# Non-Destructive Mangosteen Volume Estimation via Multi-View Instance Segmentation and Hybrid Geometric Modeling

## TL;DR

This paper introduces a new method to estimate mangosteen fruit volume using 2D images and machine learning, improving accuracy for non-destructive agricultural applications.

## Contribution

A novel hybrid geometric modeling framework combining multi-view instance segmentation and regression for accurate mangosteen volume estimation.

## Key findings

- Multi-view models outperformed single-view models with R2 improving from 0.6493 to 0.7290.
- The best model achieved a MAPE of 16.04% and RMSE of 31.9 cm³ using hybrid features and ellipsoid estimation.
- YOLO-based segmentation effectively separated fruit body from calyx, improving model performance.

## Abstract

In precision agriculture, accurate, non-destructive estimation of fruit volume is crucial for quality grading, yield prediction, and post-harvest management. While vision-based methods provided some usefulness, fruits with complex geometry—such as mangosteen (Garcinia mangostana L.)—are difficult due to their large calyx, which may lead to difficulties in solving using traditional form-modeling methods. Traditional geometric solutions such as ellipsoid approximations, diameter–height estimation, and shape-from-silhouette reconstruction often fail because the irregular calyx generates asymmetric protrusions that violate their basic form assumptions. We offer a novel study framework employing both multi-view instance segmentation and hybrid geometrical feature modeling to quantitatively model mangosteen volume with traditional 2D imaging. A You Only Look Once (YOLO)-based segmentation model was employed to explicitly separate the fruit body from the calyx. Calyx inclusion resulted in dense geometric noise and reduced model performance (R2<0.40). We trained eight regression models on a curated and augmented 900 image dataset (N=720, test N=180). The models used single-view and multi-view geometric regressors (V∝A1.5), polynomial hybrid configurations, ellipsoid-based approximations, as well as hybrid feature formulations. Multi-view models consistently outperformed single-view models, and the average predictive accuracy improved from R2=0.6493 to R2=0.7290. The best model is indeed a hybrid linear regression model with side- and bottom-area features—(As1.5, Ab1.5)—combined with ellipsoid-derived volume estimation—(Vellipsoid)—which resulted in R2=0.7290, a Mean Absolute Percentage Error (MAPE) of 16.04%, and a Root Mean Square Error (RMSE) of 31.9 cm3 on the test set. These results confirm the proposed model as a low-cost, interpretable, and flexible model for real-time fruit volume estimation, ready for incorporation into automated sorting and grading systems integrated in post-harvest processing pipelines.