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Available online at www.sciencedirect.com

Postharvest Biology and Technology 48 (2008) 52–62

Analysis of spatially resolved hyperspectral scattering images for

assessing apple fruit firmness and soluble solids content?

Yankun Penga,∗,1, Renfu Lub

aChina Agricultural University, College of Engineering, 17 Qinghua East Road, Haidian, Beijing 100083, China

bUSDA Agricultural Research Service, 224 Farrall Hall, Michigan State University, East Lansing, MI 48824, USA

Received 16 February 2007; accepted 6 September 2007

Abstract

Hyperspectral scattering is a promising technique for nondestructive sensing of multiple quality attributes of apple fruit. This research evaluated

and compared different mathematical models for describing the hyperspectral scattering profiles over the spectral region between 450nm and

1000nm in order to select an optimal model for predicting fruit firmness and soluble solids content (SSC) of ‘Golden Delicious’ apples. Ten

modified Lorentzian distribution functions of various forms were proposed to fit the spectral scattering profiles at individual wavelengths, each of

which gave superior fitting to the data with the average correlation coefficient (r) being greater than 0.995. Mathematical equations were derived

to correct the spectral scattering intensity and distance by taking into account the instrument response and individual apples’ size. The 10 modified

Lorentzian distribution functions were compared for predicting fruit firmness and SSC using multi-linear regression and cross-validation methods.

The modified Lorentzian function with three parameters (representing scattering peak value, width and slope) gave good predictions of fruit

firmness with r=0.894 and the standard error of prediction (S.E.P.) of 6.14N, and of SSC with r=0.883 and S.E.P.=0.73%. Twenty-one and 23

wavelengths were needed to obtain the best predictions of fruit firmness and SSC, respectively. This new function, coupled with the scattering

profile correction methods, improved the hyperspectral scattering technique for measuring fruit quality.

© 2007 Elsevier B.V. All rights reserved.

Keywords: Fruit; Apples; Firmness; Soluble solids content; Near-infrared; Scattering; Hyperspectral imaging; Modified Lorentzian function

1. Introduction

Fresh apples need to meet certain quality grade requirements

before they are shipped to the marketplace. These requirements

include fruit outward characteristics (i.e., color, size, and shape)

and internal quality attributes (firmness, sugar, acid, etc.). Firm-

nessandsolublesolidscontent(SSC)aretwoimportantinternal

quality attributes in determining fruit maturity and harvest time,

andinassessingandgradingpost-harvestqualityofapples.Cur-

rently, destructive techniques are routinely used for measuring

fruit firmness and SSC. Destructive testing is only suitable for

inspecting a small percent of fruit from the entire lot. Because

?Mention of commercial products is solely for providing factual informa-

tion for the reader and does not constitute endorsement by the United States

Department of Agriculture.

∗Corresponding author. Tel.: +86 10 6273 6729; fax: +86 10 6273 7333.

E-mail address: ypeng@cau.edu.cn (Y. Peng).

1Formerly with the Department of Biosystems and Agricultural Engineering,

Michigan State University, East Lansing, MI 48824, USA.

of the inherent biological variability among individual fruit, the

destructive sampling method cannot assure individual fruit to

meetthehigherqualitystandardsthatarerequiredinthetoday’s

competitive global marketplace.

Several mechanical methods have been developed for non-

destructive measurement of fruit firmness for apples and other

fresh fruits, which include dynamic force/deformation, impact,

and sonic (Chen and Tjan, 1996; Galili et al., 1998; Ozer et al.,

1998; Stone et al., 1998; Sugiyama et al., 1998; Ruiz-Altisent

and Ortiz-Canavate, 2005; Zude et al., 2006). These mechanical

methods, however, still cannot provide consistent and satisfac-

tory correlation with the standard destructive Magness–Taylor

(MT) firmness measurement for firm fruits such as apples

(Shmulevich et al., 2003; Lu, 2004).

Significantadvanceshavebeenmadeinrecentyearsonnear-

infraredspectroscopy(NIRS)technologyforqualityassessment

of fresh fruit, especially flavor-related quality attributes such as

soluble solids content (Dull et al., 1989; Kawano et al., 1992;

Slaughter, 1995; Moons et al., 1997; Lammertyn et al., 1998;

Lu et al., 2000; Lu, 2001). NIRS is now being used in some fruit

0925-5214/$ – see front matter © 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.postharvbio.2007.09.019

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Y. Peng, R. Lu / Postharvest Biology and Technology 48 (2008) 52–62

53

packinghouses for grading the SSC of apples and other fruits.

WhileNIRSispotentiallyusefulforsimultaneousmeasurement

ofmultiplequalityattributes,itcannotprovidesatisfactorymea-

surement of fruit firmness (McGlone and Kawano, 1998; Lu

et al., 2000; Lu and Ariana, 2002; Peng and Lu, 2006b). This

is because NIRS primarily measures spectral absorption in the

fruit, which is related to chemical components, whereas firm-

ness is mainly associated with the structural/physical properties

of the fruit.

Light scattering is a dominant phenomenon in turbid bio-

logical materials for the visible and near-infrared region of

500–1300nm. Light scattering is influenced by fruit tissue den-

sity, cell composition, and extra- and intra-cellular structures.

Thus scattering can provide an indirect means for assessing the

texturalpropertiesoffruit.Texturalproperties,suchasfirmness,

reflect the complex structural characteristics of a food material.

Itischallengingtoaccuratelypredictfruitfirmnessbasedonthe

measurementofsecondarypropertiessuchasspectralabsorption

and scattering. However, spectral scattering at multiple wave-

lengthsoroverabroadrangeofwavelengthscanprovidealarge

amountofusefulinformationaboutthestructural/physicalchar-

acteristics of the sample, which may enable better prediction of

fruit firmness and other quality attributes. Lu (2004) proposed

a new spatially resolved technique to characterize the spectral

scattering properties of fruit at multiple wavelengths in the visi-

ble and near-infrared (NIR) region for estimating fruit firmness.

The spectral scattering properties of fruit were quantified by

capturing and analyzing the backscattered reflectance images

generatedbyafocusedlightbeamatthesurfaceofthefruit.Peng

and Lu (2005) proposed a Lorentzian distribution (LD) function

with three parameters to describe the multispectral scattering

profilesofapplefruit.AmodifiedLorentziandistribution(MLD)

function with four parameters was found to better character-

ize spectral scattering profiles, including the saturation area, of

apple fruit (Peng and Lu, 2006a,b). These studies demonstrated

that multispectral scattering technique is useful, and superior to

NIRS, for assessing fruit firmness.

Recently, hyperspectral imaging has become a powerful tool

for quality evaluation and safety inspection of agricultural and

food products (Lu and Chen, 1998; Martinsen and Schaare,

1998; Lawrence et al., 2003; Lu, 2003a; Peirs et al., 2003).

Hyperspectral imaging provides a large amount of informa-

tion on the spatial and spectral characteristics of a sample.

Lu (2003b) applied hyperspectral imaging technique to acquire

spatially resolved reflectance images from apple fruit over the

wavelengths 500–1000nm with the use of a focused broadband

light.Spectralscatteringfeatureswereused,inconjunctionwith

an artificial neural network, to predict fruit firmness and SSC.

Good predictions of apple fruit firmness and SSC were obtained

with the correlation coefficient of 0.87 and 0.88 for ‘Golden

Delicious’ (Malus domestica Borkh) apples, respectively. In

another study on using hyperspectral imaging to measure peach

firmness, Lu and Peng (2006) utilized a simple two-parameter

Lorentzian function to describe the spectral scattering profiles

of peach fruit over the wavelengths of 600–1000nm for predic-

tionoffruitfirmness.Sincedifferentmodelsortheirvariantscan

greatlyinfluencefirmnesspredictionresults(PengandLu,2005,

2006a,b),itisthereforeimportanttoexamineandcomparethese

models and/or their variants in order to select an optimal model

with appropriate parameters for predicting fruit firmness and/or

SSC. In previous hyperspectral scattering imaging studies, the

surface of the fruit was considered to be a plane or a sphere of

thesamesizeincalculatingscatteringprofiles.Sincethesurface

curvature of fruit influences the measurement of light scattering

profiles, individual fruit’s size should be considered in order to

achieve better predictions. Moreover, it is also necessary to take

intoconsiderationtheinstrumenteffectinquantifyingscattering

profiles in apples.

ThispaperreportsonapplefruitfirmnessandSSCprediction

results obtained by using different mathematical models (i.e.,

modified Lorentzian distribution functions) to analyze spatially

resolved hyperspectral scattering profiles. Specific objectives of

this research were to

• incorporate individual fruit size and instrumental setup in

the calculations of scattering intensity and distance for the

hyperspectral scattering images of apple fruit;

• compare modified Lorentzian functions and their variants for

describingthescatteringprofilesofhyperspectralimages,and

predicting apple fruit firmness and SSC;

• develop and validate prediction models relating Lorentzian

parameter spectra of hyperspectral scattering profiles to the

fruit firmness and SSC of ‘Golden Delicious’ apples.

2. Materials and methods

2.1. Apple samples

Sixhundredandfifty‘GoldenDelicious’applesampleswere

used in the experiment. Half of the apples were harvested from

an orchard at Michigan State University (MSU) Horticultural

Teaching and Research Center in Holt, Michigan at four dif-

ferent dates in 2 weeks during the harvest season in 2005. The

otherhalfcamefromacommercialorchardinMichiganwithan

unknown harvest date. Except for 100 samples that were stored

in refrigerated air at 0◦C, the rest of 550 apples were stored

in controlled atmosphere environment (2% O2and 3% CO2at

0◦C) for about 5 months prior to the experiment. The apple

samples were kept at room temperature (21◦C) for at least 15h

beforetheexperimentwasstarted.Experimentswereperformed

onapples,whichwererandomlyselectedfromthestoragewith-

out considering the harvest date and orchard, for 5 days over a

2-week period.

2.2. Hyperspectral imaging system

A laboratory hyperspectral imaging system (Fig. 1) was used

toacquirescatteringimagesfromapplefruit.Thesystemmainly

consisted of a high performance back-illuminated CCD camera

(Model C4880-21, Hamamatsu Photonics, Hamamatsu Corp.,

Japan) and its control unit, an imaging spectrograph (ImSpector

V9, Spectral Imaging Ltd., Oulu, Finland) with a spectral range

between 450nm and 1000nm, a specially assembled light unit

with a quartz tungsten halogen lamp as the light source (Oriel

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Y. Peng, R. Lu / Postharvest Biology and Technology 48 (2008) 52–62

Fig. 1. Schematic of the hyperspectral imaging system for acquiring spectral

scattering images from apple fruit.

Instruments, Stratford, CT, USA), and the sample holder with a

circularopeningof30mmdiameter.Thelightsourceusedinthis

study was a circular beam of 1.5mm with the divergence angle

less than 15◦. As the beam hit the fruit, it illuminated a portion

of the fruit surrounding the incident point as a result of light

backscattering in the fruit tissue. This generated a backscattered

reflectance image at the surface of the fruit. The hyperspectral

imaging system line scanned the fruit 1.6mm off the incident

centersothattheCCDdetectorpixelswouldnotbesaturatedby

high intensity signals in the beam center (Fig. 2a). The imaging

spectrograph dispersed the light from the scanned line into dif-

ferent wavelengths using a prism-grating-prism configuration,

while preserving its original spatial information. The dispersed

lightsignalswerethenprojectedontotheCCDdetector,creating

a special two-dimensional image: one axis represents the spatial

dimension and the other represents the spectral. The hyperspec-

tral imaging system was calibrated both spectrally and spatially

by following the procedures described in Lu and Chen (1998).

2.3. Experimental procedure

The diameter of each apple fruit was measured around the

fruitequatorbyadigitalcaliperintwoperpendiculardirections,

and the averaged fruit diameter was used later for data process-

ing.Theaveragediameterforthe650applefruitrangedbetween

67.50mm and 82.78mm.

After measurement of its size, each fruit was placed into the

sample holder for collection of scattering images. Four images

were acquired at an exposure time of 70ms, and these images

were then averaged. Only average images were saved for fur-

theranalysis.Toimprovethesignal-to-noiseratio,2×2binning

operations were performed during the image acquisition. This

resultedinthehyperspectralscatteringimagesof256×256pix-

els at a spectral resolution of 3.28nm and a spatial resolution

of 0.21mm. In addition, scattering images were also acquired

fromawhiteTeflondiskforevery10apples.Theseimageswere

usedasreferenceimagesforcorrectingthelightsourcevariation

effect.

After the imaging, the firmness and SSC of each fruit

was measured using the standard MT firmness tester (Texture

Analyzer Model TA.XT2i, Stable Micro Systems, Goldalm-

ing, Surrey, UK) and a digital refractometer (Model PR-101,

Atago Co., Tokyo, Japan). Firmness measurement was per-

formed on the same imaging area around the equator of each

Fig. 2. Hyperspectral scattering image of an apple: (a) scanning line and scattering area; (b) raw scattering image; (c) spectral profiles from three different spatial

locations; (d) spatial scattering profiles at three wavelengths.

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Y. Peng, R. Lu / Postharvest Biology and Technology 48 (2008) 52–62

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apple by penetrating an 11mm diameter MT probe into the

peeled fruit 9.0mm at a loading speed of 2mm/s. Maximum

force recorded from the force/displacement curve was used as a

measure of MT firmness. The statistics of all test apple samples

are: mean=61.26N for MT firmness and 15.13% for SSC; the

standard deviation (S.D.)=13.12N for firmness and 1.41% for

SSC;minimum=32.05Nforfirmnessand10.60%forSSC;and

maximum=87.98N for firmness and 18.80% for SSC.

2.4. Features of hyperspectral scattering images

A typical spatially resolved hyperspectral scattering image

for an apple, covering the effective spectral range of

450–1000nm and a total spatial distance of 30mm, is shown in

Fig. 2b. The scattering image was symmetric to the spatial cen-

tral axis passing through the center of the light incident point.

A vertical line taken from the image parallel to the spectral axis

represents a spectrum (spectral profile) at a specific distance

awayfromthespatialcentralaxis.Hence,eachscatteringimage

essentially consisted of hundreds of spectra representing dif-

ferent spatial distances (or pixels) at the fruit surface. Fig. 2c

shows three raw spectra at distances from the illumination cen-

terof0mm,1mm,and2mm,respectively.Thedownwardpeaks

around 675nm resulted from the chlorophyll absorption in the

apple. On the other hand, a horizontal line parallel to the spa-

tial axis of the image represents a spatial scattering profile for a

specific wavelength. Three spatial profiles extracted at 600nm,

680nm,and720nmareshowninFig.2d;theyareconspicuously

different,indicatingthatthescatteringandabsorptionproperties

of the apple are wavelength dependent.

Comparison of scattering profiles from different apples

revealed large differences in their scattering characteristics.

Fig. 3. Original spectra taken at 1.25mm away from the spatial central axis (a)

and the original spatial scattering profiles at 720nm (b) for selected ‘Golden

Delicious’ apples.

Spectra taken at 1.25mm away from the spatial central axis

of scattering images for randomly selected 200 ‘Golden Deli-

cious’ apples are shown in Fig. 3a. Large variations in the

spectraexistedamongtheapples,reflectingpropertydifferences

in the apples. Fig. 3b shows the spatial scattering profiles of 200

Fig. 4. Correction for light intensity distortion caused by: (a) setup of the imaging system and (b) the curved apple fruit surface.

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Y. Peng, R. Lu / Postharvest Biology and Technology 48 (2008) 52–62

‘Golden Delicious’ apples at 720nm. Again large differences in

the spatial scattering profiles existed among the test apples. As

shown later, these spatial profiles were related to the firmness

and SSC of individual fruit.

2.5. Correction of scattering images for instrument

response and fruit size

Spatial scattering profiles of the hyperspectral images were

affected by two factors: one was related to the instrument setup

and the other was the curved surface of the fruit. To accurately

measure the backscattered reflectance at the surface of the fruit,

these two factors need to be considered. For a given point at the

surface of the fruit, the backscattered light will propagate in all

directions.Ideally,theinstrumentshouldmeasurethereflectance

thatcoversexactlythesameacceptanceangle(i.e.,them–m1–m2

section in Fig. 4a) for each point. However, in practical appli-

cations, the imaging system is often set at a finite distance (h)

away from the sample. Consequently, the acceptance angle for

reflectance measurement at each point for a horizontal distance

x from the center (Fig. 4a) is different, which in turn would

cause errors in the quantification of scattering profiles. Fig. 4a

shows how light intensity measured from a flat object by the

imaging system is affected by the instrument setup, specifically

the vertical distance h. Kienle et al. (1996) confirmed that the

angular intensity distribution of diffuse reflectance for a given

point at the surface of a turbid object generated by a point light

beam follows the Lambertian Cosine Law (Kort¨ um, 1969). This

means that the angular reflectance intensity I for a given point

m at an angle θ from the normal direction is equal to the maxi-

mum, normal reflectance intensity Imaxmultiplied by cosθ, i.e.,

I=Imaxcosθ. As a result, the actual reflectance Rmreceived by

the imaging system from the point m is the integration of the

reflectance intensity I over the acceptance angle (θ2−θ1) of the

zoom lens. The measured reflectance Rm, which is equal to the

area of a fan-shaped zone m–m1–m2, can be calculated by the

following equation:

?θ2

=π

π

Rm=1

2

θ1

I2

maxcos2θ dθ

4I2

max

1

?

θ2− θ1+1

2(sin2θ2− sin2θ1)

?

= fRtotal

where Rtotal= πI2

and f is a proportional factor representing the percentage of the

totalreflectanceRtotalatthepointmthatisreceivedbytheimag-

ing system. For a given imaging configuration, the proportional

factor f only depends on the horizontal distance to the center, x,

and it can be calculated by the following equation:

(1)

max/4 is the entire area of the emitted circle

f(x) =

1

π

?

atan

?

?x + k

sin

h

?

− atan

?x + k

?x − k

??

h

??

?

+1

2π

?

2atan

h

− sin2atan

?x − k

h

???

(2)

where k is the radius of the zoom lens and h is the distance

betweenthesamplesurfaceandthelens.Inthisstudy,k=26mm

andh=240mm.Eq.(2)wasusedtocorrectreflectancemeasure-

ments from a flat white Teflon disk that was used as a reference

in this research.

Individualapplesvaryinsize.Thecurvedfruitsurfacewould

introduceerrorsinthemeasurementofreflectanceintensitiesby

the imaging system. To obtain consistent reflectance measure-

ments from apple samples, the measured reflectance intensity

should be corrected for the effect of the fruit surface curvature.

The apple fruit were assumed to be spherical in this research.

Fig. 4b shows how to correct the reflectance intensity distortion

caused by the curved fruit surface. The proportional factor f in

Eq. (1) depends on the horizontal distance x and the radius s

of the apple and it can be calculated, based on the geometric

relations shown in Fig. 4b, by the following equation:

?

?

1

2πs

?

?

f(x,s) =1

π

atan

?

x + k

h + s −√s2− x2

x − k

h + s −√s2− x2

sin2

asin

?

−atan

??

+

???x

?

+atan

x + k

h + s −√s2− x2

asin

s

??

?

−sin2

?x

?

+atan

x − k

h + s −√s2− x2

???

(3)

To account for the effect of the instrument setup and sample

surfaceonthereflectanceprofile,theactualreflectanceintensity

R at each point in the horizontal direction would be calculated

with the same acceptance angle, i.e., at the central location o

(x=0). For this purpose, f(x) at x=0 is derived from Eq. (2):

?k

The total scattering intensity Rtotalshould remain the same after

the correction of light intensity for the instrument response. The

actual reflectance R at distance x from the reference Teflon disk

should be calculated by multiplying the measured scattering

intensity Rmat x by the following correction factor:

f(0) =2

πatan

h

?

+1

πsin

?

2atan

?k

h

??

(4)

Cr=f(0)

f(x)

(5)

Tocorrectfortheeffectofthecurvedfruitsurfaceandtheinstru-

mentresponseonthescatteringimages,themeasuredreflectance

Rmshould be recalculated by multiplying the correction factor

given in Eq. (6), i.e., Cs×Rm, to obtain the actual reflectance R.

f(0)

f(x,s)

Cs=

(6)

The curved fruit surface would cause the scattering distance

distortion on the scattering images, besides the light intensity

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Y. Peng, R. Lu / Postharvest Biology and Technology 48 (2008) 52–62

57

Table 1

Modified Lorentzian distribution (MLD) functions for describing the scattering

profiles of apple fruit

Function designationEquation form

MLD-41

R = a +

R = a +

R =

R = a +

R = a +

R =

R =

R =

R = a +

R = a +Rmax−a

b

1+(z/c)d

b

1+(z/c)2

MLD-31

MLD-32

b

1+(z/c)d

MLD-33

1−a

1+(z/c)d

Rmax−a

1+(z/c)d

MLD-34

MLD-21

b

1+(z/c)2

1

1+(z/c)d

Rmax

1+(z/c)d

MLD-22

MLD-23

MLD-24

1−a

1+(z/c)2

MLD-25

1+(z/c)2

Note:RisthelightintensityinCCDgrayscalecounts(itisthenormalizedinten-

sity divided by the maximum value Rmaxof the scattering profile in functions

MLD-33, MLD-22 and MLD-24); z is scattering distance; a is the asymptotic

valueoflightintensity;bispeakvalueofthescatteringprofile;cisfullscattering

width at half maximal peak value (FWHM); d is slope around FWHM.

distortion. The actual scattering distance z, as shown in Fig. 4b,

can be calculated from Eq. (7):

z = stan−1

x

√s2− x2

(7)

After corrections for the instrument response, fruit surface cur-

vatureandscatteringdistance,themeasuredreflectanceRmfrom

the reference and fruit samples was converted to the corrected

reflectance R. The corrected reflectance R was then used in

further analysis.

2.6. Functions for fitting scattering profiles

Spatial scattering profiles at different wavelengths may be

describedbyamodifiedLorentziandistribution(MLD)function

with four parameters (Peng and Lu, 2006a), three parameters

(Peng and Lu, 2005), or two parameters (Lu and Peng, 2006).

To determine the best parameters in the MLD function, vari-

ous functions derived from the four-parameter MLD function,

as shown in Table 1, were proposed to fit the scattering pro-

files for individual wavelengths. In Table 1, MLD-41, MLD-3j

(j=1, 2, ..., 4) and MLD-2j (j=1, 2, ..., 5) contain four param-

eters, three parameters, and two parameters, respectively. Each

function was evaluated and compared to determine the most

appropriate function(s) in predicting fruit firmness and SSC.

2.7. Development and validation of prediction models

Five steps were used in developing fruit firmness and SSC

prediction models:

1. After the scattering profiles for all 650 ‘Golden Delicious’

apples and the Teflon reference had been corrected for the

instrument response and fruit size effects, nonlinear regres-

sion was performed by fitting each of the 10 functions listed

in Table 1 to the corrected scattering profiles. The curve-

fitting procedure produced multiple MLD parameter spectra

for each sample corresponding to each of the 10 functions.

2. MLD parameter spectra of the fruit were divided by the

corresponding parameter spectra from the Teflon reference

standard to minimize the potential effect from the variation

ofthelightsourceduringtheexperimentonthemeasurement

of the scattering images from apple samples. While this pro-

cedure is similar, in concept, to the calculation of relative

reflectance between sample and standard in the analysis of

near-infraredspectraldata,itwasperformedonthecalculated

scattering parameters, not on the original scattering profiles.

A detailed description of the procedure is provided in Peng

and Lu (2007).

3. The650‘GoldenDelicious’applesamplesweredividedinto

two separate sets. The samples were arranged in ascending

order for fruit firmness (or SSC). The first three apples were

selected for calibration, and the fourth apple was selected

for validation for every four apples. This procedure resulted

in 488 apples (75%) for the calibration set and 162 apples

(25%) for the validation set. A stepwise multi-linear regres-

sion (MLR) method was applied to calculate the r-value and

standard error of calibration (S.E.C.) values between MT

firmness and MLD parameters of calibration samples for

eachindividualwavelengthforeachofthe10functions.This

procedure is similar to the MLR analysis of near-infrared

spectral data except that there would be two, three, or four

parameters for each wavelength from the hyperspectral scat-

tering data. All wavelengths were then ranked in ascending

order of r-values (or descending order of S.E.C.). The best

single wavelength that yielded the highest r-value (or the

lowest S.E.C.) was selected. Next, search for the best two

wavelengths was started. Each of the remaining wavelengths

was separately added to the best single wavelength, and the

corresponding r and S.E.C. values were calculated for all

two-wavelengthcombinations.Thebesttwoparameterswere

determined when they gave the highest r and lowest S.E.C.

among all two-wavelength combinations. This process was

repeated until all wavelengths had been ranked for the cali-

bration sample set. The same MLR analysis procedure was

applied to rank wavelengths for apple fruit SSC.

4. After the ranking of individual wavelengths for the cali-

bration sample set for each scattering profile function, the

leave-one-out cross-validation method was applied to indi-

vidual wavelength combinations for each of the 10 MLD

functions. Each time one sample was taken out from the cal-

ibration sample set; a calibration model was established for

the remaining samples and the model was then used to pre-

dict the sample left out. Thereafter, the sample was placed

back into the calibration sample set and a second sample

was taken out. The procedure was repeated until all cali-

bration samples had been left out once. The combination

of wavelengths that gave the least root mean squared error

of cross-validation (S.E.C.V.) was selected to be the opti-

mal combination of wavelengths. The least S.E.C.V.s were

calculated for each of the 10 functions. By comparing all

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Y. Peng, R. Lu / Postharvest Biology and Technology 48 (2008) 52–62

cross-validation results, the best scattering profile functions

and their corresponding optimal wavelength combinations

for predicting fruit firmness and SSC were determined.

5. MLRwasperformedagainforthecalibrationsamples,based

on the optimal wavelength combinations selected in Step 4,

to establish firmness and SSC prediction models. Finally, the

prediction models were used to predict the firmness and SSC

of samples in the validation set.

3. Results and discussion

3.1. Comparison of scattering profile functions

Fig. 5 shows the spectra of MLD-32 parameters (b, c and d)

for selected ‘Golden Delicious’ apple samples. The b spectra

represent the peak values of the scattering profiles for individ-

ual wavelengths, and c and d denote the full scattering width

and slope at half maximal peak value. While the parameter

b had dramatic changes in its value over the spectral region

between 550nm and 1000nm, the magnitude of change for

the parameters c and d was much smaller and more consis-

tent.Atwavelengthsbetween450nmand550nm,theparameter

d had a rapid change; on the contrary, the relative change of

the parameters b and c was smaller. There were pronounced

changes around 675nm on the spectra of parameters b and c,

which correspond to the chlorophyll absorption band. Over-

all, individual MLD-32 parameters were correlated, in various

degrees, with MT firmness at all wavelengths. As the firmness

of the samples increased, MLD parameters b and c tended to

decrease, whereas an opposite trend for MLD parameter d with

firmness was observed. Similar trends were also observed for

the spectra of scattering parameters from the other MLD func-

tions.

A comparison between the MLD functions with different

numbers of scattering profile parameters for fitting the scatter-

ing profiles of 488 calibration apples is presented in the second

and third columns of Table 2. All the MLD functions fitted the

scattering profiles accurately for wavelengths between 450nm

and1000nm.Theaverager-valueforeachfunctionwasequalto

or greater than 0.995, and the average standard deviation (S.D.)

was between 0.17% and 0.57%, relative to the maximum inten-

sity of the scattering profiles that was approximately between

6300 and 15400 CCD grayscale counts (Fig. 3b).

Valuesofthecross-validationcorrelationcoefficient(rcv)and

S.E.C.V. of the calibration sample set for estimating fruit firm-

ness with all MLD functions are shown in the fourth and fifth

columns of Table 2. The number of optimal wavelengths corre-

sponding to individual MLD functions is shown in the sixth

column of Table 2. Likewise, the seventh, eighth and ninth

columnsofTable2showrcvandS.E.C.V.valuesandwavelength

numbers for predicting apple fruit SSC.

A comparison of rcv or S.E.C.V. values in the fourth (or

the fifth) column of Table 2 for fruit firmness prediction shows

that MLD-41 gives the best predictions among the 10 functions

with the highest rcvof 0.896 and the lowest S.E.C.V. of 6.42N;

MLD-31 and MLD-32 are the best among the four functions

with three parameters; and MLD-21 is the best in the group of

Fig. 5. Parameter spectra for the modified Lorentzian function (or MLD-32 of

Table1)forselectedapplesamples:(a)themaximalvalueofscatteringintensity;

(b) the full scattering width at half maximal value (FWHM) and (c) the slope

around FWHM.

two-parameterfunctionswithrcv=0.865andS.E.C.V.=7.00N.

Hence, these four functions (i.e., MLD-41, MLD-31, MLD-32

and MLD-21) are considered more appropriate for predicting

apple fruit firmness. For apple fruit SSC prediction, the same

four functions also gave better results than other functions, as

shown in the seventh and eighth columns of Table 2. Hence,

MLD-41, MLD-31, MLD-32 and MLD-21 are more effective

than the other functions in predicting both apple fruit firm-

ness and SSC. The functions MLD-33, MLD-22 and MLD-24

requiredthenormalizationofscatteringprofilesbeforethecurve

fitting. These functions did not perform as well as those with-

out normalization. This indicated that the parameter b, which

represents the peak value for individual wavelengths, could

not be neglected for fruit quality prediction. Overall the two-

parameter functions (except for MLD-21) did not give as good

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Y. Peng, R. Lu / Postharvest Biology and Technology 48 (2008) 52–62

59

Table 2

Multi-linear regression and cross-validation analysis for determining the most appropriate scattering profile fitting functions to predict the firmness and soluble solids

content (SSC) of ‘Golden Delicious’ apples

Modified Lorentzian

distribution (MLD) functions

Average r and S.D. for curve-fittingCross-validation for firmnessCross-validation for SSC

r

S.D.a(%)

rcv

S.E.C.V. (N)Number of

wavelengths

rcv

S.E.C.V. (%)Number of

wavelengths

MLD-41

MLD-31

MLD-32

MLD-33

MLD-34

MLD-21

MLD-22

MLD-23

MLD-24

MLD-25

0.999

0.998

0.998

0.999

0.999

0.995

0.998

0.998

0.997

0.997

0.17

0.26

0.23

0.53

0.18

0.35

0.57

0.24

0.76

0.28

0.896

0.890

0.889

0.853

0.881

0.865

0.846

0.847

0.789

0.829

6.42

6.48

6.54

7.44

6.75

7.00

7.40

7.39

8.53

7.76

18

21

21

22

22

23

24

24

24

24

0.884

0.864

0.879

0.823

0.845

0.838

0.778

0.779

0.743

0.768

0.75

0.80

0.76

0.89

0.85

0.84

0.96

0.96

1.02

0.97

20

23

23

23

23

26

25

25

25

25

aExpressed in percent error relative to the maximum value of the scattering profile.

firmness and SSC predictions as the three- or four-parameter

functions.

3.2. Correlations at individual wavelengths

Fig. 6a shows the simple correlation coefficient between

multiple scattering parameters (2, 3 or 4) of the four MLD

functions and MT firmness over wavelengths 450–1000nm for

the 488 calibration samples. The correlation spectra for MLD-

Fig. 6. Simple correlation coefficient spectra between scattering parameters

(2, 3, or 4) from each of the four scattering profile models (see Table 1 for

details) and single wavelengths over the spectral region of 450–1000nm for: (a)

Magness–Taylor(MT)firmnessand(b)solublesolidscontent(SSC)of‘Golden

Delicious’ apples.

31 and MLD-41 fluctuated with wavelengths except for the

range between 580nm and 700nm. This is primarily because

light signals at wavelengths below 580nm and above 700nm

were much lower with considerable noise, which influenced the

parameter a, the fitted asymptotic value of the scattering pro-

files. MLD-21 yielded an overall smooth correlation coefficient

spectrum over the entire spectral region between 450nm and

1000nm, but values of the correlation coefficient were lower

than those from the other three functions. MLD-32 parameters

had smoother and more consistent correlation with MT firm-

ness than the other three functions for the entire wavelength

range 450–1000nm (Fig. 6). At 675nm, the MLD-32 had the

highest correlation with MT firmness with r=0.60, and this was

also true for the other three functions. This best single wave-

length is, however, not sufficient for accurate estimation of MT

firmness.

The cross-validation method allowed us to find a set of opti-

mal wavelengths that would yield the best predictions of apple

fruit firmness. The optimal wavelength numbers for the four

functions for estimating fruit firmness are 18, 21, 21, and 23,

respectively (Table 2). When the MLD-32 was used for esti-

mating apple fruit firmness, the best correlation was obtained

with21wavelengths(511nm,530nm,538nm,590nm,629nm,

649nm, 675nm, 721nm, 747nm, 752nm, 760nm, 780nm,

786nm, 793nm, 811nm, 826nm, 835nm, 872nm, 885nm,

909nm and 950nm) for the calibration set of 488 ‘Golden Deli-

cious’ apples. These wavelengths nearly span the entire spectral

range of 450nm and 1000nm.

The overall pattern of the correlation for the four functions

versus wavelength for estimating fruit SSC was similar to that

for estimating MT firmness (Fig. 6b). Again MLD-32 param-

eters had more consistent correlation with the SSC than the

other three functions. The effective wavelengths determined

by cross-validation analysis for the MLD-32 function were

645nm, 655nm, 675nm, 685nm, 707nm, 753nm, 766nm,

773nm, 785nm, 793nm, 813nm, 832nm, 884nm, 904nm,

912nm, 937nm, 944nm, 950nm, 956nm, 965nm, 976nm,

985nm and 996nm. Although higher values for the simple cor-

relation coefficient were obtained in the visible range between

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Y. Peng, R. Lu / Postharvest Biology and Technology 48 (2008) 52–62

Fig. 7. Correlation between Magness–Taylor (MT) firmness and estimated (or

predicted)firmnessfor:(a)thecalibrationsetand(b)thevalidationsetof‘Golden

Delicious’ apples.

450nm and 650nm than in the near-infrared range between

780nm and 1000nm, none of the wavelengths below 648nm

was selected in the SSC prediction model. These selected wave-

lengths for SSC prediction are consistent with the reported

works using NIR spectroscopy that the spectral range between

600nm and 1000nm is more appropriate for SSC predic-

tion (McGlone et al., 2002). The results in Fig. 6 show that

wavebands around 675nm had the most significant impact on

predictions of the firmness and SSC compared to other wave-

lengths. This demonstrated that chlorophyll content played an

importantroleininfluencingfirmnessandSSC.Thefruitmatur-

ing process is accompanied with the decrease in chlorophyll

content. As the chlorophyll content decreases, the fruit also

changes in both firmness and SSC. Hence, fruit SSC could

be indirectly related to the change in its chlorophyll con-

tent.

Results from the cross-validation (Table 2) and simple cor-

relation coefficient (Fig. 6) analysis demonstrated that both

MLD-32 and MLD-41 would be appropriate functions for pre-

dicting fruit firmness and SSC. While MLD-41 gave the best

predictions among the 10 functions with the highest rcvand

the lowest S.E.C.V, it had four parameters versus three param-

eters for MLD-32. This means that the MLR prediction model

would have more terms than MLD-32 for the same number of

wavelengths. Moreover, many useful wavelengths selected for

MLD-41 were located outside the range between 580nm and

700nm where its parameters had less consistent correlations

with fruit firmness and SSC (Fig. 6). Hence, further discussion

is focused on the MLD-32 function only.

3.3. Firmness and SSC predictions

An MT firmness prediction model was developed by MLR

using MLD-32 parameters at the 21 optimal wavelengths (total

of 63 scattering profile parameters for 21 wavelengths) for the

488calibrationsamplesof‘GoldenDelicious’apple.Thepredic-

tionmodelachievedgoodfirmnesspredictionsforthecalibration

samples with r=0.898 and S.E.C.=6.30N (Fig. 7a). The model

predicted the firmness of 162 validation samples with r=0.894

and the standard error of prediction (S.E.P.) of 6.14N (Fig. 7b).

The firmness prediction model performed well since the ratio

of the sample standard deviation (13.12N) to S.E.C. or S.E.P.

(R.P.D.) was greater than two. These prediction results are com-

parable to the results reported in Peng and Lu (2006c), but are

better than those (r∼0.50 and the S.E.P. of 11.6N for valida-

tion samples) using NIR spectroscopy technique (Peng and Lu,

2006b).

Similarly, a calibration model was developed from the same

set of 488 calibration samples for predicting the fruit SSC. The

threescatteringprofileparametersofMLD-32at23wavelengths

were used in MLR against the measured SSC for the calibra-

tion samples, which resulted in r=0.890 and S.E.C.=0.73%

(Fig. 8a). The correlation between predicted and measured SSC

for the 162 validation samples was 0.883 and the S.E.P. was

0.73%(Fig.8b).TheR.P.D.wasabouttwo.TheSSCpredictions

obtained from this study are comparable with those reported in

multispectral scattering imaging studies (Lu, 2004; Peng and

Lu, 2007). These results are also in line with reported studies on

SSC measurement using a visible/shortwave NIR spectrometer

(McGlone et al., 2002).

Fig. 8. Correlation between measured soluble solids content (SSC) and esti-

mated (or predicted) SSC for: (a) the calibration set and (b) the validation set of

‘Golden Delicious’ apples.

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61

3.4. Discussion

This study showed that the selection of an appropriate

Lorentzian distribution function could have a significant effect

on the prediction of fruit firmness and SSC. The differences in

firmnessandSSCpredictionsbyusingMLD-32orMLD-41and

MLD-24 (worst) could be as high as 19% in terms of r and up to

26% in terms of S.E.C.V., even though these functions fitted the

scatteringprofileswell(Table2).Thedatanormalizationprocess

tended to have a negative effect on the performance of the cor-

responding functions in predicting firmness and SSC, which is

evident from the cross-validation results for MLD-33, MLD-22

andMLD-24(Table2).Thiscouldbeduetothefactthatnormal-

ization resulted in the reduction of one degree of freedom, thus

removing some useful information from the dataset. Moreover,

the MLD functions with two parameters did not perform as well

as the MLD functions of three or four parameters.

Twenty-one and 23 wavelengths (or 63 and 69 MLD-32

parameters) were used in predicting fruit firmness and SSC,

respectively. The number of wavelengths and scattering profile

parameters were more than those used in the previous stud-

ies (Lu, 2004; Peng and Lu, 2006c, 2007). This was mainly

because more wavelengths between 450nm and 1000nm were

used in this study than in the previous studies. In earlier studies

of using multispectral imaging technique (Peng and Lu, 2006c,

2007), only four wavelengths were selected. While the multi-

spectralimagingtechniquehasyieldedgoodfirmnessprediction

results,itcouldnotpredictfruitSSCeffectively.Thehyperspec-

tralimagingtechnique,ontheotherhand,providesconsiderably

more information about the absorption and scattering properties

of fruit, thus enabling better prediction of fruit SSC than the

multispectral imaging technique.

The fruit softening process is very complex; it not only

changesthefruitchemicalproperties,butalsocauseschangesin

the fruit structural properties. Hence, one can expect that both

absorption and scattering properties would change during the

softening process. It is not clear how and to what degree the

softening process would affect the absorption and scattering

properties individually. This spectral scattering technique mea-

sures the combined effects of absorption and scattering in the

fruit. The technique, however, differs from NIRS techniques in

that it provides a better means for quantifying light scattering

characteristicsinthefruit.Becauseoftheintertwiningeffectsof

absorptionandscatteringandtheirpossiblecorrelationwithtime

during the fruit softening process, the prediction models devel-

opedforaparticularlotoffruitmaynotbesuitableforadifferent

lotoffruithavingdifferentpre-andpost-harvesthistoriesorcon-

ditions. Hence it is important that an effective model-updating

method be developed so that the prediction models can provide

reliable,accuratepredictionsforfruitcomingfromawiderange

of pre- and post-harvest conditions or histories.

4. Conclusions

Mathematicalequationswerederivedforcorrectingtheeffect

ofinstrumentresponseandfruitsizeonthehyperspectralscatter-

ingprofilesofthefruit.Evaluationofthe10modifiedLorentzian

distribution functions with different numbers of parameters

indicated their large influences on the fruit firmness and SSC

predictionresults.ThemodifiedLorentziandistributionfunction

(the MLD-32 of Table 1) with three parameters without includ-

ingtheparameterfortheasymptoticvaluewasmostappropriate

for predicting both fruit firmness and SSC. This function gave

good predictions of fruit firmness with r=0.894 and the stan-

dard error of prediction or S.E.P.=6.14N, and of fruit soluble

solids content with r=0.883 and S.E.P.=0.73%. The waveband

around 675nm had the highest single-wavelength correlation in

predicting the firmness and SSC of ‘Golden Delicious’ apples.

Twenty-one and 23 wavelengths were needed to achieve the

best predictions of fruit firmness and SSC, respectively. The

hyperspectral scattering technique along with an appropriate

Lorentzian function can provide good measurement of both

apple fruit firmness and SSC.

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