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Computers and Electronics in Agriculture 69 (2009) 33–39

Contents lists available at ScienceDirect

Computers and Electronics in Agriculture

journa l homepage: www.e lsev ier .com/ locate /compag

nalysis of laser light propagation in kiwifruit using backscattering imaging andonte Carlo simulation

ászló Baranyai ∗, Manuela Zudeeibniz Institute for Agricultural Engineering Potsdam-Bornim, Department of Horticultural Engineering, Max-Eyth-Allee 100, 14469 Potsdam, Germany

r t i c l e i n f o

rticle history:eceived 12 March 2009eceived in revised form 2 June 2009ccepted 17 June 2009

eywords:mage processingackscatteringonte Carlo simulation

a b s t r a c t

The propagation of laser light in kiwifruit (Actinidia deliciosa) tissue was measured by backscattering imag-ing and modelled with the Monte Carlo (MC) method. The parameters of the vision system (8 bit/channelcamera, 27.42 �m/pixel resolution) and the laser module (785 nm, 45 mW, Ø1 mm) were utilized in sim-ulation. The required number of the photons was optimized with time-resolved MC model. The injectedphoton pulse travelled further than the beam radius and the calculated intensity fell below the noiselevel of the camera within 1 ns time. This short pulse contains 2.49 × 108 photons and its applicationreduced computation load compared to the amount emitted within the integration time of 0.5–8.3 ms.The statistical effects of the optical properties of the tissue, scattering coefficient (�s) absorption coeffi-cient (�a) and anisotropy factor (g), on photon flux was evaluated within ±20% range relative to expectedmean values of �a = 0.9 cm−1 and �s = 40 cm−1. The anisotropy factor was taken into account using theHeyney–Greenstein phase function and was adjusted to g = 0.8 ± 20%. Because individual significance of

each optical property was also analysed, scattering (�s) and transport corrected reduced scattering coef-ficients (�′

s = [1 − g]�s) must be distinguished. The multi-factor ANOVA test pointed out the highestimportance (p < 0.001) of the anisotropy factor amongst scattering and absorption coefficients.

In the kiwi backscattering images, rotation of the intensity profiles was observed as a result of changinganisotropy. The measured and calculated profiles were compared to estimate the anisotropy factor ofkiwifruits. Significant difference (p < 0.01) was found between anisotropy of premium quality and overripe

fruit

pieces with respect to the

. Introduction

Kiwifruit (Actinidiaceae) is native in eastern Asia where cancers treated with these fruits and the extract of the fruit (Motohashit al., 2002) in folklore medicine. Kiwifruit consumption was alsoeported to help maintain sound genetic information in humanody (Rush et al., 2006). These traits may increase the value ofiwifruits in human nutrition and food technology. During theipening process of kiwifruit, the firmness value, fruit density,ry matter, soluble solids content (SSC), brightness of the sur-

ace, and flesh colour are changing. Dry matter and SSC werestimated successfully with non-destructive VIS–NIR spectroscopyn the wavelength range of 300–1100 nm (McGlone and Kawano,998; Schaare and Fraser, 2000; Clark et al., 2004; McGlone et al.,

007). Density measured on unripe kiwifruit was reported to cor-elate with dry matter and SSC (Jordan et al., 2000; McGlone et al.,002). The decrease in firmness was monitored by 65 kPa air-puffnd the observed deformation between 0.1 and 1 mm described

∗ Corresponding author.E-mail address: laszlo.baranyai@uni-corvinus.hu (L. Baranyai).

168-1699/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.compag.2009.06.011

texture properties.© 2009 Elsevier B.V. All rights reserved.

firmness with reasonably high correlation (McGlone and Jordan,2000). Additionally, storage conditions, such as O2 and CO2 concen-tration, affect firmness development but this difference disappearsafter longer storage (Irving, 1992). The appearance of the fruit alsochanges significantly, according to the skin brightness and fleshcolour measured by lightness (L*) and red-green axis (a*) coor-dinates of CIE L*a*b* colour space, respectively (Vilas-Boas et al.,2007; Mao et al., 2007). Particularly, the latter corresponds to theabsorption of the green appearing chlorophyll content.

Analysis of digital images of kiwifruit slices can be used to detectvisual alteration (Roudot, 1989) but magnetic resonance imagingon intact fruits failed to quantify changes in water content (Burdonand Clark, 2001). Recent studies on low power laser light inter-ference, also known as biospeckle, at 632 nm (using Helium–Neonlaser) reported success in detection of biological activity of weeds(Braga et al., 2007) and bruising of fruits (Federico and Kaufmann,2006; Passoni et al., 2005; Pajuelo et al., 2003). The laser Doppler

technique was applied successfully in detection of changes in fruittexture (Muramatsu et al., 1999).

Particularly, the description of light penetration, measured withmachine vision systems appears feasible for describing changes infruit tissue due to the reactivity of backscattering signal. This tech-

34 L. Baranyai, M. Zude / Computers and Electr

Nomenclature

Symbols and abbreviations�a absorption coefficient (cm−1)�s scattering coefficient (cm−1)�′

s reduced scattering coefficient �′s = [1 − g]�s

(cm−1)g anisotropy factor (0–1)n refractive indexr radiusw weight of single photon� uniformly distributed random number ∈(0;1)s length of free flight (cm)� polar scattering angleϕ azimuthal scattering angleANOVA analysis of variancesF statistical F-value from analysis of variancesr2 determination coefficientMC Monte Carlo

Unitsps pico-secondns nano-secondms milli-secondmin minutenm nano-meter�m micro-metermm milli-metercm centi-metermW milli-wattGHz giga-hertzdB deci-belkPa kilo-pascalpixel elementary unit of digital image

na2aenQapfmoUBa

pateisacice

bit binary digital information (0 or 1)bin quantified segment of radius

ique helped classify maturity stages of tomato (Tu et al., 2000)nd predict SSC and firmness of apples (Cho and Han, 1999; Lu,004; Peng and Lu, 2007; Qing et al., 2007a, 2008). The selection ofppropriate wavelengths is essential for such an application (Qingt al., 2007b). Multispectral method has been developed for firm-ess and SSC prediction in apple (Lu, 2004; Peng and Lu, 2007;ing et al., 2007a). The hyperspectral imaging technique has thedvantage of presenting both spatial and spectral intensity profiles,roviding additional information for wavelength optimization and

eature extraction (Noh and Lu, 2007; Peng and Lu, 2008). Com-ercial applications are already available for sorting and grading

n the basis of visible colour, NIR spectra (MAF Industries Inc.,SA; GREEFA, The Netherlands) or laser scattering (BEST, Belgium).esides high capacity lines, portable devices were developed tossess quality more flexible (CP, Germany; Unitec S.p.A., Italy).

Several computational techniques exist to calculate photonropagation through a given media. Boundary element (Fedele etl., 2005) and finite element (Aydin et al., 2005) methods were usedo simulate photon penetration in biological tissue. Stochastic mod-ls apply the Monte Carlo method to ray-trace individual photonsn chemicals and complex materials like fruit as well as human tis-ue (Wang et al., 1997; Zołek et al., 2006; Fernandez, 2007; Qin

nd Lu, 2007; Scot et al., 2007; Guo et al., 2008). More sophisti-ated 3D models apply voxelization and investigate the effect ofnternal structures (Binzoni et al., 2008). The structural anisotropyaused by aligned microstructures in biological materials and itsffect on measured intensity was also studied. Significant elliptical

onics in Agriculture 69 (2009) 33–39

distortion of backscattering signal was observed as a result of par-allel cylindrical fibres in biological tissue (Kienle et al., 2003, 2004;Sviridov et al., 2005). Isotropic models are not valid for such case.Bias parameter was derived from transition probabilities (Dagduget al., 2003) and applied to help NIRS analysis of human muscle(Binzoni et al., 2006). A diffusion tensor can describe directionaleffect (Heino et al., 2003) or the bias parameter might generalizerandom walk model (Hebden et al., 2004).

The objective of the presented work was to compare backscat-tering imaging with stochastic simulation in order to analyse therelationship between experimental data and optical parameters offruit tissue. The comparison might result in a method or at least abetter insight into the apparent optical properties of the kiwifruitthat can help the development of a non-destructive assessmentmethod.

2. Materials and methods

2.1. Kiwifruit

A panel consisting of five persons, with daily experiences onmanually sorting kiwifruits of premium quality, assessed the fruitActinidia deliciosa cultivar ‘Hayward’ according to the commercialclasses: too soft, premium, too hard. These classes represent thefruit ripeness grades for overripe, optimal for consumption, andunripe fruits. Each grade consisted of 20 pieces. Additionally, afourth class of unsorted pieces was provided (n = 38) containingrandomly selected fruits from the incoming stream, directly fromthe growers.

2.2. Backscattering imaging

The machine vision system of a 3CCD camera (KY-F50, JVC Ltd.,Japan), zoom lenses, Optimas grabber board (Bioscan Inc., USA)was used to capture images of 768 × 572 pixel size. The resolutionwas adjusted to 27.42 �m/pixel. Laser diode emitting at 785 nm(LPM785-45C, Newport Corp., USA) with 45 mW maximal powerand Ø1 mm beam diameter was applied. Image acquisition tookplace in a dark-room in order to maximize the signal to noise ratioclose to the optimal 24 dB (8 bit resolution per channel). The geom-etry of 0/15◦ was adjusted to get distortion free images and minimaldirect reflection back to the camera. The amount of this direct reflec-tion was estimated between 2.50 and 3.06% for the fruit tissue ofn = 1.4, depending on the direction of polarization. Fresnel equa-tions (Eq. (1)) define the reflection coefficients for s-polarized (Rs)and p-polarized (Rp) lights of given incident (�i) and transmission(�t) angles.

Rs =[

sin(�t − �i)sin(�t + �i)

]2

Rp =[

tan(�t − �i)tan(�t + �i)

]2

(1)

Image processing software was developed for the present studyin C++ and a graphical user interface was provided to select imagefiles for batch processing and save results in plain text file. The illu-minated area of the surface was segmented with cluster analysis.The incident point was located by the brightness of pixels and thesmallest covering rectangle was calculated to define the region ofinterest (ROI). In order to correct possible segmentation error dueto the intensity gradient along the perimeter of the backscatteringarea, the ROI size was increased to double relative to the incidentpoint. This optimized ROI was scanned and luminosity (Eq. (2))

of pixels was accumulated together with their distance measuredfrom the incident point. The average values for concentric rings of1 pixel width produced the profiles of intensity gradient (Fig. 1a).

L = 0.30R + 0.59G + 0.11B (2)

L. Baranyai, M. Zude / Computers and Electr

F(

srssoUdbLhs

2

fltadfsfa

s

cd

ig. 1. Measured apparent radial intensity profile (a) and its logarithmic transformb) for kiwifruit at 785 nm wavelength.

The logarithmic transform (Fig. 1b) consists of two differentegments. The initial plateau appears mainly due to speculareflectance of the radius of the incident laser beam (0.5 mm). Thisegment can be omitted in the analysis of the profile because theignal can be unstable and inconsistent (Lu, 2004). The second partf the logarithmic profile shows a linearly decreasing segment.nstable behavior can be also observed where luminosity valuesecrease to the noise level (L ≤ 1.0). Backscattering profiles mighte described with fitted Gompertz functions (Peng and Lu, 2007),orentzian distribution functions (Peng and Lu, 2008) or using theistogram of the segmented area (Qing et al., 2007a, 2008). In thistudy, extracted profiles and simulation results were compared.

.3. Monte Carlo simulation

This computational method is stochastic since direction and freeight length of photon movements are randomly selected. Interac-ion events experienced by a photon regarding elastic scattering andbsorption were simulated in chronological order, without the pro-uction of secondary particles or inelastic scattering. The length of

ree flight (s) between two interactions was calculated as a straightegment of the full path length (Eq. (3)), where � ∈ (0;1) is a uni-ormly distributed random number, �a and �s are the absorptionnd scattering coefficients, respectively.

−ln(�)

=�a + �s

(3)

If photon crosses the boundary between layers of different opti-al properties, the proportion of transmission and reflection isefined by Fresnel’s equations (Eq. (1)) and the refraction by Snell’s

onics in Agriculture 69 (2009) 33–39 35

law. Additionally, directional correction was necessary on exitingphotons since a CCD sensor was placed above the samples with alimited viewing angle. The refractive index of n = 1.4 was assumed.This is a commonly used value for simulation of light propagationin fruit tissue, however, Qin and Lu (2007) applied the value of1.35 in case of ‘Golden Delicious’ apples. The assumed refractiveindex of kiwifruit tissue resulted in a critical angle of 45.58◦. Thereflection coefficient within this 0–45.58◦ is usually estimated withthe combination of the s-polarized (perpendicular to refraction)and p-polarized (parallel with refraction) directions (Tickner andRoach, 2007). The laser light has directional polarization and it wascalculated as concurred with the plane of refraction.

The launch position (r) of the photons was computed accordingto the solved probability function (Eq. (4)) for given beam radius (b).Because the integral of the function results 1.0 for the range of [0;b],the selected position was proportional to the square root of a uni-formly distributed random number � ∈ [0;1] (Jacques, 1998). Thisapproach simulated a circular flat beam and resulted in a varyinglaunch position (m0) around the incident point.

� =∫ r

0

p(r) dr =∫ r

0

2�r

�b2dr = r2

b2, r = b

√� (4)

The initial weight in the stochastic simulation, when photonenters the tissue, was set to w0 = 1.0 and decreased at each inter-action by the albedo (Eq. (5)) taking the effect of absorption intoaccount.

wn+1 = wn�s

�a + �s(5)

The pathway was followed until the photon exited the mediaor its weight decreased below a limiting value of 10−20 (Zołeket al., 2006). Photons were launched with the direction vector ofd0 = (�x ∈ (−1;1), �y ∈ (−1;1), �z ∈ (0;1)) in order to force them tomove into the tissue. The iterations not only decreased the weight,but also moved photons forward by this direction vector (Eq. (6)).

mn+1 = mn + sn × dn (6)

The photon trajectory was generated with rotation of dn unitvector by polar (�) and azimuthal (ϕ) scattering angles. The appli-cation of this double rotation on d(x, y, z) is presented by Eq. (7).

x′ = x cos � + sin �√1 − z2

(xz cos ϕ − y sin ϕ)

y′ = y cos � + sin �√1 − z2

(yz cos ϕ + x sin ϕ)

z′ = z cos � −√

1 − z2 sin � cos ϕ

(7)

These equations are indeterminate for directions nearly parallelor antiparallel to the z-axis (z ∼= ±1.0). Simplified calculation wasperformed for such cases (Eq. (8)).

x′ = ±sin � cos ϕ, y′ = ±sin � sin ϕ, z′ = ±cos � (8)

The effect of anisotropy (g) was taken into account usingthe Heyney–Greenstein phase function (Eq. (9)), opposed to theapproach of the reduced scattering coefficient. The same func-tion approximately mimics the scattering function experimentallyobserved in biological tissues (Jacques, 1998).

p(cos �) = 12

1 − g2

(1 + g2 − 2g cos �)3/2(9)

The kiwifruit tissue was considered as homogeneous media free

from directional microstructures in the volume of light penetration.In this case, the above phase function described general scattererspresent in fruit flesh.

Two different types of simulation were run. The time-resolvedmodel for infinite homogeneous media without boundaries was

3 Electronics in Agriculture 69 (2009) 33–39

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3

3

ifi�Ts8daisb

3

i(tas(r�atvactitdseCitmtwcppa

factor in comparison to scattering and following absorption coef-ficients (Table 1). The individual contribution of g, �s and �a tothe simulated flux and the gradient were significant (p < 0.001).Anisotropy was also found to be a significant factor via the interac-tions with �s and �a. The statistical effect on simulated flux means

Table 1Statistical effects of tissue parameters (�a, �s, g) on simulated (MC) photon migra-tion evaluated by multi-factor ANOVA test.

Factor Effect on flux Effect on gradient

MS F P(>F)* MS F P(>F)*

g 29.30 561.4012 <2.2 × 10−16 75.19 1440.6889 <2.2 × 10−16

�a 0.95 18.1881 2.015 × 10−5 2.01 38.4427 5.803 × 10−10

�s 0.41 7.9100 0.0049 1.26 24.1479 9.026 × 10−7

6 L. Baranyai, M. Zude / Computers and

sed to optimize the timeframe of simulation and the minimalumber of required photons. The number of photons is a key param-ter of the simulation, and it can be estimated using the Planck’saw and the attributes of the laser module. The 1 s pulse of the laserf 785 nm wavelength and 45 mW power in the tissue of n = 1.4ontains 2.49 × 1017 photons, which means very high CPU (Cen-ral Processing Unit) load and long computation time. The second

odel for semi-infinite homogeneous media collected informationn photons that diffusely reflected from the surface (backscattered).uring the post-processing of the results from both models, data

ets were rescaled to the sensitivity range of the camera. The sim-lation was based on an ANSI C code system (Wang et al., 1997;

acques, 1998). Due to the changes in post-processing, validationith diffusion theory model according to Qin and Lu (2006) was

erformed.

. Results and discussion

.1. Validation of simulation results

Although the post-processing was slightly changed to collectntensity information measured by the camera, backscattering pro-le should fit well to theoretical curve. The expected mean values ofa = 0.9 cm−1, �s = 40 cm−1 and g = 0.8 were used for this purpose.he logarithmic values of calculated (MC) profile fit to the diffu-ion theory model with r2 = 0.996 and root mean square error of.28 × 10−2 cm−2. The statistical software of R version 2.8.1 (R Foun-ation for Statistical Computing, Austria) was used. Both theoreticalnd modelled profiles were on the same scale, therefore normal-zation was not required before comparison. The validation resultsuggest that the Monte Carlo method is able to provide reliableackscattering profiles to investigate measured data on kiwifruit.

.2. Time-resolved simulation

Photon flux for spherical volumes around the incident point innfinite homogeneous media has been calculated at five time points10 ps, 50 ps, 100 ps, 500 ps, 1 ns). A very short pulse (40.16 ps) con-aining 107 photons was applied. The refractive index of n = 1.4 wasssumed for kiwifruit tissue. The values of absorption and reducedcattering coefficients of kiwifruit have been measured formerlyZude, 2006) as �a = 0.9 cm−1 and �′

s = 4.0 cm−1. According to theelationship of �s > �′

s, the scattering coefficient was estimated ass = 40 cm−1. This is in agreement with the observed reduced value

ssuming that the anisotropy factor was g = 0.9. The uncertainty ofhese optical properties of kiwifruit appears in the literature andalues of �′

s = 10–15 cm−1 (Torricelli, 2009) or �′s = 7–8 cm−1 (Qin

nd Lu, 2008) may also occur for similar non-reduced scatteringoefficient with g ≈ 0.7 and g ≈ 0.8, respectively. The beam diame-er was adjusted to a relatively small value of 0.1 mm (3.65 pixel)n order to focus on the photons travelling in the central part ofhe beam. The appropriate time point for further simulations wasefined by two criteria. First, the central photons should travelignificantly further than the beam radius (0.5 mm). Second, thestimated intensity should fall below the noise level of the 3 × 8 bitCD camera, so that the steady state could be simulated. If maximal

ntensity is observed at the incident point, the second criterion giveshe limiting value of 20. Fig. 2 shows the estimations for isotropic

edia (g = 0) at the selected time points. Injected photons exceededhe beam radius already after 50 ps but the estimated intensity

as above the limiting value. The time point of 1 ns fulfilled both

riteria. As a result of the time-resolved simulation, further com-utations were limited to a 1 ns laser pulse containing 2.49 × 108

hotons. In the following runs, this interval saved computation timend CPU load compared to a rough estimation based on the elec-

Fig. 2. Estimated (MC) intensities in homogeneous infinite media 10 ps (©), 50 ps(), 100 ps (+), 500 ps (×) and 1 ns (♦) after injection of 107 photons (�a = 0.9 cm−1,�s = 40 cm−1, g = 0).

tronic shutter speed of the camera (in the range of 0.5–8.3 ms). Thecomputational time required to follow 107 photons was tested ondifferent hardware. Desktop computer with AMD AthlonTM X2 dualcore 2.11 GHz processor required approximately 26 min, worksta-tion with Intel XeonTM 2.66 GHz processor required approximately20 min to finish calculations.

3.3. Backscattering simulation

3.3.1. Sensitivity of the modelThe apparent intensity on the surface of kiwifruits has been

calculated as planar response on the boundary of a semi-infinitehomogeneous media. The profiles for the area of 1.5 cm radius with0.03 mm/bin resolution, similar to the vision system, were com-puted. The optical properties of the tissue were altered within±20% range relative to the expected mean values according to acomplete block design. The absorption and scattering coefficientswere changed in the ranges of �a = 0.72–1.08 and �s = 32–48. Theanisotropy factor was adjusted to g = 0.8 ± 20% values. Analysis ofthe interaction of intensity profiles and optical parameters withmulti-factor ANOVA test showed the highest F-values for anisotropy

�s × g 0.11 2.1532 0.1423 0.39 7.4898 0.0062�a × g 0.35 6.6665 0.0098 0.88 16.8985 3.967 × 10−5

�a × �s 0.004 0.0736 0.7862 0.01 0.2530 0.6149�a × �s × g <0.001 0.0116 0.9142 0.003 0.0548 0.8149

* Significance level.

L. Baranyai, M. Zude / Computers and Electronics in Agriculture 69 (2009) 33–39 37

Table 2Estimated amount of backscattered photons (%) according to the simulation (MC)results for changing �a, �s (g = 0).

�a (cm−1) �s (cm−1)

32 40 48

0.72 91.57 92.44 93.080.90 90.58 91.57 92.301.08 89.72 90.77 91.57

Table 3Estimated average photon path length (cm) according to the simulation (MC) resultsfor changing �a, �s (g = 0).

�a (cm−1) �s (cm−1)

32 40 48

001

twtil�twadpm

3

ho�1fi

Fv

.72 5.08 4.58 4.21

.90 4.51 4.06 3.74

.08 4.07 3.69 3.39

hat the apparent intensity at a fixed position is mainly changingith the anisotropy factor. The statistical effect on gradient belongs

o the profile of intensity. According to the low F-values for thenteractions of �a × �s × g and �a × �s, their statistical effect is neg-igible. In case of isotropic tissue (g = 0), the contribution of �s and

a coefficients can be investigated. The total apparent intensity onhe surface expressed by the amount of apparent photons decreasedith decreasing scattering and increasing absorption (Table 2). The

verage path length of the trajectories inside the fruit shows slightlyifferent tendency. Photons were simulated to travel the maximalath length with the combination of minimal scattering and mini-al absorption events (Table 3).

.3.2. Anisotropy estimation on kiwifruitThe apparent intensity on the surface of the semi-infinite

omogeneous media has been calculated for different valuesf anisotropy in the range of 0–0.99. The formerly measured

a = 0.9 cm−1 and estimated �s = 40 cm−1 values were applied withns laser pulse (2.49 × 108 photons) and 10−20 limiting value

or weight. In the calculated profiles, the intensity of the peaksncreases with decreasing value of anisotropy. Additionally, this

ig. 3. Rotation of the estimated (MC) backscattering profiles according to changingalues of anisotropy factor (g = 0–0.9).

Fig. 4. Regression models for slope of the logarithmic profile as function ofanisotropy factor (�a = 0.9 cm−1, �s = 40 cm−1).

effect also appears as rotation of the logarithmic profiles (Fig. 3).Linear segments between 0.3 and 1.0 cm were selected from thelogarithmic curves and used to fit a line from which the slope wasrecorded. The final parts, where estimated intensity fell below thenoise level of the camera, were always omitted. The simulationresulted in higher statistical noise within those sections, similarto the experimental data (Fig. 1b). The slope has the upper limit of0 since this value would result in a profile of a horizontal line. Onthe other hand, it should never predict values out of the range of ±1.Three types of mathematical functions were fitted to find the rela-tionship between slope and anisotropy (Fig. 4). All of them obtainedhigh (r2 > 0.984) determination coefficients (Table 4). The best fit-ting curve of the trigonometric function was finally selected dueto the minimal autocorrelation measured by the Durbin–Watsontest. The result of non-linear curve fitting for trigonometric functionis presented in Table 5. The standard errors of estimation and thestatistical test of their significance by t-test confirmed the accept-

able accuracy of the estimated coefficients. The inverse of this fittedfunction was applied to estimate the anisotropy for each kiwifruitmeasured. The inverse function resulted in 0.637% of root meansquared error of prediction on modelled profiles within the rangeof g = 0.5–0.9. Fig. 5 shows the estimated values of anisotropy factor

Table 4Evaluation of regression models for slope of logarithmic profile as function ofanisotropy factor.

Type Functiona r2 Durbin–Watson

Polynomial y = a + b·x + c·x2 0.9845 0.4975Exponential y = a + b·x·e(x/c) 0.9944 0.5259Trigonometric y = a + b · tan(x�/c) 0.9996 2.1255

a a, b and c are coefficients; y and x represent slope and anisotropy factor, respec-tively.

Table 5Estimated coefficients for trigonometric function y = a + b · tan(x�/c).

Coefficient Estimate Standard error t-value P(>|t|)*

a −5.90503 0.01949 −303.01 <2 × 1016

b 1.86061 0.04076 45.64 6.83 × 1014

c 2.57921 0.01611 160.12 <2 × 1016

* Significance level.

38 L. Baranyai, M. Zude / Computers and Electr

Fig. 5. Estimated values of anisotropy factor for commercial grades of kiwifruit(hard = unripe, soft = overripe).

Table 6Comparison of commercial grades of kiwifruit with two-sampleKolmogorov–Smirnov test on estimated anisotropy factor of the tissue.

Hard Soft

fmotttswgTtkCoAmlsdpa

4

ottttotn

Premium 0.25 0.55**

Soft 0.40

** p < 0.01.

or the three commercial grades of hard (unripe), premium (opti-al for consumption) and soft (overripe). Because the distribution

f premium and soft grades was different from normal (Gaussian),wo-sample Kolmogorov–Smirnov test (Conover, 1999) was usedo compare them (Table 6). Both the boxplot and the statisticalests show significant difference between grades of premium andoft. Nevertheless, only 75% of kiwifruit pieces of these two classesere successfully identified by linear discriminant analysis. The

rade hard overlaps the other two and its discrimination failed.his might occur due to the different changes of physical proper-ies and compounds during development, ripening and storage ofiwifruit (Irving, 1992; McGlone and Kawano, 1998; Burdon andlark, 2001; Clark et al., 2004; Tavarini et al., 2008). The analysisf one image took 60–70 ms on a personal computer with AMDthlonTM X2 dual core 2.11 GHz processor. This processing speedight enable the analysis of 14 pieces of fruit per second on one

ane, what meets the current options of the sorting lines. However,ingle optical parameter like the presented anisotropy factor itselfoes not provide the required accuracy for quality assessment inractice. This anisotropy factor might extend the range of attributesvailable in optical analysis of fresh food.

. Conclusions

Monte Carlo simulation was performed to follow each photonf the incident laser beam inside the kiwifruit tissue. The distribu-ion of the photon package helped to optimize further calculationso the timeframe of 1 ns and limit the required number of photonso 2.49 × 108. Within this 1 ns time, photon propagation satisfied

wo criteria. The photons travelled longer than the beam radiusf 0.5 mm and the apparent intensity fell below the noise level ofhe camera. This optimization had practical importance, since theumber of photons, and therefore computational load, was signifi-

onics in Agriculture 69 (2009) 33–39

cantly decreased compared to that of the typical camera shutter of0.5–8.3 ms. The reduced demand allowed effective use of personalcomputers in simulations.

The statistical analysis of the profiles, computed on the surface ofthe semi-infinite media, pointed out the significance of anisotropy(p < 0.001). This parameter contributed the most to estimated pho-ton flux and the apparent intensity profiles. Rotation of the profilesand their logarithmic transform was observed with changing valueof anisotropy factor. Trigonometric function was found to describewell the relationship between slope of the selected segments ofmodelled profiles and the anisotropy factor. Experimental dataacquired by the vision system were used to estimate this opticalproperty of kiwifruit tissue. Significant difference (p < 0.01) wasfound between estimated values of anisotropy factor of commercialgrades of premium quality and overripe pieces. However, commer-cial grade of unripe pieces overlapped others and statistical testswere unable to distinguish this class due to the high variance. Theobserved effect of rotation and successful discrimination of twogrades confirm the accessibility of the information from backscat-tering images on the anisotropy factor. Such approach might beused as well to describe optical changes of fruit tissue during devel-opment and ripening.

References

Aydin, E.D., Katsimichas, S., de Oliveira, C.R.E., 2005. Time-dependent diffusion andtransport calculations using a finite-element-spherical harmonics method. Jour-nal of Quantitative Spectroscopy & Radiative Transfer 95, 349–363.

Binzoni, T., Courvoisier, C., Giust, R., Tribillon, G., Gharbi, T., Hebden, J.C., Leung,T.S., Roux, J., Delpy, D.T., 2006. Anisotropic photon migration in human skeletalmuscle. Physics in Medicine and Biology 51, N79–N90.

Binzoni, T., Leung, T.S., Giust, R., Rüfenacht, D., Gandjbakhche, A.H., 2008. Light trans-port in tissue by 3D Monte Carlo: influence of boundary voxelization. ComputerMethods and Programs in Biomedicine 89, 14–23.

Braga Jr., R.A., Horgan, G.W., Enes, A.M., Miron, D., Rabelo, G.F., Barreto Filho, J.B., 2007.Biological feature isolation by wavelets in biospeckle laser images. Computersand Electronics in Agriculture 58 (2), 123–132.

Burdon, J., Clark, C., 2001. Effect of postharvest water loss on ‘Hayward’ kiwifruitwater status. Postharvest Biology and Technology 22, 215–225.

Cho, Y.-J., Han, Y.J., 1999. Nondestructive characterization of apple firmness by quan-titation of laser scatter. Journal of Texture Studies 30, 625–638.

Clark, C.J., McGlone, V.A., De Silva, H.N., Manning, M.A., Burdon, J., Mowat, A.D., 2004.Prediction of storage disorders of kiwifruit (Actinidia chinensis) based on visible-NIR spectral characteristics at harvest. Postharvest Biology and Technology 32,147–158.

Conover, W.J., 1999. Practical Nonparametric Statistics, 3. John Wiley & Sons Inc.,New York.

Dagdug, L., Weiss, G.H., Gandjbakhche, A.H., 2003. Effects of anisotropic optical prop-erties on photon migration in structured tissues. Physics in Medicine and Biology48, 1361–1370.

Federico, A., Kaufmann, G.H., 2006. Evaluation of dynamic speckle activity using theempirical mode decomposition method. Optics Communications 267, 287–294.

Fedele, F., Eppstein, M.J., Laible, J.P., Godavarty, A., Sevick-Muraca, E.M., 2005.Fluorescence photon migration by the boundary element method. Journal ofComputational Physics 210, 109–132.

Fernandez, J.E., 2007. Multiple scattering of photons using the Boltzmann transportequation. Nuclear Instruments and Methods in Physics Research B 263, 7–21.

Guo, X., Wood, M.F.G., Vitkin, A., 2008. A Monte Carlo study of penetration depth andsampling volume of polarized light in turbid media. Optics Communications 281,380–387.

Hebden, J.C., Guerrero, J.J.G., Chernomordik, V., Gandjbakhche, A.H., 2004. Experi-mental evaluation of an anisotropic scattering model of a slab geometry. OpticsLetters 29 (21), 2518–2520.

Heino, J., Arridge, S., Sikora, J., Somersalo, E., 2003. Anisotropic effects in highlyscattering media. Physical Review E 68, 031908-1–031908-8.

Irving, D.E., 1992. High concentrations of carbon dioxide influence kiwifruit ripening.Postharvest Biology and Technology 2, 109–115.

Jacques, S.L., 1998. Light distributions from point, line and plane sources for photo-chemical reactions and fluorescence in turbid biological tissues. Photochemistryand Photobiology 67 (1), 23–32.

Jordan, R.B., Walton, E.F., Klages, K.U., Seelye, R.J., 2000. Postharvest fruit density asan indicator of dry matter and ripened soluble solids of kiwifruit. Postharvest

Biology and Technology 20, 163–173.

Kienle, A., Forster, F.K., Diebolder, R., Hibst, R., 2003. Light propagation in dentin:influence of microstructure on anisotropy. Physics in Medicine and Biology 48,N7–N14.

Kienle, A., Forster, F.K., Hibst, R., 2004. Anisotropy of light propagation in biologicaltissue. Optics Letters 29 (22), 2617–2619.

Electr

L

M

M

M

M

M

M

M

N

P

P

P

P

Q

Q

Q

Q

and Programs in Biomedicine 54, 141–150.Zołek, N.S., Liebert, A., Maniewski, R., 2006. Optimization of the Monte Carlo code

L. Baranyai, M. Zude / Computers and

u, R., 2004. Multispectral imaging for predicting firmness and soluble solids contentof apple fruit. Postharvest Biology and Technology 31, 147–157.

ao, L., Wang, G., Que, F., 2007. Application of 1-methylcyclopropene prior to cuttingreduces wound responses and maintains quality in cut kiwifruit. Journal of FoodEngineering 78, 361–365.

cGlone, V.A., Kawano, S., 1998. Firmness, dry-matter and soluble-solids assess-ment of postharvest kiwifruit by NIR spectroscopy. Postharvest Biology andTechnology 13, 131–141.

cGlone, V.A., Jordan, R.B., 2000. Kiwifruit and apricot firmness measurement bythe non-contact laser air-puff method. Postharvest Biology and Technology 19,47–54.

cGlone, V.A., Jordan, R.B., Seelye, R., Martinsen, P.J., 2002. Comparing density andNIR methods for measurement of kiwifruit dry matter and soluble solids content.Postharvest Biology and Technology 26, 191–198.

cGlone, V.A., Clark, C.J., Jordan, R.B., 2007. Comparing density and VNIR methods forpredicting quality parameters of yellow-fleshed kiwifruit (Actinidia chinensis).Postharvest Biology and Technology 46 (1), 1–9.

otohashi, N., Shirataki, Y., Kawase, M., Tani, S., Sakagami, H., Satoh, K., Kurihara,T., Nakashima, H., Mucsi, I., Varga, A., Molnár, J., 2002. Cancer prevention andtherapy with kiwifruit in Chinese folklore medicine: a study of kiwifruit extracts.Journal of Ethnopharmacology 81, 357–364.

uramatsu, N., Sakurai, N., Wada, N., Yamamoto, R., Takahara, T., Ogata, T., Tanaka,K., Asakura, T., Ishikawa-Takano, Y., Nevins, D.J., 1999. Evaluation of fruit tissuetexture and internal disorders by laser Doppler detection. Postharvest Biologyand Technology 15, 83–88.

oh, H.K., Lu, R., 2007. Hyperspectral laser-induced fluorescence imaging for assess-ing apple fruit quality. Postharvest Biology and Technology 43, 193–201.

ajuelo, M., Baldwin, G., Rabal, H., Cap, N., Arizaga, R., Trivi, M., 2003. Bio-speckleassessment of bruising in fruits. Optics and Lasers in Engineering 40, 13–24.

assoni, I., Dai Pra, A., Rabal, H., Trivi, M., Arizaga, R., 2005. Dynamic speckleprocessing using wavelets based entropy. Optics Communications 246 (1–3),219–228.

eng, Y., Lu, R., 2007. Prediction of apple fruit firmness and soluble solids contentusing characteristics of multispectral scattering images. Journal of Food Engi-neering 82, 142–152.

eng, Y., Lu, R., 2008. Analysis of spatially resolved hyperspectral scattering imagesfor assessing apple fruit firmness and soluble solids content. Postharvest Biologyand Technology 48, 52–62.

in J., Lu R., 2006. Measurement of the optical properties of apples using hyperspec-tral diffuse reflectance imaging. ASABE Paper No. 063037. Portland, Oregon.

in, J., Lu, R., 2007. Monte Carlo simulation of light propagation in apples. ASABEPaper No. 073058. Minneapolis, Minnesota.

in, J., Lu, R., 2008. Measurement of the optical properties of fruits and vegetablesusing spatially resolved hyperspectral diffuse reflectance imaging technique.Postharvest Biology and Technology 49 (3), 355–365.

ing, Z., Ji, B., Zude, M., 2007a. Predicting soluble solid content and firmness inapple fruit by means of laser light backscattering image analysis. Journal of FoodEngineering 82, 58–67.

onics in Agriculture 69 (2009) 33–39 39

Qing, Z., Ji, B., Zude, M., 2007b. Wavelength selection for predicting physicochemicalproperties of apple fruit based on near-infrared spectroscopy. Journal of FoodQuality 30, 511–526.

Qing, Z., Ji, B., Zude, M., 2008. Non-destructive analyses of apple quality parametersby means of laser-induced light backscattering imaging. Postharvest Biology andTechnology 48, 215–222.

Roudot, A.C., 1989. Image analysis of kiwi fruit slices. Journal of Food Engineering 9,97–118.

Rush, E., Ferguson, L.R., Cumin, M., Thakur, V., Karunasinghe, N., Plank, L., 2006.Kiwifruit consumption reduces DNA fragility: a randomized controlled pilotstudy in volunteers. Nutrition Research 26, 197–201.

Schaare, P.N., Fraser, D.G., 2000. Comparison of reflectance, interactance and trans-mission modes of visible-near infrared spectroscopy for measuring internalproperties of kiwifruit (Actinidia chinensis). Postharvest Biology and Technology20, 175–184.

Scot, V., Fernandez, J.E., Vincze, L., Janssens, K., 2007. 3D extension of the MonteCarlo code MCSHAPE for photon–matter interactions in heterogeneous media.Nuclear Instruments and Methods in Physics Research B 263, 204–208.

Sviridov, A., Chernomordik, V., Hassan, M., Russo, A., Eidsath, A., Smith, P., Gand-jbakhche, A.H., 2005. Intensity profiles of linearly polarized light backscatteredfrom skin and tissue-like phantoms. Journal of Biomedical Optics 10 (1), 014012-1–014012-9.

Tavarini, S., Degl’Innocenti, E., Remorini, D., Massai, R., Guidi, L., 2008. Antioxidantcapacity, ascorbic acid, total phenols and carotenoids changes during harvestand after storage of Hayward kiwifruit. Food Chemistry 107, 282–288.

Tickner, J., Roach, G., 2007. PHOTON—an optical Monte Carlo code for simulatingscintillation detector responses. Nuclear Instruments and Methods in PhysicsResearch B 263, 149–155.

Torricelli, A., 2009. Determination of optical properties in turbid media: time-resolved approach. In: Zude, M. (Ed.), Optical Methods for Monitoring Fresh andProcessed Agricultural Crops. CRC Press.

Tu, K., Jancsók, P., Nicolaï, B., De Baerdemaeker, J., 2000. Use of laser-scatteringimaging to study tomato-fruit quality in relation to acoustic and compres-sion measurements. International Journal of Food Science and Technology 35,503–510.

Vilas-Boas, E.V.de B., Kader, A.A., 2007. Effect of 1-methylcyclopropene (1-MCP)on softening of fresh-cut kiwifruit, mango and persimmon slices. PostharvestBiology and Technology 43, 238–244.

Wang, L., Jacques, S.L., Zheng, L., 1997. CONV-convolution for responses to a finitediameter photon beam incident on multi-layered tissues. Computer Methods

for modeling of photon migration in tissue. Computer Methods and Programs inBiomedicine 84, 50–57.

Zude, M., 2006. Non-invasive sensing of vitamins and provitamins in horticulturalproducts. In: Laser-Optik-Berlin Congress, March 23–24, Berlin.