Early Fruit Size Prediction Model Using Cubic Smoothing Splines for ‘Washington Navel’ (Citrus SinensisL. Osbeck) Oranges in Australia

Abstract

Citrus growers need to be able to determine the expected fruit size and the proportion of export-quality fruit at harvest relatively early in the growing season. Early fruit size prediction would also help in planning harvest operations and administering marketing strategies well in advance. This will also enable growers to remove small fruits that would not attain the desired export size. Fruit diameter growth of 'Washington Navel' oranges was measured over three consecutive growing seasons during the Stage II (cell enlargement) period between January and July. Fruit were randomly selected from around the tree canopy and tagged to measure the fruit diameter at fortnightly intervals until harvest. The data were used to develop a fruit size prediction model using cubic smoothing splines. The model was able to predict the final fruit size and the final percent size distribution at early stages of fruit development in January/February in Australia. Results indicated that under the growth patterns shown by navel oranges, accurate predictions of the final fruit size and fruit size distribution were possible during early Stage II fruit development phase 5-6 months ahead of the final harvest.

A Method of Constructing Models for Estimating Proportions of Citrus Fruit Size Grade Using Polynomial Regression

“…Regarding the validation of the number of trees, the result suggested increased stability in estimating the proportion of fruit size grades as the number of sampled trees increased (Figure 8). Studies focusing on Navel oranges [10] and apples [15] also reported achieving high accuracy by aggregating data from more than 10 trees. This gradual convergence of estimations toward a consistent value with larger tree samples reaffirms the importance of sufficient sampling for robust and stable estimations at the orchard level.…”

“…Previous studies have often focused on individual fruit measurements via machine vision or direct methods [15,20,21]. For example, in the study of 'Washington Navel' oranges [10], an individual fruit size prediction model was developed using cubic smoothing splines based on data measuring fruit diameter at fortnightly intervals until harvest, and the final proportion of fruit size grades was also estimated using the model. However, these estimates relied on the distribution derived from the size grading of 50 fruits per tree across 10 trees.…”

“…This disparity was attributed to their inability to estimate fruits concealed by leaves and branches, restricting their assessment to a partial surface area of the canopy. As a study of size estimation without using machine vision in citrus, there have been reports of a model to predict the 'Washington Navel' orange fruit diameter at harvest from five to six months before harvest using a cubic smoothing spline analysis [10]. However, growth parameters must be investigated before conducting surveys.…”

Fruit Sizing in Orchard: A Review from Caliper to Machine Vision with Deep Learning

“…In another approach, a cubic smoothing splines function was used for the prediction of the harvest weight of navel oranges using a model based on data from three growing seasons [121]. Predictions of average fruit size at harvest made at early Stage II (cell enlargement) of fruit development, 5-6 months prior to harvest, achieved an R 2 value of 0.83, 0.85, and 0.81 on actual harvest weight in the three respective seasons.…”