A New Mathematical Modeling of Banana Fruit and Comparison with Actual Values of Dimensional Properties

Mahmoud Soltani, Reza Alimardani, Mahmoud Omid


Banana (Cavendish variety) volume, projected area and surface area were estimated by mathematical approximation. The actual volume of banana was measured using water displacement, also the actual projected area and surface area were measured by image processing technique. These parameters that calculated by mathematical method compared to the actual values by the paired t-test and the Bland-Altman approach. The estimated volume and projected area were not significantly different from the volume determined using water displacement (P > 0.05) and projected area measured by image processing technique (P> 0.05) respectively. Although the estimated surface area was significantly different from the measured surface area by image processing method, but this mathematical estimation represented a good approximation of actual surface area. The mean difference between estimation method and water displacement method was 1.58 cm3(95% confidence interval:- 0.011 and 3.18 cm3 ; P = 0.058 ). There was a mean difference of - 0.71 cm2 (95% confidence interval: -1.49 and 0.074cm2 ; P = 0.083) between mathematical estimation method and image processing technique for projected area and 2.33 cm2 (95% confidence interval: 0.3 and 4.6 cm2 ; P < 0.05) for surface area. Water displacement is time-consuming method, also absorbed water by banana is affected on its properties. Image processing technique is very costly method but mathematical estimation does not require to expensive apparatuses.

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DOI: https://doi.org/10.5539/mas.v4n8p104

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