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Shape and Size Variability of RoastedArabica Coffee BeansLibor Severa a , Jaroslav Buchar a & Šárka Nedomová ba Department of Physics, Mendel University, Brno, Czech Republicb Department of Food Technology, Mendel University, Brno, CzechRepublicAccepted author version posted online: 24 Jun 2011.

To cite this article: Libor Severa , Jaroslav Buchar & rka Nedomov (2012) Shape and Size Variabilityof Roasted Arabica Coffee Beans, International Journal of Food Properties, 15:2, 426-437, DOI:10.1080/10942912.2010.487967

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International Journal of Food Properties, 15:426–437, 2012Copyright © Taylor & Francis Group, LLCISSN: 1094-2912 print / 1532-2386 onlineDOI: 10.1080/10942912.2010.487967

SHAPE AND SIZE VARIABILITY OF ROASTED ARABICACOFFEE BEANS

Libor Severa1, Jaroslav Buchar1, and Šárka Nedomová2

1Department of Physics, Mendel University, Brno, Czech Republic2Department of Food Technology, Mendel University, Brno, Czech Republic

Quantification and evaluation of selected Arabica (Coffea arabica L.) coffee beans’ shapeand size was performed. Twenty different coffee types originating from 13 different countrieswere analyzed. The main dimensions for individual coffee types were quantified. Sphericity,as a useful parameter for the calculation of processing and handling operations, was alsoquantified and ranged from 0.006536 to 0.009452. Calculation of shape variability usingelliptic Fourier descriptors showed relevant differences among individual coffee samples.A dominant importance and the relevance of length-to-width ratio were quantitatively con-firmed. A simple mathematical formula describing coffee grain contour was used with asatisfying correlation coefficient. Applicability of the approach was shown on the calculationof curvature radius.

Keywords: Image analysis, Coffee beans, Shape variation, Sphericity, Fourier descriptors.

INTRODUCTION

The criteria commonly used to evaluate the quality of coffee beans include bean size,color, shape, roast potential, processing method, crop year, flavor or cup quality, and thepresence of defects;[1] however, specific studies that correlate the presence of such defectswith physical and chemical characteristics of the beans are still scarce. Balanced fillingand uniform ripening of coffee berries, thus yielding a better-quality product, is the aimof all coffee breeders. The simple tool used, for example, for on-line sorting and selectingshape-defective beans would considerably help coffee manufacturers in achieving effec-tive and superior production, but an exact mathematical description of a “regular” beanand its shape variability is essentially needed. Due to increasing computer performanceand data processing capacities and rates, such on-line evaluation based on image or videoanalysis can soon be expected. Size and shape of coffee berries and beans (as well as theirother properties) depend on many factors such as coffee variety,[2] bean quality,[3] plantingconditions,[4] geographical zone,[5] and other parameters. The Coffea arabica bean shapewas first statistically reviewed by Wormer.[6] Many other authors have later dealt with thisphenomenon and introduced different approaches.[2,7,8]

Object shape (including agricultural products) can influence its mechanical or ther-mal properties. Thus, its knowledge is critical, e.g., for designing manipulation, handling,

Received 2 December 2009; accepted 16 April 2010.Address correspondence to Jaroslav Buchar, Department of Physics, Mendel University in Brno,

Zemedelska 1, Brno 61300, Czech Republic. E-mail: buchar@mendelu.cz

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VARIABILITY OF ROASTED ARABICA COFFEE 427

and processing devices. This fact was confirmed by a number of works covering differ-ent biological and agricultural materials and products.[9−12] The evaluation of the coffeegrain shape is relatively difficult owing to its complexity. The exact evaluation of the grainshape must be generally based on the use of 3-D scanning, but for the solution of manyproblems it is sufficient to know the shape of the contour of the grain projection in givendirections. The accurate description of these grain contours can be obtained from digitalimages. A frequent problem, which occurs while manipulating with coffee beans (siev-ing, sorting, and/or grinding), is also the calculation of the exact volume and surface area.High-level mathematical formulas should be used to calculate the volume and surface area;therefore, the determination of the solid mechanical and handling properties of any gran-ular food material using sphericity is very difficult and also not very practical.[13] One ofthe objectives of this work is, therefore, to calculate the bean sphericity with the use ofa simple approach, to compare the shape variability of different coffee types by the useof Fourier descriptors, and to determine and compare bean curvature radius. In view ofthe aforementioned, the general objective of the present study was to present the power-ful tools for determination and description of shape and size attributes of Coffea arabicacoffee beans. Simple methods, mostly based on the measurement of main axial dimen-sions, were presented by other authors,[2,3,6] but these methods are not sufficient for theabove-mentioned on-line computer assisted processing.

MATERIAL AND METHODS

Coffee Samples

Roasted Arabica coffee beans were used for analyses. Arabica coffees were producedin Brazil [B1, B2], Colombia [C1, C2, C3], Costa Rica [CR], Ethiopia [E], Guatemala [G],Honduras [H], Indonesia [I1, I2, I3], Kenya [K1, K2, K3], Mexico [M], Panama [P], PapuaNew Guinea [P-NG], Peru [PE], and Tanzania [T]. The abbreviations in square bracketsindicate the coffee type and it is used in the text hereinafter. All Arabica samples weresubmitted to a light roast. The beans were ordered from a commercial distribution networkin the Czech Republic. All analyses were performed for samples of 100 beans randomlyselected from each lot. Sample details are listed in Table 1.

Quantitative Measurement of the Bean Weight and Dimensions

The weight of the roasted beans was measured using a Kern–KB electronic balance(Germany). Dimensions in the main axes (D1, D4, D7—see Fig. 1) were measured using aSOMET digital calliper (Germany). With regards to measurement accuracy and relevance,one decimal number was considered. According to indications by other authors,[2] D1, D4,and D7 dimensions correspond to W (width), D (depth), and L (length), respectively. Theremaining dimensions (D2, D3, D5, D6; Fig. 1) were determined from digital images usingCorel DRAW X3 (Corel Corporation, USA).

Image Analysis

An Olympus SP-560UZ digital camera (Olympus, Japan) was used to capture thepictures of the beans.

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428 SEVERA, BUCHAR, AND NEDOMOVÁ

Table 1 Selected physical characteristics of different coffee brands.

Coffeebrand Mean w (g)

Mean width D1(mm)

Mean depth D4(mm)

Mean length D7(mm) Mean V × 10−9 (m3)

B1 0.134a ± 0.026 8.48a ± 0.46 4.56a ± 0.32 11.08a ± 0.91 226.20a ± 42.30B2 0.130a ± 0.023 8.36a ± 0.54 4.58a ± 0.26 10.85a ± 0.99 219.00a ± 36.30C1 0.137a ± 0.022 7.98a ± 0.47 4.63a ± 0.24 10.79a ± 0.99 209.90a ± 34.30C2 0.147a ± 0.023 8.43a ± 0.47 4.79a ± 0.52 11.13a ± 2.24 247.10a ± 37.90C3 0.135a ± 0.029 8.05a ± 0.58 4.70a ± 0.35 10.83a ± 1.30 217.40a ± 47.60CR 0.117a ± 0.025 7.94a ± 0.52 4.50a ± 0.30 10.66a ± 0.97 201.50a ± 40.90E 0.123b ± 0.032 7.56a ± 1.38 4.71a ± 0.37 10.93a ± 1.47 211.90b ± 54.00G 0.128a ± 0.025 8.20a ± 0.48 4.67a ± 0.34 10.60a ± 0.85 214.00a ± 34.20H 0.141a ± 0.028 8.26a ± 0.59 4.79a ± 0.26 10.82a ± 2.05 232.80a ± 41.40I1 0.149a ± 0.026 8.26a ± 0.62 4.64a ± 0.28 11.47a ± 0.84 231.80a ± 37.70I2 0.146a ± 0.025 8.34a ± 0.57 4.79a ± 0.37 11.90a ± 1.10 247.60a ± 40.30I3 0.141a ± 0.030 8.09a ± 0.84 4.73b ± 0.58 11.51b ± 1.32 235.00a ± 44.40K1 0.152a ± 0.022 8.26b ± 1.53 4.91b ± 0.70 10.97a ± 0.92 241.80a ± 57.50K2 0.163a ± 0.028 8.78a ± 0.42 5.07a ± 0.38 11.60a ± 1.06 272.30a ± 47.10K3 0.149a ± 0.021 8.71a ± 0.45 4.90a ± 0.31 11.46a ± 0.75 257.50a ± 39.10M 0.246a ± 0.038 9.76a ± 0.37 5.62a ± 0.36 14.90b ± 1.26 430.30a ± 62.50P 0.142a ± 0.024 8.20a ± 0.49 4.75a ± 0.30 11.19b ± 2.91 246.00a ± 40.20P-NG 0.124b ± 0.037 8.02a ± 0.79 4.58a ± 0.49 10.36b ± 2.09 210.90b ± 63.10PE 0.137a ± 0.031 8.09b ± 1.47 4.78a ± 0.28 10.55b ± 1.85 228.00a ± 40.50T 0.149a ± 0.021 8.60a ± 0.49 4.78a ± 0.30 11.28a ± 0.65 242.80a ± 26.30

Superscript letter a indicates statistically significant difference at α = 0.05 and letter b indicates statisticallysignificant difference at α = 0.1 for average values for 100 samples.

Figure 1 Illustration of measuring sides for coffee beans (reworked version of Fig. 2 presented in Bayram[13]).

Calculation of Volume and Sphericity

Volume as well as sphericity was calculated using Microsoft Office Excel software(Microsoft, USA). The average volumes of the beans were calculated from measurementsof major, minor, and intermediate diameters (D1, D4, D7) of individual beans and theassumption that each bean could be taken as half a triaxial ellipsoid.[14] The sphericity wascalculated using Eq. (1), derived by Bayram,[13]

φs =∑ (

Di − D)2

(DN

)2 , (1)

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VARIABILITY OF ROASTED ARABICA COFFEE 429

where φs denotes sphericity, Di is any measured dimension, D is average dimension orequivalent diameter, and N is the number of measurements. In the given model, an equiv-alent or nominal diameter for irregularly shaped materials is accepted as the averagedimension to obtain an equivalent sphere. Differences between average diameter and actualmeasured dimensions are determined with the sum of square of differences. When this dif-ference is divided by the square of the product of the average diameter and number ofmeasurements, it gives a fraction for the approach of the slope to an equivalent sphere, i.e.,sphericity. An increase in N increases the accuracy. Seven dimensions of coffee beans weredetermined (see Fig. 1).

Evaluation of the Variation of Coffee Bean Shape Based on Image

Analyses Using Elliptic Fourier Analyses

The beans were photographed using an Olympus SP-560UZ digital camera(Olympus, Japan) and digital images with a resolution of 180 dpi were acquired. Theraw images were converted to full color (24-bit) bitmap format. This procedure wasfollowed by converting the images to greyscale. The greyscale images were convertedto binary images in which the objects and background are represented as 1 (white) and0 (black), respectively. The image analysis software SHAPE[15] was used to performall the following steps. The closed contours of the beans were obtained through binaryimages with appropriate thresholds and were described by a chain-code.[16] Namely,each contour was represented as a sequence of x and y coordinates of ordered points thatwere measured counter-clockwise from an arbitrary starting point. Assuming that thecontour between the (i - 1)th and ith chain-coded points is linearly interpolated and thatthe length of the contour from the starting point to the pth point and the perimeter of thecontour are denoted by the tp and T , respectively, then the elliptic Fourier expansions ofthe coordinates on the contour are

xp = A0 +∞∑

n=1

(an cos

2nπ tpT

+ bn sin2nπ tp

T

), (2)

and

yp = C0 +∞∑

n=1

(cn cos

2nπ tpT

+ dn sin2nπ tp

T

), (3)

where x and y denote point coordinates, A0 and C0 represent center points, a, b, c, andd denote normalized elliptic Fourier coefficients, tp is a length of the contour from thestarting point to the pth point, and T is the perimeter of the contour.

The same or similar method was used for the petal shape variation analysis,[17]

chicken egg shape analysis,[18] hazelnut shape analysis,[19] or e.g., sperm head shapeanalysis.[20] The coefficients of elliptic Fourier descriptors that were normalized to avoidvariations related to the size, rotation, and starting point of the contour traces werethen calculated from the chain-code through the procedure based on the ellipse of thefirst harmonic.[21] By this procedure, the peach shape was approximated by the first20 harmonics, which correspond to the 77 coefficients of normalized elliptic Fourierdescriptors.

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430 SEVERA, BUCHAR, AND NEDOMOVÁ

In order to summarize the information contained in the coefficients of the Fourierdescriptors, the principal components analysis based on a variance–covariance matrix ofthe coefficients was performed. The scores of the components were used in subsequentanalysis as the peach shape characteristic. The variation in shape accounted for by eachcomponent was visualized using the inverse Fourier transformation.[22]

Determination of Curvature Radius

From the dimensional measures of individual grains, the contours of single projec-tions could be accurately described in a user-defined Cartesian coordinate system. Theshape of the grain counter can be described using the polar coordinates r, ϕ as:

x = r cos ϕ y = sin ϕ, (4)

where r = r(ϕ) is obtained from the experimental data. The most effective functiondescribing this dependence is given by the Fourier approach:

r (ϕ) = ao +∞∑

i=0

ai cos

(2π

ϕ

ci

)+bi sin

(2π

ϕ

ci

). (5)

Another approximation can be given by the polynomial fit:

r (ϕ) =n∑

i=1

piϕn+1−i. (6)

If we denote

x (ϕ) = f (ϕ) y (ϕ) = g (ϕ) , (7)

the curvature radius is given by well-known relation:

R =(f 2 + g2

) 32(

f g − f g) , (8)

where dot denotes the derivation with respect to ϕ.

RESULTS AND DISCUSSION

The mean values of experimentally found weights (g), dimensions (mm) along mainbean axes, and volume (m3) (including standard deviation values) are listed in Table 1.Mean values represent the average of 100 individual measurements in each lot of coffeebeans. As can be seen in Table 1, the bean width (D1) ranged from 7.56 mm (E) to 9.76 mm(M), the bean depth (D4) from 4.50 mm (CR) to 5.07 mm (K2), and bean length (D7) from10.36 mm (P-NG) to 14.90 mm (M). Generally, the least variable bean parameter was beandepth (D4) with a coefficient of variation of 0.05, followed by bean width (D1) (CV =0.18), and bean length (D7) (CV = 0.85).

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VARIABILITY OF ROASTED ARABICA COFFEE 431

Ghosh and Gacanja[2] derived the general relationship between length (D7), width(D1), and depth (D4) of Arabica beans. The relationship has the following form: D7 =1.300, D1 = 2.082 D4. This conclusion was confirmed by the presented study, wherethe calculation of the given relationship yielded in: D7 = 1.290 to 1.534 D1 (G, M,respectively) = 2.210 to 2.655 D4 (PE, M, respectively). The only relevant difference wasfound for the length/depth (D7/D4) ratio, where the presented research revealed slightlyhigher values. The coefficient of correlation for the ratios of length/width ranged from0.301 (C2) to 0.787 (CR), length/depth from 0.376 (P) to 0.924 (P-24), and width/depthfrom 0.461 (H) to 0.813 (P-NG). The values of correlation coefficients are listed inTable 2. Figure 2 demonstrates that the parameters of the shape (length-to-width ratiosof G and M are shown as an example) are mutually dependent. Similar dependenciescan be created with the analogical result for other shape parameters and coffee types.The average volumes of the beans were calculated according to the formula reportedby Dutra et al.[14] The volumes ranged from 201.5 to 430.3 (×10−9 m3) for CR, M,respectively.

Sphericity

The applicability and proof of Eq. (1) was carried out by Bayram[13] using the follow-ing shapes: sphere, cube, rectangular solid, and cylinder. The approach was successfullyapplied for sphericity calculations of beans, chickpeas, lentils, and wheat. The valuesof Arabica bean sphericity (including standard deviation values) are listed in Table 3.The average value of sphericity ranged from 0.006536 to 0.009452 for K1, M, respec-tively. A statistically significant difference at α = 0.05 for average sphericity values

Table 2 Correlation (r) for length/width, length/depth, and width/depth ratios.

Coffee brand r, length/width r, length/depth r, depth/width

B1 0.621 0.744 0.690B2 0.583 0.428 0.573C1 0.423 0.378 0.656C2 0.301 0.468 0.478C3 0.664 0.605 0.569CR 0.787 0.659 0.731E 0.679 0.670 0.572G 0.512 0.624 0.561H 0.581 0.516 0.461I1 0.394 0.548 0.619I2 0.367 0.455 0.601I3 0.359 0.459 0.731K1 0.512 0.694 0.699K2 0.530 0.529 0.502K3 0.332 0.621 0.482M 0.378 0.635 0.497P 0.541 0.376 0.593P-NG 0.864 0.924 0.813PE 0.404 0.717 0.751T 0.421 0.413 0.531

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432 SEVERA, BUCHAR, AND NEDOMOVÁ

Figure 2 Relation between selected bean shape dimensions.

Table 3 Mean and s.d. values of calculated sphericity

Coffee brand Mean φs

B1 0.007510a ± 0.000842B2 0.007232a ± 0.001287C1 0.007222a ± 0.001386C2 0.007717a ± 0.002025C3 0.007065a ± 0.001398CR 0.007313a ± 0.000993E 0.007182a ± 0.001413G 0.006718a ± 0.000894H 0.007166a ± 0.001244I1 0.008073a ± 0.001236I2 0.008317a ± 0.001935I3 0.008148a ± 0.001698K1 0.006536a ± 0.001087K2 0.006899a ± 0.001158K3 0.007107a ± 0.000829M 0.009452a ± 0.001209P 0.008424a ± 0.001340P-NG 0.007081a ± 0.000751PE 0.006782a ± 0.001001T 0.007269a ± 0.001309

Superscript letter indicates statistically significant difference atα = 0.05 for average sphericity values for 100 samples.

for 100 samples was found for all coffee types. Due to important problems in availablemeasurement and calculation methods to determine exact volume and surface area for gran-ular materials, Eq. (1) can be used easily for solid mechanics and handling operations todetermine the sphericity of coffee beans.

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VARIABILITY OF ROASTED ARABICA COFFEE 433

Shape Variability Quantified by Fourier Descriptors

Comparative analyses of coffee bean shape variability were performed by imageanalysis, employing principal analysis components of elliptic Fourier descriptors. Themean bean shape (for each lot) was drawn using the mean values of the standardizedFourier coefficients. The first four principal components provide a good summary of thedata, accounting for almost 100% of the total variance (Table 4). The first component repre-sents the length-to-width ratio, the second component represents the position of the centerof gravity, the third component represents curvature, and the fourth component substitutesthe degree of roundness. An example (coffee B1) of a complete set of principal contributioncomponents is given in Table 5. The influence of the first and most important component(length-to-width ratio) ranges from 70.87 to 74.64 for E, I1, respectively.

Since mean values of single components of individual coffee types are known orcan be determined by the above-described method, unusual detected values can show thedefective state of a coffee bean and can serve as a tool for the definition of specific irregu-larities. Generally, there are two major advantages of using elliptic Fourier descriptors andprincipal component analysis. First, this approach can accurately detect small shape varia-tions. Detection of rather small variations is difficult for humans, but the analyses based oncomponent scores can clearly detect significant variations among individual coffee beans.Second, the analyses can evaluate the shapes of objects independently of size. This inde-pendence is a great advantage because human visual judgment of shape is often deceivedand misled by size factors. The above-mentioned method represents a relatively simplebut powerful interpretation tool, which perfectly suits for evaluating of biological shapes.This study demonstrates the potential of modern techniques using shape-based methodson digital images to achieve high efficiency performance in fruit/beans/seeds grading andclassification.

Curvature Radius

The function described by Eq. (6) has been used for evaluation of the grain shape, asdescribed in the previous section. A selected “average-like” coffee bean from each coffee

Table 4 Contributions (%) of first four principal components (cumulative) and first component.

Coffee type B1 B2 C1 C2 C3 CR E G H I1

Cumulative, % 94.50 95.74 97.89 97.60 96.12 95.04 94.66 96.87 98.11 97.731st comp., % 71.45 73.75 72.03 74.09 74.11 70.29 70.87 73.67 73.57 74.64

Coffee type I2 I3 K1 K2 K3 M P P-NG PE T

Cumulative, % 96.74 97.36 97.15 98.07 95.30 97.55 95.43 94.48 96.26 95.441st comp., % 72.68 74.30 73.14 73.98 70.96 72.05 71.34 71.25 73.59 74.31

Table 5 Contributions of individual principal components—coffee B1.

Component Proportion (%) Cumulative (%) Indicator

1 71.23 71.23 Shape index2 21.05 92.28 Position of the center of gravity3 1.31 93.59 Curvature4 0.91 94.50 Degree of roundness

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434 SEVERA, BUCHAR, AND NEDOMOVÁ

Table 6 Calculation coefficients and fit correlation coefficient for tested coffee types.

CoefficientCoffeetype p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 r2

B1 −0.0013 0.005 0.032 −0.102 −0.279 0.782 1.154 −2.457 −2.501 6.256 0.9897B2 −0.0010 0.004 0.022 −0.086 −0.172 0.715 0.648 −2.330 −1.441 6.741 0.9936C1 0.00053 0.001 −0.011 −0.039 0.074 0.418 −0.16 −1.484 0.1139 5.890 0.9910C2 −0.0017 0.005 0.044 −0.110 −0.399 0.872 1.657 −2.769 −3.304 6.856 0.9910C3 −0.0010 0.003 0.025 −0.084 −0.228 0.728 0.976 −2.459 −2.140 6.596 0.9973CR −0.0017 0.004 0.042 −0.098 −0.374 0.761 1.525 −2.441 −2.937 6.140 0.9893E 0.00017 0.002 −0.004 −0.054 0.034 0.437 −0.05 −1.367 −0.389 5.298 0.9830G −0.0010 0.003 0.023 −0.071 −0.206 0.607 0.862 −2.068 −1.828 6.068 0.9934H −0.0016 0.005 0.038 −0.114 −0.323 0.917 1.223 −2.969 −2.430 7.087 0.9936I2 −0.0031 0.008 0.074 −0.167 −0.636 1.254 2.407 −3.664 −4.254 7.099 0.9835I3 −0.0015 0.002 0.037 −0.063 −0.315 0.537 1.232 −1.871 −2.274 6.139 0.9959K1 −0.0011 0.002 0.027 −0.057 −0.243 0.482 1.030 −1.722 −2.215 5.619 0.9981K2 −0.0025 0.005 0.060 −0.126 −0.506 0.999 1.868 −3.169 −3.334 7.570 0.9951M −0.0048 0.013 0.115 −0.269 −0.969 1.932 3.595 −5.348 −6.119 9.478 0.9680P −0.0051 0.010 0.124 −0.199 −1.083 1.383 4.186 −3.856 −7.075 7.020 0.9747P-NG −0.0011 0.003 0.028 −0.068 −0.263 0.550 1.245 −2.015 −3.124 6.518 0.9986PE −0.0003 0.001 0.007 −0.037 −0.064 0.380 0.286 −1.353 −0.640 6.066 0.9792T −8E-05 0.001 0.003 −0.032 −0.039 0.349 0.215 −1.234 −0.444 5.562 0.9987

type was used for sample calculation. The results are given in Table 6. It can be seenthat the correlation coefficient between measured and computed grain profiles ranges from0.9680 to 0.9987 for M and T coffee, respectively. There is a lack of works using analo-gous procedures and focused on biological materials, although the similar procedures werealready used for technical materials and objects of non-biological nature.[23] The knowl-edge of the equation describing the grain contour is necessary, namely for the numericalsimulation of grain behavior under different mechanical loading, for numerical simula-tion of different heat treatment, and also for the determination of radius of curvature R.An example of an experimental and fitted contour for coffee C1 is given in Fig. 3. Thevalues of the curvature radius calculated by use of Eq. (8) can be plotted (and listed) forany coffee grain as can be seen in the sample picture (Fig. 4), where half of the grain C1 isshown.

CONCLUSIONS

It was found that all main dimensions, particularly length (D7), width (D1), and depth(D4) have changed for individual coffee types. The least variable bean parameter was beandepth (D4) with a coefficient of variation 0.05, followed by bean width (D1) with a coef-ficient of variation of 0.18, and bean length (D7) with a coefficient of variation of 0.85.The experiments partially confirmed partially improved previous findings concerning therelationship between length (D7), width (D1), and depth (D4) of Arabica beans. The onlysignificant difference was revealed for the length/depth (D7/D4) ratio—presented valuesare higher than those in previous works. The coefficient of correlation for the length/widthratios ranged between 0.301 (C2) and 0.787 (CR), for length/depth ratios between 0.376(P) and 0.924 (P-24), and for width/depth ratios between 0.461 (H) and 0.813 (P-NG).Sphericity, calculated according to a procedure described by Bayram[13] ranged from

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VARIABILITY OF ROASTED ARABICA COFFEE 435

Figure 3 Experimental and fitted contour of C1 coffee bean.

Figure 4 Example of curvature radius behavior—C1 coffee grain (half-display).

0.006536 to 0.009452 for K1, M, respectively. The possibility of simple quantification ofthis parameter provides a large advantage for the design and evaluation of solid mechan-ics and handling operations. The highest value of sphericity was calculated for the samecoffee type, where the highest values of D1 and D7 dimensions, and volume were found.Effort was also focused on the quantification of coffee shape variability by means of ellip-tic Fourier descriptors. Reconstructed shapes indicated that the first principal component

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436 SEVERA, BUCHAR, AND NEDOMOVÁ

(which represents the length-to-width ratio) is a very good measure of the total shape vari-ation. It represents 70.87 to 74.64% (for E and I1 coffee, respectively) of the total shapevariation in case of the front view. Numerical simulation of the coffee grain behavior underdifferent mechanical loading, heat treatment, and determination of curvature radius R canbe supported by proposed mathematical formulas describing grain contour with a satis-fying correlation coefficient between experimental and computed data ranging from r2 =0.9680 to 0.9987.

ACKNOWLEDGMENT

The research has been supported by the Grant Agency of the Czech Academy of Sciencesunder Contract No. IAA201990701.

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