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

Abstract

Banana (Cavendish variety) volume, projected area and surface area were estimated by mathematical approximation. The actual volume of banana was measured using water displacement method (WDM), also the actual projected area and surface area were measured by image processing (IP) technique. These parameters that calculated by mathematical methods were then 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 WDM (P > 0.05) and projected area measured by IP technique (P> 0.05), respectively. Although the estimated surface area was significantly different from the measured surface area by IP method, this mathematical estimation represented a good approximation of actual surface area. The mean difference between estimation method and WDM was 1.58 cm 3 (95% confidence interval: -0.011 and 3.18 cm 3 ; P = 0.058). There was a mean difference of -0.71 cm 2 (95% confidence interval: -1.49 and 0.074cm 2 ; P = 0.083) between mathematical estimation method and IP technique for projected area and 2.33 cm 2 (95% confidence interval: 0.3 and 4.6 cm 2 ; P < 0.05) for surface area. WDM is time-consuming and absorbed water by banana during test may affect its physical properties. IP technique is very costly method but mathematical estimation does not require expensive apparatus.