Mass modeling of cantaloupe based on geometric attributes: A case study for Tile Magasi and Tile Shahri

Abstract

Grading which results in easier fruit packaging not only reduces the waste but also increases the marketing value of agricultural products. The knowledge on existing relationship among the mass, length, width, thickness, volume and projected areas of fruits is useful for proper design of grading machines. The aim of this study was mass modeling of two major cultivars of Iranian cantaloupes (Tile Magasi and Tile Shahri) based on geometrical attributes. Models were classified into three: 1 – univariate and multivariate models based on the outer dimensions of fruit. 2 – Univariate and multivariate models based on the projected areas of fruit. 3 – Univariate models based on the actual volume, volume of the fruit assumed as prolate and oblate spheroid shapes. The results indicated that the models based on the fruit width, third projected area and assumed oblate spheroid volume have the highest determination coefficient (R2) and the lowest standard error of estimate (SEE). It was finally concluded that cantaloupe mass modeling based on the volume of fruit assumed as oblate spheroid shape with a nonlinear relation; M=2.198Vobl0.884, R2=0.986 these values were suitable for grading systems.

Full text

Scientia Horticulturae 130 (2011) 54–59
Contents lists available at ScienceDirect
Scientia Horticulturae
journal homepage: www.elsevier.com/locate/scihorti
Mass modeling of cantaloupe based on geometric attributes: A case study for Tile
Magasi and Tile Shahri
Esmaeel Seyedabadia, Mehdi Khojastehpourb,∗, Hassan Sadrniab, Mohammad-Hosaien Saiediradc
aDepartment of Agronomy, Faculty of Agriculture, University of Zabol, Zabol, Iran
bDepartment of Agricultural Eng. (Farm Machinery), College of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran
cAgricultural and Natural Resources Research Center, Mashhad, Iran
article info
Article history:
Received 31 August 2010
Received in revised form 29 May 2011
Accepted 2 June 2011
Keywords:
Mass modeling
Physical properties
Iranian cantaloupe
Standard error of estimate
abstract
Grading which results in easier fruit packaging not only reduces the waste but also increases the mar-
keting value of agricultural products. The knowledge on existing relationship among the mass, length,
width, thickness, volume and projected areas of fruits is useful for proper design of grading machines.
The aim of this study was mass modeling of two major cultivars of Iranian cantaloupes (Tile Magasi and
Tile Shahri) based on geometrical attributes. Models were classified into three: 1 – univariate and mul-
tivariate models based on the outer dimensions of fruit. 2 – Univariate and multivariate models based
on the projected areas of fruit. 3 – Univariate models based on the actual volume, volume of the fruit
assumed as prolate and oblate spheroid shapes. The results indicated that the models based on the fruit
width, third projected area and assumed oblate spheroid volume have the highest determination coef-
ficient (R2) and the lowest standard error of estimate (SEE). It was finally concluded that cantaloupe
mass modeling based on the volume of fruit assumed as oblate spheroid shape with a nonlinear relation;
M=2.198V0.884
obl ,R2= 0.986 these values were suitable for grading systems.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
Cantaloupe (Cucumis melo L.) has a high amount of vitamins A,
B and C with high amount of sugars. It can be consumed as fresh,
dried fruit and juice. The world’s total production of cantaloupe
is 27 ×106t per year. In Iran, the soil and climatic condition are
ideal for cantaloupe production and it is cultivated on 8 ×104ha
with an annual production of 127 ×104t(Ministry of Agriculture,
Iran, 2006; FAOSTAT, 2009). Major part of this production is used
domestically while only a small quantity is exported (Behbahani,
2005).
Knowledge about physical properties of agricultural products
is necessary for the design of handling, sorting, processing and
packaging systems. Among these properties, the dimensions, mass,
volume and projected area are the most important ones in the
design of grading system (Wright et al., 1986; Safwat, 1971;
Mohsenin, 1986). Consumers prefer fruits with equal weight and
uniform shape. Mass grading of fruit can reduce packaging and
transportation costs, and also may provide an optimum packag-
ing configuration (Peleg, 1985). Recent researches in the field of
fruit sorting focused on automated sorting strategies (eliminating
∗Corresponding author. Tel.: +98 511 8796843; fax: +98 511 8796843.
E-mail addresses: mkhpour@ferdowsi.um.ac.ir,mkhpour@yahoo.com
(M. Khojastehpour).
human errors). It provides more efficient and accurate sorting sys-
tems which either improve the classification success or speed up
the process (Polder et al., 2003; Kleynen et al., 2003).
Fruits are often classified based on the size, mass, volume and
projected areas. Electrical sizing mechanisms are more complex
and expensive. Mechanical sizing mechanisms work slowly. There-
fore it may be more economical to develop a machine, which grades
fruits by their mass. Besides, using mass as the classification param-
eter is the most accurate method of automatic classification for
more fruits. Therefore, the relationships between mass and length,
width and projected areas can be useful and applicable (Khoshnam
et al., 2007; Stroshine and Hamann, 1995; Marvin et al., 1987).
A number of studies have been conducted on mass modeling
of fruits. A quadratic equation (M= 0.08c2+ 4.74c+ 5.14, R2= 0.89)
recommended to calculate apple mass based on its minor diameter
(Tabatabaeefar and Rajabipour, 2005). Lorestani and Tabatabaeefar
(2006) determined models for predicting mass of Iranian kiwi fruit
by its dimensions, volumes, and projected areas. They reported that
the intermediate diameter was more appropriate to estimate the
mass of kiwi fruit. Naderi-Boldaji et al. (2008) also used this method
for predicting the mass of apricot. They found a nonlinear equation
(M= 0.0019c2.693,R2= 0.96) between apricot mass and its minor
diameter. Also Khanali et al. (2007) achieved models for tangerine.
Some researchers modeled the mass of pomegranate fruit (Kingsly
et al., 2006; Fadavi et al., 2005; Kaya and Sozer, 2005). There are
some other researches about modeling of the volume and surface
0304-4238/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.scienta.2011.06.003

E. Seyedabadi et al. / Scientia Horticulturae 130 (2011) 54–59 55
Nomenclature
alength (mm)
bwidth (mm)
cthickness (mm)
Wamass of fruit in air (g)
Wwmass of fruit in water (g)
Vvolume (cm3)
Vpro volume of prolatespheroid (cm3)
Vmactual volume (measured) (cm3)
Vobl volume of oblate spheroid (cm3)
CPA criteria projected area (mm2)
PA1first projected area (mm2)
PA2second projected area (mm2)
PA3third projected area (mm2)
Mmass (g)
Kiregression coefficient
R2coefficient of determination
SEE standard error of estimate
Greek symbols
ffruit density (g/cm3)
wwater density (g/cm3)
area of different fruits as well (Chuma et al., 1982; Humeida and
Hoban, 1993).
The suitable technique to develop sizing machine of large and
heavy fruits i.e. melons is using machine vision systems (Moreda
et al., 2009). In these systems, fruit mass was calculated from 2D
and 3D image attributes such as length, width, and projected area.
The aim of this study was the mass modeling of two cultivars of
Iranian cantaloupe, Tile Magasi and Tile Shahri, based on geometric
attributes to be applicable in machine vision for grading systems.
2. Materials and methods
In order to determine the physical properties of cantaloupe, 30
samples were randomly selected from each cultivar and transferred
to Agricultural and Natural Resources Research Center of Mash-
had. Selected samples were healthy and free from any injuries and
obtained from a farm close to Mashhad (latitude: 36◦16N and lon-
gitude: 59◦38E).
Optimum conditions for keeping cantaloupe are temperature of
3–5 ◦C and relative humidity of 90–95% (Hurst, 1999). For ignor-
ing the effect of environmental parameters, the samples were kept
in these conditions for 24 h. For each fruit, the three principal
dimensions (Fig. 1), namely length, width and thickness were mea-
sured using an improved caliper, which had an accuracy of 0.05 mm
(Fig. 2).
To obtain the mass, each fruit was weighed with an electronic
balance of 0.1 g accuracy. Also the volume and density were deter-
mined by the water displacement method. A sinker was used for
the immersion since cantaloupe was lighter than water. The vol-
ume and density were calculated using the following equations
(Mohsenin, 1986).
V=(Wa−Ww)both −(Wa−Ww)sinker
w
(1)
f=(Wa)object
(Wa−Ww)both −(Wa−Ww)sinker
w(2)
where Waand Wware the mass of fruit in air and water and; fand
ware the fruit and water densities (g/cm3), respectively.
Fig. 1. Main dimensions defined for fruit.
To determine the volume, the fruit was assumed as prolate and
oblate spheroid. Therefore, the volume was estimated as follows
(Mohsenin, 1986):
Vpro =4
3a
2b
22
(3)
Vobl =4
3a
22b
2(4)
where aand bare the major and minor diameters, respectively.
Image processing is another method to estimate the mass of
agricultural products. Projected areas of the cantaloupe (PA1,PA
2
and PA3) were determined from pictures taken with a digital cam-
era (SONY DSC-W35), and then the reference area was compared
to a sample area using the Photoshop cs3 program. The average
Fig. 2. Improved caliper for measuring fruit size.

56 E. Seyedabadi et al. / Scientia Horticulturae 130 (2011) 54–59
Table 1
Physical attributes of two Iranian cultivars of cantaloupe (Tile Magasi and Tile
Shahri).
Characteristics Cultivars
Tile Magasi Tile Shahri Total observations
Dimensions (cm)
a12.57 ±0.29 18.40 ±0.51 14.81 ±0.43
b13.28 ±0.23 18.78 ±0.54 15.77 ±0.45
c12.98 ±0.23 19.17 ±0.51 15.35 ±0.43
Mass (g) 1469.3 ±80.64 3587.9 ±215.2 2118.1 ±154.2
Volume (cm3)
Vm1297.6 ±90.62 4240.6 ±408.7 2769.1 ±341.9
Vobl 1470.88 ±109.8 4535.6 ±452.1 3003.3 ±365
Vpro 1345.9 ±115.2 4099.7 ±405.4 2722.8 ±329.0
Density (g/cm3) 1.08 ±0.016 0.89 ±0.029 0.99 ±0.098
Projected area (mm2)
PA115,156 ±1899 30,483 ±2347 24,735 ±2227
PA215,237 ±1887 29,306 ±2541 24,030 ±2222
PA314,780 ±1804 28,396 ±2349 23,290 ±2100
CPA 15,058 ±1860 29,395 ±2401 24,018 ±2177
projected area (known as criteria projected area) was calculated as
suggested by Mohsenin (1986):
CPA =PA1+PA2+PA3
3(5)
After measuring the size, mass, volume and projected areas,
SPSS 16.0 program was used for regression analysis. In order to
estimate the cantaloupe mass from the measured dimensions, pro-
jected areas and volume, the following three categories of models
were considered.
(1) Univariate and multivariate regressions of dimensional character-
istics: length (a), width (b), thickness (c) and all three diameters.
The general form of these models is shown in the following
equation:
M=k1a+k2b+k3c+k4(6)
where k1,k2,k3and k4are constants.
Table 3
Models based on all diameters for cantaloupe.
Cultivar Model R2SEE
Tile Magasi M= 141.9a+ 81.5b+ 3.7c−1610 0.908 131.18
Tile Shahri M= 167.5a+ 142.5b+ 126.9c−4912 0.933 334.68
Total observation M= 104.08a+ 203.9b+ 37.08c−3211 0.950 301.5
(2) Univariate and multivariate regressions of projected areas:PA
1,
PA2,PA
3and all three projected areas. The general form of these
models is shown in the following equation.
M=k1PA1+k2PA2+k3PA3+k4(7)
where k1,k2,k3and k4are constants. PA1,PA
2and PA3are the
first, the second and the third projected areas, respectively.
(3) Univariate regression of volumes: actual volume (Vm), volume
of the fruit assumed as prolate spheroid (Vpro) and oblate shapes
(Vobl). The general form of these models is shown in the follow-
ing equations.
M=k1Vm+k2(8)
M=k1Vobl +k2(9)
M=k1Vpro +k2(10)
where k1and k2are constants.
Coefficient of determination (R2) and standard error of estimate
(SEE) were used to evaluate the regression models. It is evident that
models which have the higher value of R2and the lower value of
SSE represent a better estimation.
3. Results and discussion
3.1. Physical properties of cantaloupe
The average values of physical properties for cantaloupe are
shown in Table 1. According to the obtained results, the mean val-
Table 2
Coefficient of determination (R2) and standard error of estimate (SSE) for linear regression models for two Iranian cultivars of cantaloupe (Tile Magasi, Tile Shahri) and the
total observations.
No. Model Parameter Tile Magasi Tile Shahri Total
observations
Category 1
1M=k1a+k2R20.808 0.854 0.908
SEE 185.4 473.5 402.25
2M=k1b+k2R20.866 0.904 0.943
SEE 142.86 384.6 317.5
3M=k1c+k2R20.778 0.878 0.931
SEE 199.39 432.8 349.1
4M=k1a+k2b+k3c+k4R20.908 0.933 0.950
SEE 131.18 334.68 301.5
Category 2
5M=k1PA1+k2R20.976 0.968 0.980
SEE 105.65 242.3 219.4
6M=k1PA2+k2R20.988 0.969 0.975
SEE 74.194 238.7 247.16
7M=k1PA3+k2R20.994 0.975 0.981
SEE 58.29 213.89 215.93
8M=k1PA1+k2PA2+k3PA3+k4R20.995 0.980 0.985
SEE 54.29 206.6 199.5
Category 2
9M=k1Vm+k2R20.982 0.971 0.978
SEE 11.88 61.04 72.34
10 M=k1Vobl +k2R20.956 0.921 0.969
SEE 78.06 379.6 271.13
11 M=k1Vpro +k2R20.938 0.915 0.967
SEE 93.01 393.3 279.16

E. Seyedabadi et al. / Scientia Horticulturae 130 (2011) 54–59 57
Fig. 3. Linear and nonlinear models for total observations based on cantaloupe
width.
ues of many properties which were studied in this research (length,
width, thickness, mass, projected areas, actual volume, prolate
and oblate spheroid volumes) for Tile Shahri cultivar were signifi-
cantly greater than for Tile Magasi cultivar. But the mean value of
density for Tile Magasi (1.08 g/cm3) was less than for Tile Shahri
(0.89 g/cm3). Density and mass for Galia melons were reported
1.019 ±0.027 g/cm3and 971 ±136 g, respectively by Chen et al.
(1996). The differences in morphology and content (i.e. percent of
cavity volume) in melons cause variation in their physical attribute.
Table 1 shows that the average mass variation between two cul-
tivars was very high, the average mass of Tile Shahri (3587 g) was
about 2.45 times more than the average mass of Tile Magasi (1469 g)
while the average volume of Tile Shahri (4240 cm3) was about 3.27
times more than the average volume of Tile Magasi (1469 cm3).
Since small melons have more losses than larger ones, so many
consumers prefer Tile Shahri variety.
Regression models obtained for two Iranian cultivars of can-
taloupes in three different categories are shown in Table 2. All of the
model coefficients were analyzed using F-test. The results showed
that all of them were significant at 5% probability level.
3.2. The classification based on dimensions
Among the investigated classification models based on dimen-
sions (models No. 1–4 shown in Table 2), model 4 with three
diameters, had the highest R2value and the lowest SSE value.
However, the three diameters must be measured for this model,
which make the sizing mechanism more complicated and expen-
sive. Table 3 shows the mass models based on three diameters for
each cultivar and total observations.
Among the applied three one-dimensional models (1–3), model
2 showed higher R2value and lower SEE value. Therefore, the model
which expresses the width as independent variable was selected
as the best choice. Fig. 3 shows linear and nonlinear mass models
for total observations based on cantaloupe width. By comparing
the resulted estimates, the power model was introduced for sizing
mechanisms (M= 2.614b2.391,R2= 0.957, SEE = 0.118).
Tabatabaeefar et al. (2000) suggested a nonlinear model for
orange mass based on fruit width too. Their recommended
model was with the following values: M= 0.069b2−2.95b−39.15,
R2= 0.97.
Table 4
Models based on all projected areas for cantaloupe.
Cultivar Model R2SEE
Tile Magasi M= 0.039PA1+ 0.013PA2+ 0.145PA3−196.2 0.995 58.297
Tile Shahri M= 0.058PA1+ 0.043PA2+ 0.0.38PA3−368.5 0.980 206.6
Total
observations
M= 0.071PA1+ 0.03PA2+ 0.041PA3−507.8 0.985 199.58
Fig. 4. Linear and nonlinear models for total observations based on cantaloupe third
projected area.
The correlation among Mango mass and the single dimension
length (L), maximum width (Wmax) and maximum thick-
ness (Tmax) was estimated by Spreer and Müller (2011) as
a power function; M= 0.000136(L)3.0682,M= 0.001(Wmax )2.9249,
M= 0.00265(Tmax)2.7935 with R2= 0.84, 0.92 and 0.88, respectively.
Another research showed that apricot mass model obtained based
on the minor diameter (M= 2.6649c−66.412, R2= 0.954) is recom-
mended (Naderi-Boldaji et al., 2008). The spatial fruit distribution
patterns vary among melon cultivars, and therefore must be con-
sidered in the design of all mechanized systems, as mentioned and
shown by Edan and Simon (1997), but the shape of a fruit (small
or large) is constant in a special variety as presented in grading
standards, and variations occur only in their sizes. Therefore, mass
modeling can be applicable for all fruits based on dimensions.
3.3. The classification based on projected areas
Among the investigated classification models based on pro-
jected areas (models No. 5–8 shown in Table 2), model 8 with the
three projected areas had the highest value of R2and the low-
est value of SSE. Table 4 shows the mass models based on three
projected areas for each cultivar and total observations.
If these models were used for the classification of fruits in grad-
ing system, all three projected areas will be required for each
variety of cantaloupes. Therefore, the costs of sorting and grad-
ing will be increased while the speed of system will be decreased.
Then it is evident that one of univariate models must be selected.
Among the models of 5–7, model 7 was preferred because of the
highest value of R2and the lowest value of SSE. Fig. 4 shows lin-
ear and nonlinear mass models for total observations based on
cantaloupe’s third projected area. By comparing the obtained esti-

58 E. Seyedabadi et al. / Scientia Horticulturae 130 (2011) 54–59
Table 5
Models based on actual volume of cantaloupe.
Cultivar Model R2SEE
Tile Magasi M= 1.025Vm+ 66.43 0.982 11.86
Tile Shahri M= 0.823Vm+ 252.66 0.971 61.04
Total observations M= 0.809Vm+ 326.73 0.978 72.34
Fig. 5. Linear and nonlinear models for total observations based on the volume of
assumed oblate spheroid shape.
mates, the power model was introduced for sizing mechanisms
(M= 0.012PA31.229,R2= 0.985, SEE = 0.73).
Lorestani and Tabatabaeefar (2006) developed the mass
model for sizing kiwi fruits based on one projected area
as: M= 1.098(PA3)1.273,R2= 0.97. Khoshnam et al. (2007) rec-
ommended M= 1.29(PA1)1.28,R2= 096, for pomegranate and
Naderi-Boldaji et al. (2008) reported M= 0.0004(PA2)1.586,R2= 0.98
for apricot mass modeling.
3.4. The classification based on volume
In this classification group (models 9–11), the R2and SSE values
of model 9 were higher and lower, respectively. Therefore, model
9 was supposed for predicting cantaloupe mass. Table 5 shows the
mass models based on actual volume for each cultivar and total
observations. Because measuring actual volume is time consum-
ing, it was preferred to model the mass of cantaloupe based on the
volume of assumed oblate spheroid shape. Fig. 5 shows linear and
nonlinear mass models for total observations based on the volume
of assumed oblate spheroid shape. By comparing the all resulted
estimates, the power model was introduced for sizing mechanisms
(M= 2.198 Vobl0.884 ,R2= 0.986, SEE = 0.07).
Khoshnam et al. (2007) determined the mass of pomegranate
by measuring volume as M= 0.96Vm+ 4.25, R2= 0.99. Naderi-
Boldaji et al. (2008) modeled the mass of overall apricots as
M= 0.997Vm+ 0.301; R2= 0.98.
4. Conclusions
The mass models for Tile Magasi and Tile Shahri cantaloupe cul-
tivars were introduced in this study. The main obtained results are
as follows:
(1) The recommended dimensional mass model based on
cantaloupe width was as nonlinear form: M= 2.614b2.391,
R2= 0.957, SSE = 0.118.
(2) The mass model recommended for sizing cantaloupes
based on the third projected area was as nonlinear form:
M= 0.012PA31.229,R2= 0.985, SSE = 0.73.
(3) There was a very good relationship between the mass and mea-
sured volume of cantaloupe for both cultivars with the higher
coefficient of determination value (R2= 0.986).
(4) The model to predict the mass of cantaloupe based on
the estimated volume of cantaloupe (oblate spheroid shape)
was found to be most appropriate for sorting systems: M=
2.198V0.884
obl ,R
2=0.986,SEE =0.07.
Acknowledgements
The authors are grateful for financial support and valuable
technical assistance to Department of Agricultural Eng. (Farm
Machinery) of Ferdowsi University of Mashhad and Khorasan
Razavi Agricultural and Natural Resources Research Center.
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