Prediction of egg mass based on geometrical attributes

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1 AGRICULTURE AND BIOLOGY JOURNAL OF NORTH AMERICA ISSN Prt: , ISSN Ole: , do: /abja , SceceHuβ, Predcto of egg mass based o geometrcal attrbutes Majd Rashd* ad Mohammad Gholam Departmet of Agrcultural Machery, Takesta Brach, Islamc Azad Uversty, Takesta, Ira *Correspodg author s e-mals: majdrashd81@yahoo.com, m.rashd@tau.ac.r ABSTRACT Eggs are ofte graded o the bass of sze, but t may be more sutable ad ecoomcal to develop a system whch grades by mass. Thus, a relatoshp betwee egg mass ad some geometrcal attrbutes of egg s eeded. I ths study, e lear regresso models for predctg egg mass from some geometrcal attrbutes of egg such as legth (L), dameter (D), geometrcal mea dameter (GMD), frst projected area (PA 1 ), secod projected area (PA 2 ), crtera area (CAE) ad estmated volume or volume calculated from a oblate spherod assumed shape (V OSP ) were suggested. Models were dvded to three ma classfcatos ad the egg mass was estmated as a fucto of some depedet varables. The statstcal results of the study dcated that order to predct egg mass based o outer dmesos, the mass model based o geometrcal mea dameter as M = GMD wth R 2 = 0.595, ad the mass model based o legth ad dameter as M = L D wth R 2 = ca be recommeded. Also, to predct egg mass based o projected areas, the mass model based o the frst projected area as M = PA 1 wth R 2 = ca be suggested. These models ca be used to desg ad develop szg maches equpped wth a mage processg system. Keywords: Egg mass, Predcto, Geometrcal attrbutes, Gradg, Szg INTRODUCTION Egg s cosdered as oe of the basc foodstuffs due to ts very hgh utrtve value. Besdes a rch source of prote, t cotas a far amout of utrets (Sodum, Potassum, Calcum, Phosphorus, Magesum, Iro, Zc, Copper, Iode, Sulfur ad Seleum) ad vtams (A, B 1, B 2, B 3, B 6, B 12, D ad E). Egg cotas 87-90% edble porto, 65-70% mosture, % prote ad % ol (Hasa et al., 2000; Ashraf et al., 2003; Rashd et al., 2008). Egg sze s oe of the most mportat qualty parameters for evaluato by cosumer preferece. Cosumers prefer eggs of equal sze ad shape (Rashd et al., 2008). Sortg ca crease uformty sze ad shape, reduce packagg ad trasportato costs ad also may provde a optmum packagg cofgurato (Sadra et al., 2007; Rashd ad Seyf, 2007a,b; Rashd ad Gholam, 2008). Moreover, sortg s mportat meetg qualty stadards, creasg market value ad marketg operatos ( Wlhelm et al., 2005; Rashd ad Seyf, 2008a,b). Sortg maually s assocated wth hgh labor costs addto to subjectvty, tedousess ad cosstecy whch lower the qualty of sortg (We ad Tao, 1999). However, replacg huma wth a mache may stll be questoable where the labor cost s comparable wth the sortg equpmet (Kavdr ad Guyer, 2004). Studes o sortg recet years have focused o automated sortg strateges (elmatg huma efforts) to provde more effcet ad accurate sortg systems whch mprove the classfcato success or speed up the classfcato process (Kleye et al., 2003; Polder et al., 2003). The sze of produce s frequetly represeted by ts mass because t s relatvely smple to measure. However, sortg based o some geometrcal attrbutes may provde a more effcet method tha mass sortg. Moreover, the mass of produce ca be easly estmated from geometrcal attrbutes f the mass model of the produce kow (Rashd ad Seyf, 2008c). Therefore, modelg of egg mass based o some geometrcal attrbutes may be useful ad applcable. Physcal characterstcs of products are the most mportat parameters desg of sortg systems. Amog these physcal characterstcs, mass, projected area ad ceter of the gravty are the most mportat oes szg systems (Malcolm et al., 1986). Other mportat parameters are outer

Agrc. Bol. J. N. Am., 2011, 2(4): 638-644 dmesos (Marv et al., 1987; Khojastapour, 1996; Carro et al., 1998).

2 Agrc. Bol. J. N. Am., 2011, 2(4): dmesos (Marv et al., 1987; Khojastapour, 1996; Carro et al., 1998). Therefore, the ma objectves of ths research were: (a) to determe optmum mass model(s) based o some geometrcal attrbutes of egg ad (b) to verfy determed mass model(s) by comparg ther results wth those of the measurg method. MATERIALS AND METHODS Expermetal procedure: Nety radomly selected eggs of varous szes were purchased from a local market. Eggs were selected for freedom from defects by careful vsual specto, trasferred to the laboratory ad held at 5±1 C ad 90±5% relatve humdty utl expermetal procedure. I order to obta requred parameters for determg mass models, the mass of each egg was measured to 0.1 g accuracy o a dgtal balace. Moreover, the volume of each egg was measured usg the water dsplacemet method. Each egg was submerged to water ad the volume of water dsplaced was measured. Water temperature durg measuremets was kept at 25 C. The desty of each egg was the calculated from the mass dvded by the measured volume. Fg 1: The outer dmesos of a egg,.e. legth (L) ad dameter (D) by assumg the shape of egg as a oblate spherod By assumg the shape of eggs as a oblate spherod (Fgure 1), the outer dmesos of each egg,.e. legth (L) ad dameter (D) was measured to 0.1 mm accuracy by a dgtal calper. The geometrc mea dameter (GMD) of each egg was the calculated by equato (1). GMD = (LD 2 ) 1/3 (1) Two projected areas of each egg,.e. frst projected area (PA 1 ) ad secod projected area (PA 2 ) was also calculated by usg equato (2) ad equato (3), respectvely. The average projected area kow as crtera area (CAE) of each egg was the determed from equato (4). PA 1 = π LD/4 (2) PA 2 = π D 2 /4 (3) CAE = (2PA 1 +PA 2 )/3 (4) I addto, the volume of assumed shape or estmated volume of each egg (V OSP) was calculated by usg equato (5). Table 1 shows some physcal ad geometrcal propertes of the eggs used to determe mass models. V OSP = π LD 2 /6 (5) Also, order to verfy mass models, physcal ad geometrcal propertes of te radomly selected eggs of varous szes were determed as abovemetoed methods. Table 2 shows some physcal ad geometrcal propertes of the eggs used to verfy mass models. Table 1: The mea values, stadard devato (S.D.) ad coeffcet of varato (C.V.) of some physcal ad geometrcal propertes of the 90 radomly selected eggs used to determe mass models Parameter Mmum Maxmum Mea S.D. C.V. (%) Mass (M), g Legth (L), mm Dameter (D), mm Geometrcal mea dameter (GMD), mm Frst projected area (PA 1 ), cm Secod projected are a (PA2), cm Crtera area (CAE), cm Estmated volume (V OSP ), cm

3 Agrc. Bol. J. N. Am., 2011, 2(4): Measured volume (V M ), cm Desty (ρ), g cm Table 2: The mea values, s tadard devato (S.D.) ad coeffcet of varato (C.V.) of some physcal ad geometrcal propertes of the te radomly selected eggs used to verfy mass models Parameter Mmum Maxmum Mea S.D. C.V. (%) Mass (M), g Legth (L), mm Dameter (D), mm Geometrcal mea dameter (GMD), mm Frst projected area (PA 1 ), cm Secod projected area (PA 2 ), cm Crtera area (CAE), cm Estmated volume (V OSP ), cm Measured volume (V M ), cm Desty (ρ), g cm Table 3: Ne lear regresso mass models three classfcatos Model classfcato Model No. Frst Model 1 M = k 0 + k 1 L 2 M = k 0 + k 1 D 3 M = k 0 + k 1 GMD 4 M = k 0 + k 1 L + k 2 D 5 M = k 0 + k 1 PA 1 Secod 6 M = k 0 + k 1 PA 2 7 M = k 0 + k 1 CAE 8 M = k 0 + k 1 PA 1 + k 2 PA 2 Thrd 9 M = k 0 + k 1 V OSP Regress o models: A typcal lear multple measured by dgtal balace wth the egg mass regresso model s show equato (6): values predcted by mass models, root mea squared Y=k 0 +k 1 X 1 +k 2 X k X error (RMSE) ad mea relatve percetage devato (6) (MRPD) were calculated us g the equatos (7) ad Where: (8), respectvely (Rashd et al., 2005a,b; Rashd et al., 2006, Rashd et al., 2007; Rashd ad Gholam, 2010; Rashd et al., 2010): Y = Depedet varable, for example mass of egg X 1, X 2,, X = Idepedet varables, for example geometrcal attrbutes of egg k 0, k 1, k 2,, k = Regresso coeffcets I order to estmate egg mass from geometrcal attrbutes, e lear regresso mass models were suggested. Models were dvded to three ma classfcatos (Table 3). Statstcal aalyss: A pared samples t-test was used to compare the egg mass values predcted usg models wth the egg mass values measured by dgtal balace (Rashd et al., 2008). Also, to check the dscrepaces betwee the egg mass values RMSE * 2 ( M M ) 1 (7) Where: = root mea squared error, g RMSE M = egg mass measured by dgtal balace, g * M = egg mass predcted by mass model, g = umber of samples 640

4 Agrc. Bol. J. N. Am., 2011, 2(4): MRPD 1 M M M * (8) M= L+1.01D (10) Secod classfcato: I ths classfcato egg Where: mass ca be predcted usg sgle varable lear MRPD = mea relatve percetage devato, % regressos of frst projected area (PA 1 ), secod projected area (PA 2 ) ad crtera area (CAE) of egg or multple varable lear regresso of frst ad RESULTS secod projected areas of egg. As dcated Table For mathematcal descrbg mass models, all the 4, amog the secod classfcato models (models data were subjected to lear regresso aalyss No. 5-8), model No. 6 ad model No. 7 had the usg the Mcrosoft Excel The p-value of the lowest R 2 value (0.367 ad 0.657, respectvely). depedet varables ad coeffcet of Coversely, model No. 5 ad model No. 8 had the determato (R 2 ) of all the lear regresso mass hghest R 2 value (0.599 ad 0.599, respectvely). models are show Table 4. Model No. 5 ad model No. 8 are gve equatos (11) ad (12), respectvely. Frst classfcato: I ths classfcato egg mass M= PA 1 (11) ca be predcted usg sgle varable lear M= PA PA 2 regressos of legth (L), dameter (D) ad (12) geometrcal mea dameter (GMD) of egg or multple varable lear regresso of legth ad dameter of Thrd classfcato: I ths classfcato egg mass egg. As dcated Table 4, amog the frst ca be predcted usg sgle varable lear classfcato models (models No. 1-4), model No. 1 regresso of estmated volume calculated from a 2 ad model No. 2 had the lowest R value (0.344 ad oblate spherod assumed shape (V OSP ) of egg. As , respectvely). However, model No. 3 ad dcated Table 4, the R value of model No. 9 was model No. 4 had the hghest R 2 value (0.595 ad Model No. 9 s gve equato (13) , respectvely). Model No. 3 ad model No. 4 M= V OSP (13) are gve equatos (9) ad (10), respectvely. M= G MD (9) Table 4: Lear regresso mass models, p-value of model varable(s) ad coeffcet of determato (R 2 ) Model No. p-v alue R 2 L D GMD PA 1 PA 2 CAE V OSP E E E E E E E E E E DISCUSSION Amog the lear regresso models (models No. 1-9), models No. 3, 4 ad 5 were chose due to hgher R 2 value ad smplcty, ad a pared samples t-test was used to compare the egg mass values predcted usg models No. 3, 4 ad 5 wth the egg mass values measured by dgtal balace. Also, to check the dscrepaces betwee the egg mass values predcted by models wth the egg mass values measured by dgtal balace, RMSE ad MRPD were calculated. Comparso of model No. 3 wth measurg method: The egg mass values predcted by model No. 3 were compared wth the egg mass values measured by dgtal balace ad are show Table 5. The pared samples t-test results dcated that the egg mass values predcted wth model No. 3 were sgfcatly less tha the egg mass values measured 641

5 Agrc. Bol. J. N. Am., 2011, 2(4): by dgtal balace (Table 6). The mea egg mass dfferece betwee two methods was g (95% cofdece terval: ad g; P = 0.983). RMSE ad MRPD were also used to check the dscrepaces betwee the two methods. The amouts of RMSE ad MRPD were 1.7 g ad 2.3%, respectvely. Thus, egg mass predcted by model No. 3 may be 1.7 g or 2.3% less tha egg mass measured by a dgtal balace. Comparso of model No. 4 wth measurg method: The egg mass values predcted by model No. 4 were compared wth the egg mass values measured by dgtal balace ad are show Table 5. Aga, the pared samples t-test results dcated that the egg mass values predcted wth model No. 4 were sgfcatly less tha the egg mass values measured by dgtal balace (Table 6). The mea egg mass dfferece betwee two methods was g (95% cofdece terval: ad g; P = 0.992). RMSE ad MRPD were also used to check the dscrepaces betwee the two methods. The amouts of RMSE ad MRPD were 1.8 g ad 2.4%, respectvely. Therefore, egg mass predcted by model No. 4 may be 1.8 g or 2.4% less tha egg mass measured by a dgtal balace. Table 5: Geometrcal attrbutes of the te eggs used evaluatg selected mass models Geometrcal attrbutes of egg Egg mass (g) Sample No. L (mm) D (mm) GMD (mm) PA 1 2 (cm ) Measured by dgtal b alace Predcted by model No. 3 Predcted by model No. 4 Predcted by model No Table 6: Pared samples t-test aalyses o comparg egg mass determato methods Determato methods Average dfferece (g) Stadard dev ato of dfferece (g) p -value 95% cofdece tervals for t he dfferece meas (g) Measurg vs. model No , Measurg vs. model No , Measurg vs. model No , Comparso of model No. 5 wth measurg method: The egg mass values predcted by model No. 5 were compared wth the egg mass values measured by dgtal balace ad are show Table 642

6 Agrc. Bol. J. N. Am., 2011, 2(4): Oce more, the pared samples t-test results dcated that the egg mass values predcted wth model No. 5 were sgfcatly less tha the egg mass values measured by dgtal balace (Table 6). The mea egg mass dfferece betwee two methods was g (95% cofdece terval: ad g; P = 0.992). Aga, RMSE ad MRPD were used to check the dscrepaces betwee the two methods. The amouts of RMSE ad MRPD were 1.9 g ad 2.6%, respectvely. As a result, egg mass predcted by model No. 5 may be 1.9 g or 2.6% less tha egg mass measured by a dgtal balace. CONCLUSIONS It ca be cocluded that order to predct egg mass based o some geometrcal attrbutes, the mass model based o geometrcal mea dameter as M = GMD wth R 2 = 0.595, ad the mass model based o legth ad dameter as M = L D wth R 2 = ca be recommeded. I addto, to predct egg mass based o projected areas, the mass model based o the frst projected area as M = PA 1 wth R 2 = ca be suggested. These models ca be used to desg ad develop szg maches equpped wth a mage processg system. ACKNOWLEDGMENTS The authors are very grateful to the Islamc Azad Uversty, Takesta Brach, Ira for gvg all type of support coductg ths expermet. The authors also wsh to thak Eg. Srous Am Deylama for collectg requred data. REFERENCES Ash raf M., Mahmood S. ad Ahmad F. (2003). Comparatve reproductve effcecy ad egg qualty characterstcs of Lyallpur Slver Black ad Rhode Islad Red breeds of poultry. Iteratoal Joural of Agrculture ad Bology, 5: Carro J., Torregrosa A., Ort E. ad Molto E. (1998). Frst result of a automatc ctrus sortg mache based o a usupervsed vso system. I: Proceedg of Euro. Agr. Eg., Olsa. Paper 98-F-019. Hasa Z.U., Sulta J.I. ad Akram M. (2000). Nutrtoal mapulato durg duced moult whte leghor layers 2. Effects of percet he day egg producto, body weght ad reproductve system. Iteratoal Joural of Agrculture ad Bology, 2: Kavdr I. ad Guyer D.E. (2004). Comparso of artfcal eural etworks ad statstcal classfers apple sortg usg textural features. Bosystems Egeerg, 89: Khojastapour M. (1996). Desg ad fabrcato method of potato sortg mache accordg to Ira codtos. M.Sc. thess, Tehra Uversty, Ira. Kleye O., Leemas V. ad Desta M.F. (2003). Selecto of the most effectve wavelegth bads for Joagold apple sortg. Postharvest Bology ad Techology, 30: Malcolm E.W., Toppa J.H. ad Sster F.E. (1986). The sze ad shape of typcal sweet potatoes. TRANS. A.S.A.E., 19: Marv J.P., Hyde G.M. ad Cavaler R.P. (1987). Modelg potato tuber mass wth tuber dmesos. TRANS. A.S.A.E., 30: Polder G., va der Hejde G.W.A.M. ad Youg I.T. (2003). Tomato sortg usg depedet compoet aalyss o spectral mages. Real-Tme Imagg, 9: Ras hd M., Keyha A. ad Tabatabaeefar A. (2006). Multplate peetrato tests to predct sol pressureskage behavor uder rectagular rego. Iteratoal Joural of Agrculture ad Bology, 1: 5-9. Ras hd M. ad Seyf K. (2007a). Classfcato of frut shape cataloupe usg the aalyss of geometrcal attrbutes. World Appled Sceces Joural, 3: Rashd M. ad Seyf K. (2007b). Classfcato of frut shape kwfrut applyg the aalyss of outer dmesos. Iteratoal Joural of Agrculture ad Bology, 9: Rashd M. ad Seyf K. (2008a). Determato of cataloupe volume usg mage processg. World Appled Sceces Joural, 2: Rashd M. ad Seyf K. (2008b). Determato of kwfrut volume usg mage processg. World Appled Sceces Joural, 3: Rashd M. ad Seyf K. (2008c). Modelg of kwfrut mass based o outer dmesos ad projected areas. Amerca-Eurasa Joural of Agrcultural ad Evrometal Sceces, 3: Ras hd M. ad Gholam M. (2008). Classfcato of frut shape kwfrut usg the aalyss of geometrcal attrbutes. Amerca-Eurasa Joural of Agrcultural ad Evrometal Sceces, 3: Rashd M. ad Gholam M. (2010). Predcto of sol skage by multple loadgs usg the fte elemet methods. Iteratoal Joural of Agrculture ad Bology, 12: Rashd M., Tabatabaeefar A., Attarejad R. ad Keyha A. (2005a). No-lear modelg of sol pressureskage behavor applyg the fte elemet method. I: Proceedgs of Iteratoal Agrcultural 643

7 Agrc. Bol. J. N. Am., 2011, 2(4): Egeerg Coferece. 6-9 December 2005 Bagkok, Thalad. Rashd M., Tabatabaeefar A., Attarejad R. ad Keyha A. (2007). No-lear modelg of pressure-skage behavor sols usg the fte elemet method. Joural of Agrcultural Scece ad Techology, 9: Rashd M., Gholam M., Rajbar I. ad Abbass S. (2010). Fte elemet modelg of sol skage by multple loadgs. Amerca-Eurasa Joural of Agrcultural ad Evrometal Sceces, 8: Rashd M., Malekya M. ad Gholam M. (2008). Egg volume determato by spherod approxmato ad mage processg. World Appled Sceces Joural, 3: Rashd M., Attarejad R., Tabatabaeefar A. ad Keyha A. (2005b). Predcto of sol pressure-skage behavor usg the fte elemet method. Iteratoal Joural of Agrculture ad Bology, 7: Sadra H., Rajabpour A., Jafary A., Javad A. ad Mostof Y. (2007). Classfcato ad aalyss of frut shapes log type watermelo usg mage processg. Iteratoal Joural of Agrculture ad Bology, 9: We Z. ad Tao Y. (1999). Buldg a rule-based machevso system for defect specto o apple sortg ad packg les. Expert Systems wth Applcato, 16: Wlhelm L.R., Suter D.A. ad Brusewtz G.H. (2005). Physcal Propertes of Food Materals. Food ad Process Egeerg Techology. ASAE, St. Joseph, Mchga, USA. 644

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