A recursive method for updating apple firmness prediction models based on spectral scattering images

Multispectral scattering is effective for nondestructive prediction of fruit firmness. However, the established prediction models for multispectral scattering are variety specific and may not perform appropriately for fruit harvested from different orchards or at different times. In this research, a recursive least squares method was proposed to update the existing prediction model by adding samples from a new population to assure good performance of the model for predicting fruit from the new population. Multispectral scattering images acquired by a multispectral imaging system from Golden Delicious apples that were harvested at the same time but had different postharvest storage time periods were used to develop the updating method. Radial scattering profiles were described by the modified Lorentzian distribution (MLD) function with four profile parameters for eight wavelengths. Multi-linear regression was performed on MLD parameters to establish prediction models for fruit firmness for each group. The prediction model established in the first group was then updated by using selected samples from the second group, and four different sampling methods were compared and validated with the rest apples. The prediction model corrected by the model-updating method gave good firmness predictions with the correlation coefficient (r) of 0.86 and the standard error of prediction (SEP) of 6.11 N. This model updating method is promising for implementing the spectral scattering technique for real-time prediction of apple fruit firmness.