Modeling of Apricot Mass Based on Geometrical Properties

Transcription

1 World Journal of Fungal and Plant Biology (3): 60-64, 011 ISSN IDOSI Publications, 011 Modeling of Apricot Mass Based on Geometrical Properties Fereydoun Keshavarzpour Department of Agriculture, Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran Abstract: In this study, eighteen linear regression models for modeling apricot mass based on some geometrical properties of apricot such as major diameter (a), intermediate diameter (b), minor diameter (c), geometrical mean diameter (GMD), first projected area (PA 1), second projected area (PA ), third projected area (PA 3), criteria area (CAE), estimated volume based on an ellipsoid assumed shape (V Ell) and measured volume (V M) were suggested. Models were divided into three main classifications, i.e. first classification (outer dimensions), second classification (projected areas) and third classification (volumes). The statistical results of the study indicated that in order to predict apricot mass based on outer dimensions, the mass model based on GMD as M = GMD with R = 0.93 can be recommended. Moreover, to predict apricot mass based on projected areas, the mass model based on CAE as M = CAE with R = 0.93 can be suggested. Besides, to predict apricot mass based on volumes, the mass model based on V Ell as M = V Ell with R = 0.9 can be utilized. These models can also be used to design and develop sizing machines equipped with an image processing system. Key words: Apricot Mass Modeling Outer dimensions Projected areas Volumes INTRODUCTION Turkey, Iran, Italy, Pakistan and France are the principal apricot producer countries. Apricot trees are also grown Apricot (Prunus armenia L.) is classified under the in Spain, Japan, Syria and Algeria. Iran has exported more Prunus genus, Prunaidea sub-family and the Rosaceae than 680 tones to different countries in 005 [5]. In Iran, family of the Rosales group [1]. Average fruit mass ranges the most widely produced types are Tabarzeh, Kardi, between 0 and 60 g, dried substance percentage in fruit Damavandi, Nakhjavan and Sonnati [, 4]. is 18-8%, ph value is between 4.0 and 5.0 and fruit color Similar to other fruits, apricot size is one of the most is yellow. Apricot has an important place in human important quality parameters for evaluation by consumer nutrition and apricot fruits can be used as fresh, dried or preference. Consumers prefer fruits of equal size and processed fruit []. Also, the fruit of apricot is not only shape. Sorting can increase uniformity in size and shape, consumed fresh but also used to produce dried apricot, reduce packaging and transportation costs and also may frozen apricot, jam, jelly, marmalade, pulp, juice, nectar and provide an optimum packaging configuration [6-9]. extrusion products. Moreover, apricot kernels are used in Moreover, sorting is important in meeting quality the production of oils, cosmetics, active carbon and aroma standards, increasing market value and marketing perfume [3]. Apricot has an important place in terms of operations [10-1]. Sorting manually is associated with human health. Apricot is rich in minerals such as high labor costs in addition to subjectivity, tediousness potassium and vitamins such as vitamin A. Vitamin A is and inconsistency which lower the quality of sorting [13]. necessary for epithelia tissues covering our bodies and However, replacing human with a machine may still be organs, eye-health, bone and teeth development and questionable where the labor cost is comparable with the working of endocrine glades. In addition, it plays sorting equipment [14]. Studies on sorting in recent years important role in reproduction and growing functions of have focused on automated sorting strategies and our bodies, in increasing body resistance against eliminating human efforts to provide more efficient and infections [4]. Iran is the second apricot producer in the accurate sorting systems which improve the classification world with 75,580 tons production and 8.% share. success or speed up the classification process [15, 16]. Corresponding Author: Fereydoun Keshavarzpour, Department of Agriculture, Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran 60

2 World J. Fungal & Plant Biol., (3): 60-64, 011 Physical and geometrical characteristics of products are the most important parameters in design of sorting systems. Among these characteristics, mass, outer dimensions, projected areas and volume are the most important ones in sizing systems [17-19]. The size of produce is frequently represented by its mass because it is relatively simple to measure. However, sorting based on some geometrical properties may provide a more efficient method than mass sorting. Moreover, the mass of Fig. 1: The outer dimensions of an apricot, i.e. major produce can be easily estimated from geometrical diameter (a), intermediate diameter (b) and minor properties if the mass model of the produce is known [0]. diameter (c) by assuming the shape of apricot as Thus, modeling of apricot mass based on some an ellipsoid geometrical properties may be useful and applicable. Therefore, the main objective of this research was to PA 1 = ab/4 () determine optimum mass model(s) based on some PA = ac/4 (3) geometrical properties of apricot. PA 3 = bc/4 (4) CAE = (PA 1+PA +PA 3)/3 (5) MATERIALS AND METHODS In addition, the volume of ellipsoid assumed shape or Experimental Procedure: One hundred randomly selected estimated volume of each apricot (V Ell) was calculated by apricots (cv. Damavandi) of various sizes were purchased using equation 6. from a local market. Apricots were selected for freedom from defects by careful visual inspection, transferred to V Ell = abc/6 (6) the laboratory and held at 5±1 C and 90±5% relative humidity until experimental procedure. Table 1 shows some physical and geometrical In order to obtain required parameters for determining properties of the apricots used to determine mass models. mass models, the mass of each apricot was measured to 0.1 g accuracy on a digital balance. Moreover, the volume Regression Models: A typical linear multiple regression of each apricot was measured using the water model is shown in equation 7: displacement method. Each apricot was submerged into water and the volume of water displaced was Y = k 0+ k1x 1+ kx + + knx n (7) measured. Water temperature during measurements was kept at 5 C. where: By assuming the shape of apricots as an ellipsoid (Fig. 1), the outer dimensions of each apricot, i.e. major Y = Dependent variable, for example mass diameter (a), intermediate diameter (b) and minor diameter of apricot (c) was measured to 0.1 mm accuracy by a digital caliper. X 1, X,, X n = Independent variables, for example The geometric mean diameter (GMD) of each apricot was geometrical properties of apricot then calculated by equation 1. k, k, k,, k = Regression coefficients 0 1 n 1/3 GMD = (abc) (1) In order to model apricot mass based on geometrical properties, eighteen linear regression models were Three projected areas of each apricot, i.e. first suggested and all the data were subjected to linear projected area (PA 1), second projected area (PA ) and regression analysis using the Microsoft Excel 007. third projected area (PA3) was also calculated by using Models were divided into three main classifications equation, 3 and 4, respectively. The average projected (Table ), i.e. first classification (outer dimensions), area known as criteria area (CAE) of each apricot was then second classification (projected areas) and third determined from equation 5. classification (volumes). 61

3 World J. Fungal & Plant Biol., (3): 60-64, 011 Table 1: The mean values, standard deviation (S.D.) and coefficient of variation (C.V.) of some physical and geometrical properties of the 100 randomly selected apricots used to determine mass models Parameter Minimum Maximum Mean S.D. C.V. (%) Mass (M), g Major diameter (a), mm Intermediate diameter (b), mm Minor diameter (c), mm Geometrical mean diameter (GMD), mm First projected area (PA 1), cm Second projected area (PA ), cm Third projected area (PA 3), cm Criteria area (CAE), cm Estimated volume (V Ell), cm Measured volume (V M), cm Table : Eighteen linear regression mass models and their relations in three classifications Classification Model No. Model Relation Outer dimensions 1 M = k 0 + k 1 a M = a M = k 0 + k 1 b M = b 3 M = k 0 + k 1 c M = c 4 M = k 0 + k 1 GMD M = GMD 5 M = k 0 + k 1 a + k b M = a b 6 M = k 0 + k 1 a + k c M = a c 7 M = k 0 + k 1 b + k c M = b c 8 M = k 0 + k 1 a + k b + k 3 c M = a b c Projected areas 9 M = k 0 + k 1 PA1 M = PA1 10 M = k 0 + k 1 PA M = PA 11 M = k 0 + k 1 PA3 M = PA3 1 M = k 0 + k 1 CAE M = CAE 13 M = k 0 + k 1 PA 1 + k PA M = PA PA 14 M = k 0 + k 1 PA 1 + k PA3 M = PA PA3 15 M = k 0 + k 1 PA + k PA3 M = PA PA3 16 M = k 0 + k 1 PA 1 + k PA 3 + k 3 PA3 M = PA PA PA3 Volumes 17 M = k 0 + k 1 VEll M = VEll 18 M = k 0 + k 1 VM M = VM RESULTS AND DISCUSSION M = GMD (8) The p-value of the independent variable(s) and Second Classification Models (Projected Areas): In this coefficient of determination (R ) of all the linear regression classification apricot mass can be predicted using single mass models are shown in Table 3. variable linear regressions of first projected area (PA 1), second projected area (PA ), third projected area (PA 3) First Classification Models (Outer Dimensions): In this and criteria area (CAE) of apricot or multiple variable linear classification apricot mass can be predicted using single regressions of apricot projected areas. As showed in variable linear regressions of major diameter (a), Table 3, among the second classification models (models intermediate diameter (b), minor diameter (c) and No. 9-16), model No. 1 had the highest R value (0.93). geometrical mean diameter (GMD) of apricot or Moreover, the p-value of independent variable (CAE) multiple variable linear regressions of apricot diameters. was 5.05E-48. Again, based on the statistical results model As indicated in Table 3, among the first classification No. 1 was chosen as the best model of second models (models No. 1-8), model No. 4 had the classification. Model No. 1 is given in equation 9. highest R value (0.93). Also, the p-value of independent variable (GMD) was 3.3E-47. Based on the M = CAE (9) statistical results model No. 4 was selected as the best model of first classification. Model No. 4 is given in Third Classification Models (Volumes): In this equation 8. classification apricot mass can be predicted using single 6

4 World J. Fungal & Plant Biol., (3): 60-64, 011 Table 3: Mass models, p-value of model variable(s) and coefficient of determination (R ) p-value Model No. a b c GMD PA1 PA PA3 CAE VEll VM R E E E E E E E E E E E E E E E E E E E E E E E E E E E variable linear regressions of estimated volume calculated REFERENCES from an ellipsoid assumed shape (V Ell) or measured volume (V M) of apricot. As indicated in Table 3, between the third 1. Ozbek, S., Special Horticulture. Cukurova classification models (models No. 17 and 18), model No. 17 University, Faculty of Agriculture Publications, had the highest R value (0.9). In addition, the p-value of No. 18, Adana, Turkey. independent variable (V Ell) was 4.05E-48. Once more,. Ahmadi, H., H. Fathollahzadeh and H. Mobli, 008. based on the statistical results model No. 17 was preferred Some physical and mechanical properties of apricot as the best model of third classification. Model No. 17 is fruits, pits and kernels (cv. Tabarzeh). Americangiven in equation 10. Eurasian Journal of Agricultural and Environmental Science, 3: M = V Ell (10) 3. Yildiz, F., New technologies in apricot processing. Journal of Standard, Apricot Special CONCLUSION Issue, Ankara, pp: Fathollahzadeh, H., H. Mobli, A. Jafari, S. Rafiee and To predict apricot mass (M) based on outer A. Mohammadi, 008. Some physical properties of dimensions, the mass model based on geometrical Tabarzeh apricot kernel. Pakistan Journal of Nutrition, mean diameter (GMD) as M = GMD with 7: R = 0.93 can be recommended. Moreover, to predict 5. Food and Agriculture Organization (FAO), 005. apricot mass based on projected areas, the mass model Report, Rome. based on criteria area (CAE) as M = CAE with 6. Sadrnia, H., A. Rajabipour, A. Jafary, A. Javadi and R = 0.93 can be suggested. Besides, to predict apricot Y. Mostofi, 007. Classification and analysis of fruit mass based on volumes, the mass model based on shapes in long type watermelon using image estimated volume calculated from an ellipsoid assumed processing. International Journal of Agriculture and shape (V Ell) as M = V Ell with R = 0.9 can be Biology, 9: utilized. These models can also be used to design and 7. Rashidi, M. and K. Seyfi, 007. Classification of fruit develop sizing machines equipped with an image shape in cantaloupe using the analysis of geometrical processing system. attributes. World Applied Sciences J., 3:

5 World J. Fungal & Plant Biol., (3): 60-64, Rashidi, M. and K. Seyfi, 007. Classification of fruit 15. Kleynen, O., V. Leemans and M.F. Destain, 003. shape in kiwifruit applying the analysis of outer Selection of the most effective wavelength bands for dimensions. International Journal of Agriculture and Jonagold apple sorting. Postharvest Biology and Biology, 9: Technology, 30: Rashidi, M. and M. Gholami, 008. Classification of 16. Polder, G., G.W.A.M. Van Der Heijden and fruit shape in kiwifruit using the analysis of I.T. Young, 003. Tomato sorting using independent geometrical attributes. American-Eurasian Journal of component analysis on spectral images. Real-Time Agricultural and Environmental Sciences, 3: Imaging, 9: Wilhelm, L.R., D.A. Suter and G.H. Brusewitz, Malcolm, E.W., J.H. Toppan and F.E. Sister, Physical Properties of Food Materials. Food and The size and shape of typical sweet potatoes. Process Engineering Technology. ASAE, St. Joseph, TRANS. A.S.A.E., 19: Michigan, USA. 18. Marvin, J.P., G.M. Hyde and R.P. Cavalieri, Rashidi, M. and K. Seyfi, 008. Determination of Modeling potato tuber mass with tuber dimensions. cantaloupe volume using image processing. TRANS. A.S.A.E., 30: World Applied Sciences Journal, : Carrion, J., A. Torregrosa, E. Orti and E. Molto, Rashidi, M. and K. Seyfi, 008. Determination of First result of an automatic citrus sorting machine kiwifruit volume using image processing. World based on an unsupervised vision system. In: Applied Sciences Journal, 3: Proceeding of Euro. Agr. Eng., Olsa. Paper 13. Wen, Z. and Y. Tao, Building a rule-based 98-F-019. machine-vision system for defect inspection on apple 0. Rashidi, M. and K. Seyfi, 008. Modeling of kiwifruit sorting and packing lines. Expert Systems with mass based on outer dimensions and projected areas. Application, 16: American-Eurasian Journal of Agricultural and 14. Kavdir, I. and D.E. Guyer, 004. Comparison of Environmental Sciences, 3: artificial neural networks and statistical classifiers in apple sorting using textural features. Biosystems Engineering, 89: