Analytically derived sphere correction enables transferable RGB-D fruit sizing across fruit shapes and depth-sensing principles.

Abstract

Abstract Depth cameras measure the distance to a fruit's surface, whereas converting its silhouette into physical dimensions requires the depth of its center; corrections for this offset have so far been empirical, and therefore bound to the crop, sensor, and dataset they were fitted on. This paper derives the correction analytically. For a spherical fruit, integrating the surface-depth distribution over the visible hemisphere yields a closed-form sphere correction whose coefficient follows from sampling geometry, together with a theoretical justification of the median mask depth as the representative statistic. Combined with deep instance segmentation on RGB-D imagery of hydroponic melons, the empirically optimal coefficient coincided with the derived value, and the pipeline reached R 2 of 0.966 for fruit length (MAE 1.43 mm), 0.959 for width (1.84 mm), and 0.861 for end-to-end fresh weight (MAPE 4.6%). The analytical form made the measurement transferable. Applied unchanged to cylindrical mini-cucumbers, the pipeline held mm-level accuracy (width MAE 0.52 mm; fresh weight R 2 0.955 after coe cient refitting), with the correction's negligibility predicted in advance by an R / Z corollary; across active-stereo and time-of-flight cameras, the optimal coefficients proved non-interchangeable, identifying the coefficient as a physical parameter that absorbs geometry, sensor physics, and fruit shape. A field system that fuses and cross-verifies the two sensors, with an error-propagation confidence gate and parameterized grading logic, reproduced 2-3% fresh-weight error and 90.9% confirmed-judgment grading accuracy over four validation sessions in a commercial greenhouse unseen during development. Throughout, geometric components transferred unchanged while learned and regression components required recalibration - a boundary the model predicts and the system itself monitors.

Plant phenotyping relevance

RGB-D画像と深度補正を用いて果実の寸法・重量を推定する手法を開発し、異なる果形・センサー・圃場で精度検証しており、植物表現型取得が中心である。

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