MARS ROVER COLOUR VISION: GENERATING THE TRUE COLOURS OF MARS

Dave Barnes

Aberystwyth University, Penglais, Aberystwyth, SY23 3DB, UK{dpb@aber.ac.uk}

ABSTRACT

Mars rover colour vision typically employs multi-spectralimaging to generate natural-colour images that allow aplanet to be viewed as if a human was present on the sur-face. As surface colour is dependent upon both surfacereflectance/absorption properties and the surface illumi-nation, getting the surface solar spectrum irradiance cor-rect is vital for planetary colourimetry. Associated with asolar spectral power distribution (SPD) is its correlatedcolour temperature (CCT) which determines the refer-ence white point for the colour image processing. If theCCT is wrong, then the white point will be wrong, andhence the colours will be wrong. New methods are be-ing developed whereby a ‘typical’ Mars sol-light spectraldistribution can be computed based upon the actual or de-sired CCT. Knowledge of the CCT allows the applicationof new chromatic adaptation transformations, wherebythe martian surface can be viewed as if it had been illumi-nated by other terrestrial light sources as opposed to justMars sol-light. The paper presents early results towardsgenerating ‘typical’ Mars illuminants, and provides ex-amples of CCT-based natural-colour image generation,and chromatic adaptation.

Key words: Natural Colour; Correlated Colour Tempera-ture; Chromatic Adaptation.

1. INTRODUCTION

Given the previous science cameras flown to Mars, agood deal of research has been conducted in the areaof processing multi-spectral image data to generate ter-rain Region of Interest (ROI) reflectance spectra, andcolour corrected image products. The missions includethe Viking Landers (VL) (1976) [10], the Mars Pathfinder(MPF) lander and the Sojourner rover (1997) [16], theMars Exploration Rovers (MER) Spirit (2004 to 2010)and Opportunity (2004, still operational) [4], the Phoenix(PHX) lander (2008) [15], and the Mars Science Lab-oratory (MSL) (2012) [9]. Throughout these missions,multi-spectral image data have been captured and radio-metrically and colorimetrically processed, and an impor-tant product has been the generated colour images.

As surface colour is dependent both upon surface re-flectance/absorption properties, and the surface illumi-nation, then getting the surface solar spectrum correctfor Mars colourimetry is vital. The term surface solarspectrum is used here to refer to the solar spectral irradi-ance having passed through the atmosphere. Associatedwith a solar spectral power distribution (SPD) is its cor-related colour temperature (CCT) which determines thereference white point for the colour image processing.If careful attention is not paid to using the correct solarspectrum and therefore CCT, then the white point willbe wrong and hence the colours will be wrong. A com-mon approach in Mars exploration has been to use theAir Mass Zero (AM0) reference solar spectral irradianceat the top of Earth’s atmosphere. This is usually scaledusing an inverse-square law to the average heliocentricdistance of Mars, and then an attenuation estimate of theeffects of dust in the atmosphere is applied. Howeversuch an approach is not without a number of drawbackssuch as the highly eccentric solar orbit of Mars, and dustattenuation models based upon limited true optical depthknowledge.

An alternative approach is to take reflectance measure-ments of an in-situ calibration target that has been char-acterised and calibrated prior to launch. All of the Marsmissions mentioned previously have flown a radiometriccalibration target which has been accommodated on thelander or rover so that it can be imaged by the multi-spectral cameras. By sampling the radiometrically cor-rected data files generated after calibration target imag-ing, and comparing the measured calibration target re-gions with pre-flight data, then using a standard radiomet-ric relationship, the surface solar spectrum can be foundfor various Sun angles [13]. Whilst this direct measure-ment of the solar spectral irradiance may offer an im-provement over the AM0 related approach, the methodis limited by the total number of available spectral pointsamples for each derived solar spectrum. Essentially acalibration target is imaged multi-spectrally, and hencethe total spectral point sample number is limited by thenumber of available filters. For example each of the twoNASA MER rover Pancam instruments has only elevenfilters in the range 432 nm to 1009 nm.

The in-situ measured solar spectra are also very specificto the particular Sun angle and the atmospheric condi-tions present during image capture, and hence they can-

not be described as typical SPDs of Mars sol-light. Incomparison to a specific in-situ measured surface solarspectrum that is ‘tied’ to a given imaging activity, theavailability of typical Mars spectral distributions wouldbe advantageous because they could be used in a muchlarger number of colorimetric processing situations, forexample the comparison of natural-colour images gen-erated from image data captured at different locations,times, and seasons.

Historically, terrestrial colourimetry faced a similar prob-lem in that there are in effect an infinite number of pos-sible solar illumination conditions given the number ofpossible locations, times of day, different seasons, andhence different weather conditions. The solution to thisproblem was the introduction of standard illuminants thatallowed for objective colour comparisons, and which re-moved one key source of variation from calculations orthe measurements of colour. Judd et al. [11] pioneeredthe work that led to the now CIE (Commission Interna-tionale de l’Eclairage/International Commission on Illu-mination) standard daylight illuminants [6]. For exam-ple, D65 which is a typical daylight solar spectrum witha CCT = 6504 K.

The introduction of the CIE standard illuminants has hada profound impact upon terrestrial colourimetry. It hasallowed many techniques such as natural-colour imagegeneration, chromatic adaptation, and colour matching tobe developed, and allowed practitioners to compare re-sults irrespective of image capture locations and illumi-nation conditions. Given such strengths then the ques-tion arises, ”Could the same be done for Mars?” Thepaper presents early results using 50 SPDs of Mars sol-light samples that have been derived from Mars rover im-age data. Using these data, methods have been formu-lated whereby a ‘typical’ Mars sol-light spectral distribu-tion can be computed based upon the desired correlatedcolour temperature (CCT). The paper explores the appli-cation of CCT-based Mars illuminants to natural-colourimage generation. Given the knowledge of the CCT usedduring image processing, the paper presents results fromthe application of new chromatic adaptation transforma-tions, whereby the Martian surface can be viewed as ifit had been illuminated by daylight as opposed to Marssol-light.

It should be noted that work reported here is ongoing, andthe aim is to increase the current Mars SPD sample set byincluding data from MPF, PHX, and MSL (when NASAPDS Mastcam data are released). Thus a final SPD sam-ple set will be several hundred in number. Because thislarger sample set will cause (slight) changes to the re-sults reported here, some items of detail (e.g. xM andyM equations) have been omitted from this paper. A fullpaper [1] will be published in the literature based uponthe final Mars SPD sample set.

Figure 1. Radiometrically corrected (RAD) image of theMER Spirit rover calibration target captured using thePancam instrument on sol 5, using filter L5 with a centrewavelength of 535 nm.

2. CURRENT EXPERIMENTAL DATA

Judd et al. [11] used a composite of 622 daylight spec-tral irradiance samples covering the wavelength range330 nm to 700 nm. The composite was composed of99 independently measured daylight samples from Ot-tawa Canada, 249 from Rochester USA, and 274 fromEnfield UK, and thus represented daylight data measuredat different locations, times of day, different seasons, andhence different weather conditions. To extend the com-posite data to the wavelength range of 300 nm to 830 nm,the compilation of [18] was added which contained thespectral absorptance of the Earth’s atmosphere due toozone and water vapour.

To generate an early composite of Mars sol-light spec-tral irradiance samples (currently 50 in number), NASAPlanetary Data System (PDS) image data of the radiomet-ric calibration targets from the Mars Exploration RoversSpirit & Opportunity (MER) were obtained. Radiometri-cally corrected (RAD) files were collected for all of thefilters within the range 432 nm to 1009 nm. Future workwill extend the current Mars sol-light spectral irradiancesamples to several hundred in number using image datafrom the MPF and PHX instruments, and the MSL Mast-cam.

Figure 1 shows an example of the MER calibration tar-get data downloaded from the PDS archive. The ‘white’,and grey regions on each calibration target were sampled(> 100 pixels) for each filter to measure the spectral ra-diance (L(λ)). Due to dust deposition on the calibrationtargets during the mission, which would cause measure-ment errors, the sampling was restricted to the first 50 sols(Martian days) for each rover. The amount of accumu-lated dust during this period was deemed to be relativelyinsignificant [17].

400 450 500 550 600 650 700 750 800600

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Simonds Characteristics Vectors for Mars Sol-light

Wavelength

Com

pone

nts

of M

ars

Sol-

ligh

t Dis

trib

utio

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Figure 2. Graph of the first four characteristic vectors(V ) derived from the composite Mars sol-light spectraldistributions (currently 50 samples).

Pre-flight laboratory measured spectral reflectance ρ(λ)data for the two targets were obtained. Using the stan-dard radiometric relationship between spectral irradianceE(λ), spectral radiance L(λ), and spectral reflectanceρ(λ) [22], the Mars solar SPDs were calculated for thetwo targets.

Rather than simply average the SPD data for the whiteand grey regions, a first-order Kalman filter was appliedto ‘fuse’ the two data samples. This process accountedfor the associated measurement variance with the resul-tant SPD data points each having a reduced variance andhence improved probability density function (PDF).

To complete the experimental data acquisition process, acubic-spline was then applied to each sample. The resul-tant SPDs were normalised to 560 nm, and then down-sampled in increments of 5 nm to generate the compositeMars solar spectral data set. The spline-fitting, normali-sation and down-sampling was undertaken to produce thedata in a format that was consistent with the publishedCIE illuminants. Hence a direct comparison with the fi-nal generated Mars illuminants could be made.

3. MEANS AND CHARACTERISTIC VECTORS

A key technique that underpinned the work of [11] wasthe application of characteristic vector analysis to theobtained sample distributions of spectral daylight. Amethod adapted from [21] was used to derive the meansand first four characteristic vectors using the composite ofthe 622 daylight samples. Simonds’ characteristic vectoranalysis is equivalent to the method of Principal Compo-nent Analysis (PCA). The power of this approach comesfrom the fact that a large percentage of the variabilityamongst a family of daylight spectral irradiance samplesmay be explained by using only a few characteristic vec-tors.

Simonds [21] observed that any spectral irradiance curveE(λ) can be reconstituted from the mean, E(λ), and

characteristic vectors derived from a family of measuredspectral irradiance distributions. This can be expressedby Eq. 1 where M represents a scalar multiple, V (λ) acharacteristic vector, and p is equal to the total number ofcharacteristic vectors generated from the PCA analysis.

E(λ) = E(λ) +M1V1(λ) +M2V2(λ)

+M3V3(λ) + · · ·MpVp(λ) . (1)

For the research reported here the non-linear iterative par-tial least squares (Nipals) algorithm was used to generateresultant cumulative percentage of variance, Loadings(which are equivalent to PCA eigenvectors), and eigen-values (which are equivalent to Simonds’ characteristicroots). The Nipals algorithm uses a different normalisa-tion method to that used by Simonds, so to convert theresultant Loadings (L(λ)) to the equivalent of Simonds’characteristic vectors (V (λ)) a simple eigenvalue (eval)scaling was performed using V (λ) = L(λ) [eval]

1/2.The Nipals algorithm employs a mean-centered PCA ap-proach [5].

Judd et al. [11] went on to use the first two characteris-tic vectors obtained from the set of 622 measured spec-tral radiant power distributions. Whilst it was reportedthat the use of the mean and first two characteristic vec-tors allowed the original distributions, “to be reconsti-tuted remarkably well” [22], no cumulative percentageof variance results were ever published in the original pa-per. These results are a measure of what percentage ofthe original SPD set is being ‘explained’ by the resul-tant principal components. Examination of the cumula-tive percentage of variance results for the (currently 50)Mars composite SPD data set shows that the use of themean and first characteristic vector alone generates a re-sult of just 83.96%. As more characteristic vectors areadded, then the cumulative percentage of variance resultsimprove. For the two, three and four characteristic vectorcases then the percentage increases to 96.71%, 98.58%,and 99.58% respectively.

4. MARS SOL-LIGHT CHROMATICITY

For a relative spectral (colour) power distribution, ϕ(λ),then using the standard CIE chromaticity equations forthe emissive case, it is possible to calculate the XY Ztristimulus values, Eqs. 2-4. Here x(λ), y(λ), z(λ) arethe respective colour matching functions of the 1931 CIEstandard colorimetric observer [6].

X =∑λ

ϕ(λ)x(λ)∆λ , (2)

Y =∑λ

ϕ(λ)y(λ)∆λ , (3)

Z =∑λ

ϕ(λ)z(λ)∆λ . (4)

0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39

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4200 K4800 K5500K6500 KJudd Chroma LocusPlanckian LocusMars Chroma LocusIsoT-42IsoT-48IsoT55IsoT-65IsoT-75Illuminant ESpirit C. Temp.Opp C. Temp.Phx C. Temp.

4200 K4800 K5500K6500 KJudd Chroma LocusPlanckian LocusMars Chroma LocusIsoT-42IsoT-48IsoT55IsoT-65IsoT-75Illuminant ESpirit C. Temp.Opp C. Temp.Phx C. Temp.

ALL Mars solar spectra chromaticity versus Planckian locus and Chromaticity Loci

CIE x

CIE

y

Figure 3. Chromaticities of Mars sol-light compared tothe locus of chromaticities implied by the Planck radia-tion law. The daylight locus discovered by [11] was foundto lie slightly to the ‘green’ side of the Planckian locus.In comparison, the Mars sol-light locus has been found tolie slightly to the ‘purple’ side of the Planckian locus. Thestraight lines intersecting the Planckian locus are exam-ples of isotemperature lines which define loci of constantcorrelated colour temperature.

Substituting each derived Mars SPD for ϕ(λ), the tristim-ulus values were calculated for the current Mars compos-ite SPD data set. As the fundamental colourimetric tablesare the 1 nm tables in the CIE standards, a cubic-splinewas applied to each SPD and the numerical summationswere performed at wavelength intervals, ∆λ, equal to1nm. Once the tristimulus values for each Mars SPD hadbeen obtained, then the CIE chromaticity coordinates (x,y, and z) for each SPD were calculated by normalisingthe tristimulus values using Eqs. 5-7.

x = X/(X + Y + Z) , (5)

y = Y/(X + Y + Z) , (6)

z = Z/(X + Y + Z) . (7)

The resultant chromaticity coordinates were then plottedon a CIE (x, y) (chromaticity) diagram, Fig. 3. Thisshows the chromaticities of Mars sol-light samples com-pared to the locus of chromaticities implied by the Planckradiation law. The Planckian locus was plotted by gener-ating a set of blackbody radiator spectral power distribu-tions for a range of temperatures using Planck’s law, andthen converting the resultant distributions to x, y chro-maticity coordinates. The straight lines intersecting thePlanckian locus at 4200 K, 4800 K, 5500 K, and 6500 Kare examples of isotemperature lines which define loci ofconstant correlated colour temperature.

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ativ

e S

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rrad

ianc

e (n

o un

its)

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Figure 4. Relative spectral distributions of typical Marssol-light for correlated colour temperatures: 4600 K,4800 K, 5000 K, 5200 K, and 5400 K reconstituted fromthe mean and first three characteristic vectors of the com-posite Mars data (currently 50 samples). The spectra arenormalised to 560 nm, and the CIE daylight illuminantD65, and the theoretical ‘equal-energy’ illuminant E areshown for comparison.

Judd et al. [11] applied the same process to their terres-trial spectral radiant power distributions, and discoveredthat the chromaticity points from the 622 samples sug-gested that the phases of daylight could be represented bya ‘daylight locus’ in the CIE chromaticity diagram. Theyfound that this locus could be modeled by the quadraticrelation yD = −3.000xD

2 + 2.870xD − 0.275, wherexD, and yD, are the daylight chromaticity coordinates.The daylight locus is shown in Fig. 3, and follows thePlanckian locus but stays slightly to the (chromaticity di-agram) ‘green’ side.

Inspection of the chromaticity points from the current 50Mars samples has shown that the phases of Mars sol-lightcan be represented also by a locus. Numerical methodshave been used to determine the polynomial coefficientsfor this Mars sol-light locus [1].

Sastri [19] observed that the proportion or absence ofRayleigh scattering in the atmosphere could affect wherea daylight chromaticity point fell with respect to thePlanckian locus. In an earlier paper, [20] had observedthat the dust storms common in Delhi during the summermonths caused daylight chromaticity points to lie on thepurple side of the Planckian locus. He states, “Because ofthe neighboring desert, even a windy day fills the atmo-sphere in Delhi to some extent with fine dust, which mayaccount for the sizeable number of points appearing onthe purple side of the locus.” There is significant researchdescribing the presence of fine dust particles in the Mar-tian atmosphere [14], therefore it is entirely appropriatethat the Mars sol-light locus should be found to fall onthe purple side of the Planckian locus.

The CIE determined the relationship between correlatedcolour temperature (Tcp) and xD, thus allowing the day-

Table 1. Mars chromaticity coordinates for exampleCCTs based upon the current 50 Mars SPD samples.Correlated colour

temperature Mars chromaticity coordinates(K) xM yM4600 0.3566 0.35644800 0.3505 0.35195000 0.3448 0.34765200 0.3395 0.34345400 0.3347 0.3393

light chromaticity coordinates (xD and yD) to be calcu-lated for a specified CCT. Using the CIE equations relat-ing Tcp to xD as the baseline [6], new coefficients havebeen calculated for the Mars case using numerical meth-ods to solve for a set of isotemperature line interceptswith the Mars sol-light locus. Table 1 shows the chro-maticity coordinates (xM , yM ) of typical Mars sol-lightfor various example values of CCT. As will be seen insection 5, values for zM will be required and these canbe obtained by exploiting the chromaticity relationship:xM + yM + zM = 1.

5. SCALAR MULTIPLES AND CHROMATICITYCOORDINATES

The significant step made by [11] was to recognise therelation between scalar multiples and CIE chromaticitycoordinates. Using the CIE tristimulus value X as an ex-ample, then the irradiance specified by the distribution inEq. 1 may by expressed as a component within Eq. 8,where x(λ) is one of the CIE colour matching functionsdefined in section 4.

X =∑λ

E(λ)x(λ)∆λ . (8)

Given that the scalar multiples are constants that are inde-pendent of wavelength for any single reconstituted spec-tral distribution, then the tristimulus values X , Y , and Zmay be written as:

X = X0 +M1X1 +M2X2 +M3X3 + · · ·MpXp , (9)

Y = Y0 +M1Y1 +M2Y2 +M3Y3 + · · ·MpYp , (10)

Z = Z0 +M1Z1 +M2Z2 +M3Z3 + · · ·MpZp . (11)

Therefore the relation between scalar multiples and theCIE chromaticity coordinates x, y and z follows directlyfrom Eqs. 9-11 given the CIE definitions for x, y, andz in Eqs. 5-7. This results in Eqs. 12-14, where Sn =Xn + Yn + Zn and 1 ≤ n ≤ p.

x =X0 +M1X1 +M2X2 +M3X3 + · · ·MpXp

S0 +M1S1 +M2S2 +M3S3 + · · ·MpSp, (12)

y =Y0 +M1Y1 +M2Y2 +M3Y3 + · · ·MpYp

S0 +M1S1 +M2S2 +M3S3 + · · ·MpSp, (13)

z =Z0 +M1Z1 +M2Z2 +M3Z3 + · · ·MpZp

S0 +M1S1 +M2S2 +M3S3 + · · ·MpSp. (14)

Given that the CIE chromaticity space is three-dimensional, then the number of (unknown) scalar multi-ples has to be limited to three, and hence a maximum ofonly three characteristic vectors can be used in the SPDreconstitution process.

For the first three characteristic vectors case, then by sub-stituting xM , yM , and zM for x, y, and z into Eqs. 12-14,and replacing X0, X1, . . ., Xp, etc. with the coefficientsa1, a2, . . ., a4, etc., the relationship between CCT-basedchromaticity coordinates and scalar multiples can be ob-tained, Eqs. 15-17.

xM =a1 + a2M1 + a3M2 + a4M3

d1 + d2M1 + d3M2 + d4M3, (15)

yM =b1 + b2M1 + b3M2 + b4M3

d1 + d2M1 + d3M2 + d4M3, (16)

zM =c1 + c2M1 + c3M2 + c4M3

d1 + d2M1 + d3M2 + d4M3. (17)

To find the scalar multiples M1, M2, and M3 requiredto generate a reconstituted Mars solar spectral distribu-tion, it was necessary to solve for M1, M2, and M3 fromEqs. 15-17. The details of these results will be publishedin [1].

6. SPECTRAL DISTRIBUTIONS OF MARSSOL-LIGHT FOR VARIOUS CORRELATEDCOLOUR TEMPERATURES

Having obtained the characteristic vectors for the com-posite Mars sol-light SPD data, and generated a solutionfor the scalar multiples, it was then possible to generateCCT-based Mars illuminants. Modification of Eq. 1 forthe three characteristic vector case yields:

EM (λ) = E(λ) +M1V1(λ) +M2V2(λ)

+M3V3(λ) , (18)

where EM (λ) is the CCT-based Mars relative spectral so-lar irradiance (Mars illuminant). E(λ) and V1(λ), V2(λ),V3(λ), are the mean and first three characteristic vectorsobtained from the Nipals work described in section 3. Forany desired CCT (Tcp), the scalar multiples M1, M2, andM3, can be calculated and substituted into Eq. 18.

Tab. 2 shows the obtained scalar multiples required to re-constitute spectral distribution curves of typical Mars sol-light for five example values of CCT. Using these values,EM (λ) has been calculated for each case, and the resul-tant Mars illuminant spectra are shown in Fig. 4. As theCCT increases, then it can be seen that the ‘blue’ spectralregion increases with respect to the relative irradiance,whilst the ‘red’ spectral region decreases. All of the Marsspectra shown have a relatively large ‘hump’ in the ‘or-ange’ spectral region. The CIE daylight illuminant D65is shown for comparison.

7. APPLICATION OF CCT AND MARS ILLUMI-NANTS

Having established a method whereby Mars illuminantscould be reconstructed for any given correlated colourtemperature, it was then possible to explore the applica-tion of CCT and Mars illuminants to a number of areas ofMars surface science.

7.1. Generating Mars Natural-Colour Images

An important data product for all of the past surfacemissions to Mars has been the natural-colour imagesthat have been generated from the measured surface re-flectance spectra [10, 16, 4, 15]. The term ‘natural-colour’ is used here to differentiate between false-colourproducts whereby surface objects may be assigned arti-ficial image pixel colours, for example to enhance thecontrast between different objects during science analy-sis. In comparison natural-colour images seek to repre-sent the colours of the planetary surface as if viewed bya human physically present on the planet’s surface. Assuch, they should be a faithful and accurate representa-tion of the colour physics for the given scene.

Using the CIE standardised method for the reflective (ortransmissive) case, then for Eqs. 2-4, ϕ(λ) = R(λ)S(λ),where R(λ) is the spectral reflectance of the objectcolour, and S(λ) is the relative spectral power distri-bution of the illuminant. Substitution for ϕ(λ) yieldsEqs. 19-21:

Table 2. Example scalar multiples based upon the current50 Mars SPD samples.Correlated colour

temperature Scalar Multiples(K) M1 M2 M3

4600 0.0126 0.0031 −0.00074800 0.0992 0.0436 −0.01385000 0.1809 0.0916 −0.03035200 0.2583 0.1454 −0.04955400 0.3317 0.2037 −0.0707

Figure 5. Example natural-colour image created usingRCIPP and the generated Mars illuminant - M54. Thedata were captured by MER Opportunity on sol 346, andthe image shows a discovered Mars meteorite informallynamed “Heat Shield Rock”.

X = k∑λ

R(λ)S(λ)x(λ)∆λ , (19)

Y = k∑λ

R(λ)S(λ)y(λ)∆λ , (20)

Z = k∑λ

R(λ)S(λ)z(λ)∆λ , (21)

where k is a normalisation constant and is chosen to giveY = 100 for the case of a perfect white Lambertian re-flector, (R(λ) = 1), i.e. when an object reflects 100%for all wavelengths. Further details for generating Marsnatural-colour images can be found in [3]. This describesa software-based Radiometric and Colourimetric ImageProcessing Pipeline (RCIPP), which has been designedand implemented by the author in Mathcad R⃝ and subse-quently ported to IDL R⃝ (for inclusion into ENVI R⃝). Anenhanced version of RCIPP will be used to process imagedata captured by the multi-spectral Panoramic Camera(PanCam) instrument [8, 7], which is part of the sciencepayload for the ESA/Roscosmos ExoMars 2018 mission.This mission will see a rover [2] being sent to Mars thatsupports many science instruments dedicated to the ex-ploration of Mars and the search for past or present life.

Using NASA PDS image data from the MPF, MER andPHX missions, it was possible to generate natural-colourimages using the RCIPP software together with the ap-propriate Mars illuminant. Fig. 5 shows an example of anatural-colour image produced using RCIPP and a gener-ated Mars illuminant.

Figure 6. Example of Mars colour image chromatic adaptation. Left: The NASA MER Opportunity Pancam PDS data(sol 15) has been processed using the Mars illuminant M48. Middle: The left-hand (M48) image has been chromaticallyadapted to the standard CIE daylight illuminant D65. Right: The left-hand (M48) image has been chromatically adaptedto the standard CIE illuminant A for a tungsten filament lamp.

7.2. Chromatic Adaptation of a Mars Illuminant

A natural spin-off from the Mars illuminant work is theability to apply accurate chromatic adaptation to Marsimage data. For example, the Mars illuminant used togenerate natural-colour image data can be transformed toa standard terrestrial daylight illuminant, and hence Marscolour images can be created as if the scene had beenexposed to typical daylight illumination so creating animage as it would look if the same surface region hadbeen transported back to Earth. Given that planetary ge-ologists base their experience upon terrestrial field trials,then presenting Mars colour image data in this way couldbe most informative, and provide an improved way to vi-sualise and hence understand the Martian environment.

Eq. 22 shows that chromatic adaptation can be im-plemented as a linear transform of a source colour(XS , YS , ZS) into a destination colour (XD, YD, ZD) bythe linear transform (MCA). Knowing the source tristim-ulus reference white (XWS , YWS , ZWS) and the desti-nation tristimulus reference white (XWD, YWD, ZWD),and using the Bradford chromatic adaptation trans-form [12] for example, then MCA can be determined.

[XD

YD

ZD

]= [MCA]

[XS

YS

ZS

]. (22)

A set of MCA transforms from M46, M48, M50, M52and M54 to D65 have been calculated [1]. For those sit-uations where it might be useful to see what the martianterrain would look like if imaged under typical labora-tory illumination, then the transforms from M48 to illu-minants A (tungsten filament lamp, CCT = 2856 K) andF2 (cool white fluorescent lamp, CCT = 4230 K) havealso been calculated.

Fig. 6 shows a chromatic adaptation example. For theadaptation to illuminant D65 case, it can be seen thatblue/grey colours have been elevated due to the raiseddaylight SPD in the 450 nm region, and the orange andreds have been lowered due to the decrease in daylightSPD in the 560 nm to 830 nm region. In comparisonfor the adaptation to illuminant A case, then the bluesare minimised whilst the oranges, yellows and reds areelevated due to the increasing SPD in these wavelengthregions.

8. CONCLUSIONS

The remarkably close correspondence between the CCTof a given phase of daylight and its relative SPD [22]has been the inspiration for the research reported here.The paper presents the results from only 50 SPD samplestaken from the MER mission, but the work is ongoing toinclude SPD samples from the MPF and PHX missions,plus MSL data when these are released on the NASA PDSweb site. The Mars solar SPD irradiance samples weresubjected to PCA to obtain the mean and characteristicvectors (eigenvectors). Using numerical methods newformulae have been derived that allow the Mars sol-lightchromaticity coordinates, xM , and yM to be obtained forany given correlated colour temperature (Tcp). Formu-lae to determine the scalar multiples for the three charac-teristic vector case have been derived which incorporatexM , and yM . This allows CCT-based Mars relative spec-tral solar irradiances (Mars illuminants) to be generatedgiven the PCA mean and characteristic vectors obtainedfrom the Mars solar SPD irradiance samples. ExampleMars illuminants have been generated. Using the reflec-tive case of the CIE equations for generating XY Z tris-timulus values from input spectra, and selected Mars illu-minants, example Mars natural-colour images have beencreated from the NASA PDS data archive. Transformsfrom a selection of Mars illuminants to the CIE standard

illuminants such as D65 and A were generated, and anexample of the application of these transforms has beenshown. Upon collection of the proposed MPF, PHX, andMSL SPD samples, then any details omitted from this pa-per will be published in full in the future literature [1].

ACKNOWLEDGMENTS

The research leading to these results has been fundedby the UK Space Agency, Grant No. ST/G003114/1,and Grant No. ST/I002758/1, together with contribu-tions from The European Community’s Seventh Frame-work Programme (FP7/2007-2013), Grant AgreementNo. 218814 PRoVisG, and Grant Agreement No. 241523PRoViScout.

REFERENCES

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