Shape and Size Variability of Roasted Arabica Coffee Beans

Abstract

Quantification and evaluation of selected Arabica (Coffea arabica L.) coffee beans' shape and size was performed. Twenty different coffee types originating from 13 different countries were analyzed. The main dimensions for individual coffee types were quantified. Sphericity, as a useful parameter for the calculation of processing and handling operations, was also quantified and ranged from 0.006536 to 0.009452. Calculation of shape variability using elliptic Fourier descriptors showed relevant differences among individual coffee samples. A dominant importance and the relevance of length-to-width ratio were quantitatively confirmed. A simple mathematical formula describing coffee grain contour was used with a satisfying correlation coefficient. Applicability of the approach was shown on the calculation of 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 the presence of defects;[1] however, specific studies that correlate the presence of such defects with physical and chemical characteristics of the beans are still scarce. Balanced filling and uniform ripening of coffee berries, thus yielding a better-quality product, is the aim of all coffee breeders. The simple tool used, for example, for on-line sorting and selecting shape-defective beans would considerably help coffee manufacturers in achieving effective and superior production, but an exact mathematical description of a “regular” bean and its shape variability is essentially needed. Due to increasing computer performance and data processing capacities and rates, such on-line evaluation based on image or video analysis can soon be expected. Size and shape of coffee berries and beans (as well as their other properties) depend on many factors such as coffee variety,[2] bean quality,[3] planting conditions,[4] geographical zone,[5] and other parameters. The Coffea arabica bean shape was first statistically reviewed by Wormer.[6] Many other authors have later dealt with this phenomenon and introduced different approaches.[2,7,8]

Object shape (including agricultural products) can influence its mechanical or thermal properties. Thus, its knowledge is critical, e.g., for designing manipulation, handling, and processing devices. This fact was confirmed by a number of works covering different biological and agricultural materials and products.[9–12 The evaluation of the coffee grain shape is relatively difficult owing to its complexity. The exact evaluation of the grain shape must be generally based on the use of 3-D scanning, but for the solution of many problems it is sufficient to know the shape of the contour of the grain projection in given directions. The accurate description of these grain contours can be obtained from digital images. A frequent problem, which occurs while manipulating with coffee beans (sieving, 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 granular food material using sphericity is very difficult and also not very practical.[13] One of the objectives of this work is, therefore, to calculate the bean sphericity with the use of a simple approach, to compare the shape variability of different coffee types by the use of Fourier descriptors, and to determine and compare bean curvature radius. In view of the aforementioned, the general objective of the present study was to present the powerful tools for determination and description of shape and size attributes of Coffea arabica coffee beans. Simple methods, mostly based on the measurement of main axial dimensions, were presented by other authors,[2,3,6] but these methods are not sufficient for the above-mentioned on-line computer assisted processing.

MATERIAL AND METHODS

Coffee Samples

Roasted Arabica coffee beans were used for analyses. Arabica coffees were produced in 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], Papua New Guinea [P-NG], Peru [PE], and Tanzania [T]. The abbreviations in square brackets indicate the coffee type and it is used in the text hereinafter. All Arabica samples were submitted to a light roast. The beans were ordered from a commercial distribution network in the Czech Republic. All analyses were performed for samples of 100 beans randomly selected from each lot. Sample details are listed in Table 1.

Table 1 Selected physical characteristics of different coffee brands

Coffee brand	Mean w (g)	Mean width D1 (mm)	Mean depth D4 (mm)	Mean length D7 (mm)	Mean V × 10^−9 (m^3)
B1	0.134^a ± 0.026	8.48^a ± 0.46	4.56^a ± 0.32	11.08^a ± 0.91	226.20^a ± 42.30
B2	0.130^a ± 0.023	8.36^a ± 0.54	4.58^a ± 0.26	10.85^a ± 0.99	219.00^a ± 36.30
C1	0.137^a ± 0.022	7.98^a ± 0.47	4.63^a ± 0.24	10.79^a ± 0.99	209.90^a ± 34.30
C2	0.147^a ± 0.023	8.43^a ± 0.47	4.79^a ± 0.52	11.13^a ± 2.24	247.10^a ± 37.90
C3	0.135^a ± 0.029	8.05^a ± 0.58	4.70^a ± 0.35	10.83^a ± 1.30	217.40^a ± 47.60
CR	0.117^a ± 0.025	7.94^a ± 0.52	4.50^a ± 0.30	10.66^a ± 0.97	201.50^a ± 40.90
E	0.123^b ± 0.032	7.56^a ± 1.38	4.71^a ± 0.37	10.93^a ± 1.47	211.90^b ± 54.00
G	0.128^a ± 0.025	8.20^a ± 0.48	4.67^a ± 0.34	10.60^a ± 0.85	214.00^a ± 34.20
H	0.141^a ± 0.028	8.26^a ± 0.59	4.79^a ± 0.26	10.82^a ± 2.05	232.80^a ± 41.40
I1	0.149^a ± 0.026	8.26^a ± 0.62	4.64^a ± 0.28	11.47^a ± 0.84	231.80^a ± 37.70
I2	0.146^a ± 0.025	8.34^a ± 0.57	4.79^a ± 0.37	11.90^a ± 1.10	247.60^a ± 40.30
I3	0.141^a ± 0.030	8.09^a ± 0.84	4.73^b ± 0.58	11.51^b ± 1.32	235.00^a ± 44.40
K1	0.152^a ± 0.022	8.26^b ± 1.53	4.91^b ± 0.70	10.97^a ± 0.92	241.80^a ± 57.50
K2	0.163^a ± 0.028	8.78^a ± 0.42	5.07^a ± 0.38	11.60^a ± 1.06	272.30^a ± 47.10
K3	0.149^a ± 0.021	8.71^a ± 0.45	4.90^a ± 0.31	11.46^a ± 0.75	257.50^a ± 39.10
M	0.246^a ± 0.038	9.76^a ± 0.37	5.62^a ± 0.36	14.90^b ± 1.26	430.30^a ± 62.50
P	0.142^a ± 0.024	8.20^a ± 0.49	4.75^a ± 0.30	11.19^b ± 2.91	246.00^a ± 40.20
P-NG	0.124 ^b ± 0.037	8.02^a ± 0.79	4.58^a ± 0.49	10.36^b ± 2.09	210.90^b ± 63.10
PE	0.137^a ± 0.031	8.09^b ± 1.47	4.78^a ± 0.28	10.55^b ± 1.85	228.00^a ± 40.50
T	0.149^a ± 0.021	8.60^a ± 0.49	4.78^a ± 0.30	11.28^a ± 0.65	242.80^a ± 26.30
Superscript letter a indicates statistically significant difference at α = 0.05 and letter b indicates statistically significant difference at α = 0.1 for average values for 100 samples.

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 a SOMET 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. The remaining dimensions (D2, D3, D5, D6; Fig. 1) were determined from digital images using Corel DRAW X3 (Corel Corporation, USA).

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

Image Analysis

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

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 measurements of major, minor, and intermediate diameters (D1, D4, D7) of individual beans and the assumption that each bean could be taken as half a triaxial ellipsoid.[14] The sphericity was calculated using Eq. (1), derived by Bayram,[13]

(1)

where φ _s denotes sphericity, D_i is any measured dimension, is average dimension or equivalent diameter, and N is the number of measurements. In the given model, an equivalent or nominal diameter for irregularly shaped materials is accepted as the average dimension to obtain an equivalent sphere. Differences between average diameter and actual measured dimensions are determined with the sum of square of differences. When this difference is divided by the square of the product of the average diameter and number of measurements, 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 were determined (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. The raw images were converted to full color (24-bit) bitmap format. This procedure was followed by converting the images to greyscale. The greyscale images were converted to binary images in which the objects and background are represented as 1 (white) and 0 (black), respectively. The image analysis software SHAPE[15] was used to perform all the following steps. The closed contours of the beans were obtained through binary images 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 that were measured counter-clockwise from an arbitrary starting point. Assuming that the contour between the (i - 1)th and ith chain-coded points is linearly interpolated and that the length of the contour from the starting point to the pth point and the perimeter of the contour are denoted by the t_p and T, respectively, then the elliptic Fourier expansions of the coordinates on the contour are

(2)

and

(3)

where x and y denote point coordinates, A ₀ and C ₀ represent center points, a, b, c, and d denote normalized elliptic Fourier coefficients, t_p is a length of the contour from the starting 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 shape analysis.[20] The coefficients of elliptic Fourier descriptors that were normalized to avoid variations related to the size, rotation, and starting point of the contour traces were then calculated from the chain-code through the procedure based on the ellipse of the first harmonic.[21] By this procedure, the peach shape was approximated by the first 20 harmonics, which correspond to the 77 coefficients of normalized elliptic Fourier descriptors.

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

Determination of Curvature Radius

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

(4)

where is obtained from the experimental data. The most effective function describing this dependence is given by the Fourier approach:

(5)

Another approximation can be given by the polynomial fit:

(6)

If we denote

(7)

the curvature radius is given by well-known relation:

(8)

where dot denotes the derivation with respect to .

RESULTS AND DISCUSSION

The mean values of experimentally found weights (g), dimensions (mm) along main bean 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 coffee beans. 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) from 10.36 mm (P-NG) to 14.90 mm (M). Generally, the least variable bean parameter was bean depth (D4) with a coefficient of variation of 0.05, followed by bean width (D1) (CV = 0.18), and bean length (D7) (CV = 0.85).

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, where the 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 was found for the length/depth (D7/D4) ratio, where the presented research revealed slightly higher values. The coefficient of correlation for the ratios of length/width ranged from 0.301 (C2) to 0.787 (CR), length/depth from 0.376 (P) to 0.924 (P-24), and width/depth from 0.461 (H) to 0.813 (P-NG). The values of correlation coefficients are listed in Table 2. Figure 2 demonstrates that the parameters of the shape (length-to-width ratios of G and M are shown as an example) are mutually dependent. Similar dependencies can 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 reported by Dutra et al.[14] The volumes ranged from 201.5 to 430.3 (×10⁻⁹ m³) for CR, M, respectively.

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

Figure 2 Relation between selected bean shape dimensions.

Sphericity

The applicability and proof of Eq. (1) was carried out by Bayram[13] using the following shapes: sphere, cube, rectangular solid, and cylinder. The approach was successfully applied for sphericity calculations of beans, chickpeas, lentils, and wheat. The values of 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, respectively. A statistically significant difference at α = 0.05 for average sphericity values for 100 samples was found for all coffee types. Due to important problems in available measurement and calculation methods to determine exact volume and surface area for granular materials, Eq. (1) can be used easily for solid mechanics and handling operations to determine the sphericity of coffee beans.

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

Coffee brand	Mean φ s
B1	0.007510^a ± 0.000842
B2	0.007232^a ± 0.001287
C1	0.007222^a ± 0.001386
C2	0.007717^a ± 0.002025
C3	0.007065^a ± 0.001398
CR	0.007313^a ± 0.000993
E	0.007182^a ± 0.001413
G	0.006718^a ± 0.000894
H	0.007166^a ± 0.001244
I1	0.008073^a ± 0.001236
I2	0.008317^a ± 0.001935
I3	0.008148^a ± 0.001698
K1	0.006536^a ± 0.001087
K2	0.006899^a ± 0.001158
K3	0.007107^a ± 0.000829
M	0.009452^a ± 0.001209
P	0.008424^a ± 0.001340
P-NG	0.007081^a ± 0.000751
PE	0.006782^a ± 0.001001
T	0.007269^a ± 0.001309
Superscript letter indicates statistically significant difference at α = 0.05 for average sphericity values for 100 samples.

Shape Variability Quantified by Fourier Descriptors

Comparative analyses of coffee bean shape variability were performed by image analysis, employing principal analysis components of elliptic Fourier descriptors. The mean bean shape (for each lot) was drawn using the mean values of the standardized Fourier coefficients. The first four principal components provide a good summary of the data, accounting for almost 100% of the total variance (Table 4). The first component represents the length-to-width ratio, the second component represents the position of the center of gravity, the third component represents curvature, and the fourth component substitutes the degree of roundness. An example (coffee B1) of a complete set of principal contribution components 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.

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	97.73
1st 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	95.44
1st 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 index
2	21.05	92.28	Position of the center of gravity
3	1.31	93.59	Curvature
4	0.91	94.50	Degree of roundness

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

Curvature Radius

The function described by Eq. (6) has been used for evaluation of the grain shape, as described in the previous section. A selected “average-like” coffee bean from each coffee type was used for sample calculation. The results are given in Table 6. It can be seen that the correlation coefficient between measured and computed grain profiles ranges from 0.9680 to 0.9987 for M and T coffee, respectively. There is a lack of works using analogous procedures and focused on biological materials, although the similar procedures were already used for technical materials and objects of non-biological nature.[23] The knowledge of the equation describing the grain contour is necessary, namely for the numerical simulation of grain behavior under different mechanical loading, for numerical simulation 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. The values of the curvature radius calculated by use of Eq. (8) can be plotted (and listed) for any coffee grain as can be seen in the sample picture (Fig. 4), where half of the grain C1 is shown.

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

	Coefficient
Coffeetype	p1	p2	p3	p4	p5	p6	p7	p8	p9	p10	r ^2
B1	−0.0013	0.005	0.032	−0.102	−0.279	0.782	1.154	−2.457	−2.501	6.256	0.9897
B2	−0.0010	0.004	0.022	−0.086	−0.172	0.715	0.648	−2.330	−1.441	6.741	0.9936
C1	0.00053	0.001	−0.011	−0.039	0.074	0.418	−0.16	−1.484	0.1139	5.890	0.9910
C2	−0.0017	0.005	0.044	−0.110	−0.399	0.872	1.657	−2.769	−3.304	6.856	0.9910
C3	−0.0010	0.003	0.025	−0.084	−0.228	0.728	0.976	−2.459	−2.140	6.596	0.9973
CR	−0.0017	0.004	0.042	−0.098	−0.374	0.761	1.525	−2.441	−2.937	6.140	0.9893
E	0.00017	0.002	−0.004	−0.054	0.034	0.437	−0.05	−1.367	−0.389	5.298	0.9830
G	−0.0010	0.003	0.023	−0.071	−0.206	0.607	0.862	−2.068	−1.828	6.068	0.9934
H	−0.0016	0.005	0.038	−0.114	−0.323	0.917	1.223	−2.969	−2.430	7.087	0.9936
I2	−0.0031	0.008	0.074	−0.167	−0.636	1.254	2.407	−3.664	−4.254	7.099	0.9835
I3	−0.0015	0.002	0.037	−0.063	−0.315	0.537	1.232	−1.871	−2.274	6.139	0.9959
K1	−0.0011	0.002	0.027	−0.057	−0.243	0.482	1.030	−1.722	−2.215	5.619	0.9981
K2	−0.0025	0.005	0.060	−0.126	−0.506	0.999	1.868	−3.169	−3.334	7.570	0.9951
M	−0.0048	0.013	0.115	−0.269	−0.969	1.932	3.595	−5.348	−6.119	9.478	0.9680
P	−0.0051	0.010	0.124	−0.199	−1.083	1.383	4.186	−3.856	−7.075	7.020	0.9747
P-NG	−0.0011	0.003	0.028	−0.068	−0.263	0.550	1.245	−2.015	−3.124	6.518	0.9986
PE	−0.0003	0.001	0.007	−0.037	−0.064	0.380	0.286	−1.353	−0.640	6.066	0.9792
T	−8E-05	0.001	0.003	−0.032	−0.039	0.349	0.215	−1.234	−0.444	5.562	0.9987

Figure 3 Experimental and fitted contour of C1 coffee bean.

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

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 bean depth (D4) with a coefficient of variation 0.05, followed by bean width (D1) with a coefficient 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 the relationship between length (D7), width (D1), and depth (D4) of Arabica beans. The only significant difference was revealed for the length/depth (D7/D4) ratio—presented values are higher than those in previous works. The coefficient of correlation for the length/width ratios 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 0.006536 to 0.009452 for K1, M, respectively. The possibility of simple quantification of this parameter provides a large advantage for the design and evaluation of solid mechanics and handling operations. The highest value of sphericity was calculated for the same coffee 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 elliptic Fourier descriptors. Reconstructed shapes indicated that the first principal component (which represents the length-to-width ratio) is a very good measure of the total shape variation. It represents 70.87 to 74.64% (for E and I1 coffee, respectively) of the total shape variation in case of the front view. Numerical simulation of the coffee grain behavior under different mechanical loading, heat treatment, and determination of curvature radius R can be supported by proposed mathematical formulas describing grain contour with a satisfying correlation coefficient between experimental and computed data ranging from r ² = 0.9680 to 0.9987.

ACKNOWLEDGMENT

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