Geometrical Model of Lemon Fruit

Leszek Mieszkalski


A proposal of a mathematical method of modelling of the lemon shape with Bézier's curves was presented. Lisbon, Verna, Genoa lemon cultivars were selected for verification of the modelling method. The lemon contour, which is its meridian, was described with three smoothly combined Bézier's curves. Pictures taken in 10 locations changing every 36o were the basis for description of lemon contours. Bézier's curves, which approximate meridians located on the surface of lemons, are their 3D models. The presented method may be applied for mathematical modelling of the lemon shape.


Lemons; shape; Bezier's curves; mathematical models

Full Text:



Alchanatis, V., Peleg, K., Ziv, M. (1993). Classification of tissue culture segments by color machine vision. JAER, 55, 299-311.

Al-Juhaimi, F.Y., Ghafoor, K. (2013). Bioactive compounds, antioxidant and physico-chemical properties of juice from lemon, mandarin and orange fruits cultivated in Saudi Arabia. Pakistan Journal Botany, 45(4), 1193-1196.

Anders, A., Markowski, P., Kaliniewicz, Z. (2014). Badanie właściwości geometrycznych i fizycznych owoców wybranych odmian gruszy na podstawie modeli numerycznych uzyskanych za pomocą skanera 3D. Zeszyty Problemowe Postępów Nauk Rolniczych, 577, 3-12.

Baradaran Motie, J., Miraei Ashtiani, S. H., Abbaspour-Fard, M. H., Emadi, B. (2014). Modeling physical properties of lemon fruits for separation and classification. International Food Research Journal, 21(5), 1901-1909.

Bozokalfa, M. K., Kilic, M. (2010). Mathematical modeling in the estimation of pepper (Capsicum annum L.) fruit volume. Chilean Journal of Agricultural Research, 70(4), 626-632.

Burt, S.A. (2004). Essential oils: Their antibacterial properties and potential applications in foods: Av review. International Joutnal of Food Microbiology, 94, 223-253.

Ghulam, M. (2015). Date Fruites Classification Using Texture Descriptors and Shape-Size Features. Engineering Applications of Artificial Intelligence, 37, 361-367.

Growe, T. G., Delwiche, M. J. (1996). A system for fruit defect detection in real-time. AGENG, 96F-023.

Guyer, D.E., Miles, G. E., Gaultney, L. D., Schereiber, M. M. (1993). Application of machine vision to shape analysis in leaf and plant identification, TASAE, 36(1), 163-171.

Ho, Q. (2011). A Three-Dimensional Multiscale Model for Gas Exchange in Fruit. Plant Physiology, 155(3), 1158-1168.

Iqbal, S., Gopal, A., Sarma, A. (2011). Volume Estimation of Apple Fruits Using Image Processing. 2011 International Conference on Image Information Processing, Himachal Pradesh, 1-6.

Kakadiya, D., Shah, R., Shah, N., Kachariya, C., Patel, M., Sukhwani, K. (2015). Shape Extraction Methods for Fruits: Technical Review. International Journal of Computer Applications, 111(1), 43-48.

Khojastehnazhand, M., Omid, M., Tabatabaeefar, A. (2010). Development of a lemon sorting system based on color and size. African Journal of Plant Science, 4(4), 122-127.

Lalitha, K., Muthulakshmi, K., Vinothini, A. (2015). Proficient acquaintance based system for citrus leaf disease recognition and categorization. International Journal of Computer Science and Information Technologies, 6(3), 2519-2524.

Lino, A.C.L., Sanches, J., Fabbro, I.M.D. (2008). Image processing techniques for lemons and tomatoes classification. Bragantia, Campinas, 67(3), 785-789.

Mebatsion, H.K., Boudon, F., Godin, C., Pradal, C., Génard, M., Goz-Bac, C., Bertin, N. (2011). A novel profile based model 415 for virtual representation of quasi-symmetric plant organs. Computers and Electronics in Agriculture, 75(1), 113-124.

Miller, B. K., Delwiche, M. J. (1991). Peach defect detection with machine vision. TASAE, 34(6), 2588-2597.

Mohanapriya, M., Ramaswamy, L., Rajendran, R. (2013). Health and medicinal properties of lemon (Citrus limonum). International Journal Of Ayurvedic And Herbal Medicine, 3(1), 1095-1100.

Moltó, E., Aleixos, N., Ruiz, L. A., Vázquez, J., Juste, F. (1996). An artificial vision system for fruit quality assessment. AGENG 96, Madrid, 96F-078.

Moreda, G.P., Muñoz, M.A., Ruiz-Altisent, M., Perdigones, A. (2012). Shape determination of horticultural produce using two-dimensional computer vision–A review. Journal of Food Engineering, 108(2), 245-261.

Ortuño, A.A., Baidez, P., Gomez, M.C., Arcas, I., Porras, A.G., Del Rio, J.A. (2006). Citrus paradise and Citrus sinensis flavonoids: Their influence in the defence mechanism against Penicilliumdigitatum. Food Chemistry, 98(2), 351-358.

Rakun, J. (2012). Detecting Natural Objects by Means of 2D and 3D Shape Analysis. Optija, Croatia, 345-354.

Rondeau-Mouroa, C., Bouchetb, B., Pontoirea, B., Roberta, P., Mazoyerc, J., Buléona, A. (2003). Structural features and potential texturising properties of lemon and maize cellulose microfibrils. Carbohydrate Polymers, 53, 241-252.

Ruiz, L. A., Moltó, E., Juste, F., Aleixos, N. (1995). Aplicación de métodosópticos para la inspecciónautomática de productoshortofrutícolas, VI Congreso de la Sociedad Española de Ciencias Hortícolas, Barcelona.

Sarkar, N., Wolfe, R.R. (1985). Feature extraction techniques for sorting tomatoes by computer vision. TASAE, 28(3), 970-974.

Satya Priya, N., Nivetha, E., Khilar, R. (2016). Efficient Knowledge Based System to Detect Diseases in Lemon Leaf. Imperial Journal of Interdisciplinary Research (IJIR), 2(5), 275-280.

Seng, W.C., Mirisaee, S.H. (2009). A new method for fruits recognition system. Conference: Electrical Engineering and Informatics. ICEEI '09. International Conference on, 01, 130-134.

Swapnil, S.P., Dale, M.P. (2016). Computer vision based fruit detection and sorting system. Special Issue on International Journal of Electrical, Electronics and Computer Systems, ISSN (Print): 2347-2820 V-4 I-2. For 3rd National Conference on Advancements in Communication, Computing and Electronics Technology [ACCET-2016]

Taheri-Garavand, A., Nassiri, A. (2010). Study on some morphological and physical Characteristics of sweet lemon used in mass models. International Journal of Environmental Sciences, 1(4), 580-590.

Tao, Y., Morrow, C. T., Heinemann, P. H., Sommer, J. H. (1990). Automated machine vision inspection of potatoes. American Society of Agricultural Engineers, 90-3531, 23-27.

Uyar, R., Erdoğdu, F. (2009). Potential use of 3-dimensional scanners for food process modeling. Journal of Food Engineering, 93, 337-343.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

ISSN: 2083-1587 (print)
ISSN: 2449-5999 (online)

Copyright Notice

The journal offers access to the contents in the open access system on the principles of non-exclusive license Creative Commons (CC BY-ND 4.0)