaching the color of the horizon. This effect clearlyinfluences image contrast and can be easily dis-cerned by looking at a distant mountain ridge. Thisairlight process may well have conditioned previousreports of color distribution in natural scenarios.
The loss in contrast due to airlight can be assessedby the magnitude of visibility. This magnitude is ameasurement of the capacity to distinguish an objectagainst the horizon (taken here to be the back-ground), and it is given in terms of the limiting dis-tance at which discernment is still possible. Visibilitydepends to a great extent on the predominant parti-cle size in the atmosphere together with its density:clear air, haze, mist, fog, rain, or snow [5]. As thedistance between the object and the observer in-creases, the object tends towards invisibility becausethe object and the background (horizon) becomeindistinguishable.
An object’s bluishness is sometimes not evidentdue to the fact that Mie scattering can be more im-portant than Rayleigh scattering and possibly due tosome kind of ability in the human visual system tomaintain the distant object’s hue. Henry et al. [8]have shown through psychophysical experimentsthat in spite of the fact that distant objects appear
to be less color-saturated, the human visual systemis able to discount the bluish effect and maintainthe object’s hue. This effect is known as atmosphericcolor constancy [9].
Changes in the color of objects with distance havealso been qualitatively described on many occasions[10], but there seems to be nothing published aboutcolorimetric measurements of these changes. Thefirst objective of our work, therefore, was to addressthe question of how the color of objects changes ac-cording to their distance from the viewer. To this endwe used a physical atmospheric model, both for clearand overcast days. The evolution of the color of ob-jects with distance was calculated on the basis ofsome known experimental atmospheric parameters.Thus it was possible to ascertain color ranges at anydistance.
Our second aim deals with the concept of visibility.At present, the visibility of an object is evaluated as afunction of the brightness contrast between theobject and background, the horizon in our case, i.e.,taking into account only the human capacity to dis-criminate between luminances. But at the photopiclevel of illumination, as during the day, object percep-tion involves color vision, so why is color not takeninto account in the definition of visibility? Thus wewondered whether taking the chromaticity of theobjects into account might affect our visibilitymeasurements.
The third aim of this work relates to the constantcolor appearance of an object when daylight changes,that is, to color constancy. The appearance of objectsdoes not change for different days, hours of the day,or atmospheric conditions in spite of the colorimetricchanges provoked by the changes in illumination.Working with a wide range of objects, several authors[1,11–14] have found a linear relationship with ahigh correlation coefficient representing the pairs ofexcitation values for each cone photoreceptor (L, M,or S) determined for each object under daylight illu-mination at two different color temperatures. Fosterand Nascimento [12] explain the color-constancyphenomenon based on these linear relationships.We have tested to see whether these linear relation-ships hold good when studying cone-excitationvalues for objects located at different distances. Inthis way, we hope to contribute to the theories basedon these assumptions or make some insights into themaintenance of hue and the atmospheric color con-stancy of objects according to their distance fromthe observer, as Henry et al. [8] have described.
2. Method
To evaluate the color of an object with a spectral re-flectance ρðλÞ in a natural scene, either directly or in-directly illuminated by the sun, and observed at acertain distance, we must assess the spectral radi-ance shown by the object at the location of the obser-ver. Such spectral radiance is composed of two terms:one induced by direct light coming from the objecttoward the observer, which undergoes atmospheric
attenuation, and the other by added light in the ob-server’s cone of vision due to atmospheric scattering,or airlight. The physical model that supports theseassumptions is named the “dichromatic atmosphericscattering model” [15,16] and is illustrated in theschematic representation shown in Fig. 1.
According to [15–18] the object’s spectral radianceobserved at a distance d can be expressed as
where L0ðλÞ is the object’s spectral radiance at zerodistance, βðλÞ is the extinction coefficient in the atmo-sphere, and L
∞ðλÞ is the spectral radiance of the
horizon. This equation supposes a homogeneous at-mosphere, that is, βðλÞ is taken to be the samethroughout the trajectory from the object to the ob-server. The first term represents attenuated directlight, whilst the second one represents the airlightphenomenon.
On overcast days the light impinging upon theobject comes from the whole sky dome [19,20], andnow the object’s spectral radiance will be
LðλÞ ¼ L∞ðλÞρðλÞ expð−βðλÞdÞ
þ L∞ðλÞð1 − expð−βðλÞdÞÞ; ð2Þ
where ρðλÞ is the object’s spectral reflectance. For thisequation to hold good, it must be presumed that theobject’s surface exhibits Lambertian behavior andthat the only light source is the sky, thus disregard-ing other possible sources such as light reflected bythe terrain or by other objects in the scene.
On clear days, under the same assumptions madefor overcast days, the following expression can bededuced [21]:
LðλÞ ¼ EdðλÞρðλÞπ expð−βðλÞdÞ
þ L∞ðλÞð1 − expð−βðλÞdÞÞ; ð3Þ
whereEdðλÞ is the spectral irradiance upon the objectilluminated by the sun.
Using Eqs. (2) and (3) the color coordinates for dif-ferent objects can be obtained for different distances.These coordinates have been obtained in the CIE1931 ðx; y;YÞ and in the CIELAB color spaces [22].The objects, of known spectral reflectance, were ta-ken from the Macbeth ColorChecker [23].
The spectral radiance of the horizon, L∞ðλÞ, was
measured with a telespectroradiometer (SpectraCo-lorimeter, PR-650, Photo Research Inc., Chatsworth,California). The spectral irradiance of the light illu-minating the objects was measured with the same in-strument at zero distance of observation and waspresumed to be the same at any distance from theobserver at which the object might be located, bothon clear and overcast days. The spectroradiometer isaffected by shot noise, as is any photodetector. A si-mulation of this noise, using Poisson statistics[24,25], was taken into account to study its influenceon the evaluation of the chromaticity coordinates. Wefound that for the levels of luminance during thedays in question, the effect on the assessment of thechromaticity coordinates was negligible, yielding acolor difference between the measured sample andthe noisy one of below 0.1 of a CIELAB unit.
The atmospheric extinction coefficient, βðλÞ, wasmeasured with a nephelometer in the CEAMA(Centro Andaluz de Medio Ambiente) laboratory[26]. The extinction coefficient is the sum of the scat-tering coefficient and the absorption coefficientβabðλÞ, [5]. The scattering coefficient was measuredat three wavelengths (450, 550, and 700nm) [18]and extrapolated for the rest of the visibility rangeby obtaining the value of parameter u in theexpression
βscðλÞ ∝1λu : ð4Þ
Parameter u is related to the amount and type ofaerosols present in the atmosphere [27]. Equation (4)shows the typical spectral dependence of the scatter-ing coefficient [5]. The u values range from 0 fordense fog to 4 for a perfectly clear atmosphere andare thus directly related to the concept of visibility inthe atmosphere: on foggy days the values of u arelower, as is visibility.
The range of variation in the extinction coefficientsfor the days measured was between 50 and 150Mm−1
at 550nm wavelength. Under the atmospheric condi-tions studied in this work we have assumed thesingle scattering approach [5]. Typical values of ufor haze are between 1 and 2 [27]. The u coefficientis shown in Table 1 for the days when the measure-ments weremade. Only one day has a coefficient witha value of u lower than 1, corresponding to a day withhigh dust content in the atmosphere. In the visiblerange, the absorption coefficient was taken to beconstant and measured at 670nm [28].Fig. 1. Schematic representation of different light contributions.
A. Variations in an Object’s Color According toObservation Distance
Table 2 shows an example of the change in the colorcoordinates of an object according to the distance be-tween it and the observer. The color coordinates areexpressed in terms of CIE 1931 and CIELAB colorspaces. Table 2 corresponds to a yellowish-green ob-ject on a clear hazy day (day one). As can be seen, thechromaticity coordinates change according to dis-tance, with a tendency to stabilize at long distances.It can be deduced from Eq. (3) that this tendencymoves toward the chromaticity coordinates of thehorizon. For the a�, b�, and L� coordinates the ten-dency is to (0, 0, 100). We have taken the reference“white” in the CIELAB expressions as a perfect whitereflecting surface illuminated to the same extent asthe object at each distance. Table 3 shows the sameobject for an overcast day (day four) with a lower uvalue. In this case, the horizon chromaticity coordi-nates are reached more quickly at shorter distances.This day presented lower visibility than the previousones. Color trend according to observation distance
for an orange object in four days (two overcast andtwo clear) is set out in the CIE 1931 ðx; yÞ diagramin Fig. 2. The extremes of each of the curves corre-spond to the object’s color at zero distance and theconvergence point to the horizon color, for a longdistance.
In Fig. 2 hook-shaped curves can be seen for threedays, both clear and overcast. The same hook-shapedcurves were obtained for the rest of the samples. Ifthe u value were less than one, this kind of curvewould not be found. Because the extinction coeffi-cient reduces their dependence on the wavelength, λ,the evolution of the curves becomes an almoststraight desaturation line toward the horizon chro-maticity coordinates.
For the remaining days it is possible to distinguishtwo sections in the curves. The first, correspondingto the chromaticity coordinates of the object from 0 tomiddle distances, shows strong desaturation due tothe airlight component. This desaturation is alsoaffected by the wavelength dependence of the extinc-tion coefficient. According to Eqs. (2) and (3), at-tenuation is higher in the short-wavelength range forlight coming directly from the object (the first term ofthe equations). On the other hand, the airlight
Table 1. Measure Days, Sky Conditions, and u Coefficient
Day (Year 2010) Sky Condition u
9 March Clear 1.915 March Clear 1.816 March Clear 1.918 March Overcast 1.419 March Overcast 0.414 April Clear 1.716 April Overcast 1.919 April Clear 1.720 April Overcast 1.921 April Clear 1.928 April Clear 1.623 November Overcast 1.924 November Overcast 1.826 November Overcast 1.69 December Clear 1.313 December Clear 1.614 December Clear 1.515 December Clear 1.516 December Clear 1.6
Table 2. Chromaticity Coordinate Evolution for the 6G Sample ofColorChecker DC in CIE 1931 xy and CIE 1976 L�a�b� for Different
component is more relevant at short wavelengths,giving a bluish component to the object’s color. Theresult is a combination of both opponent terms, withthe airlight term acquiring greater importance con-comitantly with the increase in distance from theobserver.
For long distances, however, the term expð−βðλÞdÞbecomes lower in value, and consequently the air-light component depends less on wavelength, result-ing in the chromaticity of an object tending towardthe chromaticity of the horizon, whatever its originalcolor. Thus the second part of the curve, the bentzone, appears.
Figure 3 shows the trend of several samples on thesame day in terms of the CIELAB [Fig. 3(a)] and CIE1931 [Fig. 3(b)] color systems. Every sample chroma-ticity moves toward the chromaticity of the horizon,and thus it may be deduced that the color gamut in anatural scene at a long distance will be narrowerthan that at a short distance. Figures 4 and 5 repre-sent the evolution of color gamut for the MacbethColorChecker [23] samples according to distance(Fig. 4 on a clear day and Fig. 5 on an overcastday). The color gamut for distance 0m is similar tothat found in [1] for natural scenes. The color gamutbecomes smaller concomitantly with an increase indistance; this behavior is more noticeable on an over-cast day, when the extinction coefficient is higher invalue and the u parameter is lower than on a clearday, thus leading to lower visibility.
B. Color and the Visibility Criterion
The visibility criterion used in the literature concern-ing atmospheric optics is related to the perceptualability to distinguish an object at a certain distanceagainst the background. It is usually based on the
maximum distance that a black object can be madeout against the horizon. A black object seen at a longdistance has a certain luminance due to airlight,which can be discerned or not against the horizon.The visibility criterion is based on the luminance-contrast threshold between the object and theuniform background (horizon) [5]. This criterion,therefore, is based on the perceived brightness ofan object and the background and does not take intoaccount any chromatic aspect.
Does the color of an object influence its visibilityagainst the horizon? To address this question, thedifference in lightness (ΔL�), chromaticity (ΔEa�b� ),and color (ΔEL�a�b� ) between the object and the back-ground (horizon), calculated in terms of the CIELABsystem, are represented in Fig. 6 at different dis-tances. It can be deduced that at short distancesthe total color difference (ΔEL�a�b�) and the lightnessdifference (ΔL�) are close, the relative contribution ofchromaticity difference (ΔEa�b� ) being less impor-tant. Nonetheless, the three curves are close for longdistances, the chromaticity difference being higherthan the lightness difference.
Visibility as a magnitude has classically been cal-culated according to a luminance threshold criterion[29,30], taking the Weber’s fraction ΔL�=L� limitingvalue as 0.02. Weber’s fraction measures the contrastbetween the object (black object) and the back-ground. The numerator measures the luminance dif-ference at the limit of discrimination between both,and the denominator is the background luminance.This criterion is based on psychophysical data of lu-minance discrimination in photopic vision. A 0.02classical Weber’s fraction is adopted [5] instead ofthe 0.01 usually used in psychophysical experimentsunder ideal observation conditions. A 0.02 value
Fig. 3. Chromaticity coordinate evolution for several samples of ColorChecker DC, 20 April 2010, overcast day. (a) CIELAB (a�b�
components) and (b) CIE 1931 (xy components) color systems.
gives a restricted visibility range, which could be ad-vantageous in certain circumstances such as airportsecurity.
Instead of considering a black object, we took sixcolored objects of different hues, and using assessed
lookup tables (see Table 4 for the results for threedays) we estimated the distance at which Weber’sfraction, taking lightness, L�, as the variable, has avalue close to 0.02 against the horizon. For the samedistance we determined the chromaticity difference
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
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x
y
2 km
10 km
5 km
0.3 km
30 km
1 km
0 km
16 March 2010 clear, u=1.89
Fig. 4. Color gamut reduction as the distance increases in CIE 1931 color system (xy components), 16 March 2010, clear day.
Fig. 5. (a) Color gamut reduction as the distance increases in CIE 1931 color system (xy components), 19 March 2010, overcast day;(b) enlarged version of the figure.
between the objects and the horizon. We could thencheck to ascertain whether at the distance whereWe-ber’s fraction reached the discrimination thresholdvalue between the object and the background, thecolor difference would still be enough to distinguishthem. The answer to this query depends on acceptedcolor tolerance. When the colors are adjacent, a colordifference of one CIELAB unit is accepted. Some-times color differences of three CIELAB units areadmitted, since one CIELAB color difference is toostrict [31,32].
The results set out in Table 4 show that threeCIELAB color difference units and aWeber’s fraction
of 0.02 are very similar in many cases. As can beseen in Table 4, however, in some cases a Weber’sfraction of 0.02 corresponds to a lower value thanthree CIELAB color difference units, and conse-quently the object is indistinguishable at shorter dis-tances than the ones specified by the classicalvisibility criterion.
Depending on the atmospheric conditions on theday of observation (see Table 4), the visibility of sev-eral objects is less than that assessed on the basis ofthe classical criteria. On the other hand, under opti-mum illumination conditions, such as high photopiclevel and an optical field of view wider than 1°, if wetake a color tolerance close to one CIELAB unit, thedistance at which the object is indistinguishable fromthe horizon might be much longer than the distancegiven by the classical visibility criterion. Thus it maybe concluded that color can influence the contrast ofobjects against the horizon.
C. Cone-Excitation Ratios and Distance
The human capacity to maintain the appearance ofthe color of an object under changes in illuminationis known as color constancy. This holds good whendaylight changes spectrally, for instance, for differentphases of daylight on different days or differenthours of the same day. There are various theoriesto explain this phenomenon [9]; one of these, calledrelational color constancy, is based on the constancyof the excitation ratio of the cones for the objectswhen the illuminant changes. When, for any specificcone receptor [33], the excitation values of several ob-jects under a specific illuminant are represented as afunction of those obtained under another illuminant,the result is a straight line with a high correlationcoefficient [1]. Some color constancy theories used todevelop object-recognition algorithms are also basedon cone-excitation ratio constancy [9,11]. Figure 7(a)shows an example of cone-excitation ratio constancy.
Fig. 6. Difference in lightness (ΔL�), chromaticity (ΔEa�b� ), and color (ΔEL�a�b� ) between an object and the background (horizon), calcu-lated in terms of the CIELAB system, are shown in order to demonstrate the influence of the color of an object on its visibility against thehorizon. (a) Color differences as a function of the distance for sample 5F of ColorChecker DC against the horizon, 20 April 2010, overcastday; (b) enlarged version of the figure.
Table 4. Color Differences and Weber’s Fraction Thresholdsfor Different Samples of ColorChecker DC against the Horizon,15 March (Clear), 16 April (Overcast), and 20 April (Overcast)
The L-cone excitation under a daylight illuminant(ordinate axis) and under an equi-energetic illumi-nant (abscissa axis) has been represented for thesamples of the Macbeth ColorChecker. In this case,we considered the samples as being seen at zero dis-tance to the observer, and so neither attenuation norairlight were taken into account in the calculation ofthe values in daylight. As may be supposed, this re-sults in a high value for the linear correlation coeffi-cient. In Fig. 7(b) a similar example is representedfor M cones, but in this case the objects were situatedat increasing distances. The value of the linear cor-relation coefficient is also high, but the intercept isother than zero (see Table 5).
The intercept increases concomitantly with a de-crease in the slope as the object gets farther andfarther away from the observer. These results mightbe expected, because the color gamut of the object col-lection lessens the farther the distance, while thecone response remains much the same. This valuecorresponds to the cone excitation value for the hor-izon. The explanation for the nonzero value of the
intercept is to be found in the airlight phenomenon.The cone response at a certain distance had a valueother than zero, even for a black object, the L, M, andS values of which are (0,0,0) for close distance, due tothe airlight contribution. The results shown in Fig. 7were found for each day measured and for every conetype. They can help to explain atmospheric color con-stancy. Henry et al. [8] showed hue constancy for ob-jects observed at different distances, which can berelated to the linear correlation found for the coneexcitation values. Hagedorn and D’Zmura [34] re-lated contrast constancy for objects seen in foggy con-ditions to an affine model to represent the light thatis received from an object under foggy conditions,called a dichromatic model. In this case, we have de-monstrated that this affine model also holds goodwhen cone excitation is considered.
4. Conclusions
We have studied alterations in the color coordinatesof objects in natural scenes caused by atmosphericscattering according to changes in the distance of ob-servation. Representations of the evolution of an ob-ject’s color in the chromaticity diagram result inhook-shaped curves as the object moves from zeroto long distances, where the object chromaticity coor-dinates approach the color coordinates of the horizon.This trend is the result of the combined effect of at-tenuation in the direct light arriving to the observerfrom the object and the airlight added during itstrajectory. These hook-shaped curves are more pro-nounced when the dependence of the extinction coef-ficient upon wavelength is more pronounced, that isto say, on hazier days with high u values. The desa-turation process observed in the color of the objectsas the distance of observation increases is a result ofan increase in the airlight component. Thus we can
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
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L
L’
16 April 2010 overcast, u=1.88
(a)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0
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16 April 2010 overcast, u=1.88
(b)
Fig. 7. Cone-excitation ratio constancy for 20 samples (1F, 2C, 2G, 2I, 2R, 4I, 4K, 5F, 5M, 5R, 6G, 6F, 6H, 7M, 9M, 10F, 10H, 11H, 11I, 11N)of ColorChecker DC, 16 April 2010, overcast day. (a) L sensor ratio constancy at zero distance, (b) M sensor ratio constancy at differentdistances.
Table 5. Data Analysis Results for Different Distances Simulatedfor 20 Samples (1F, 2C, 2G, 2I, 2R, 4I, 4K, 5F, 5M, 5R, 6G, 6F,
6H, 7M, 9M, 10F, 10H, 11H, 11I, 11N) of ColorChecker DC
deduce that airlight has the effect of reducing the col-or gamut as the distance between the observer andthe object increases. Atmospheric scattering leadsto a lessening of the object’s visibility that can beevaluated as a color difference between the objectand the background (horizon). Focusing on color dif-ference rather than luminance difference could pro-duce different visibility values depending on thecolor tolerance used.
Cone-excitation ratio constancy was assessed forseveral objects at different distances. Affine relationswere obtained when the cone excitations producedby the objects were represented both at zero andat farther distances. The intercept increases conco-mitantly with distance, while the slope decreases.These results could contribute to the explanationof color constancy in natural scenes for objects at dif-ferent distances, as has been mentioned by differentauthors [1–4,9]. In this work we have not made anyestimation of noise for the cone receptors. We mayask in the future whether the inclusion of receptor-noise models might affect these results.
This work was supported by the Junta de Andalu-cía, Spain, under research grant P07.TIC.02642. Wealso thank the referees for their advice.
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