PEOS-Net: a Prototype-Energy Open-Set Network for robust tomato leaf disease recognition beyond the closed-world assumption

Introduction Deep convolutional networks now reach high accuracy on curated plant disease benchmarks such as PlantVillage, but nearly all reported systems assume a closed world in which every test image belongs to a known class. In the field, a diagnostic system will meet symptoms, crops, backgrounds or damage types absent from its training taxonomy, and a closed-set classifier will confidently mislabel them, undermining trust in automated crop-advisory tools. Methods We introduce the Prototype-Energy Open-Set Network (PEOS-Net), built on a frozen EfficientNet-B0 backbone with a Convolutional Block Attention Module (CBAM) and two parameter-distinct heads that share this representation: an exponential moving average (EMA) prototype memory that drives classification, and a classifier-head branch that yields a free-energy out-of-distribution score. The two scores are fused into one hybrid open-set score; the normalization ranges, fusion weight and rejection threshold are selected on a held-out calibration split and never on the final test partition. We evaluated on an eight-class tomato subset of PlantVillage with two disease classes held out as unknowns, and compared against maximum softmax probability (MSP), out-of-distribution detector for neural networks (ODIN) and OpenMax baselines sharing the same backbone. Results PEOS-Net reached 93.87% closed-set accuracy (weighted F1 0.9392). Over five random seeds it achieved an area under the receiver operating characteristic curve (AUROC) of 0.8695 ± 0.0202, an area under the precision-recall curve (AUPR) of 0.8723 ± 0.0192, an open-set classification rate (OSCR) of 0.8363 ± 0.0142 and a false-positive rate at 95% true-positive rate (FPR@95%TPR) of 0.4853 ± 0.0645 (mean ± SD). It outperformed all three baselines on every open-set metric, although the baselines had higher closed-set accuracy (96.5%). In a same-model ablation the hybrid score (AUROC 0.8610) exceeded the distance-only (0.7208) and energy-only (0.8413) scores; a paired bootstrap gave a gain over energy-only of +0.0198 (95% CI 0.0134–0.0262). Discussion Weak correlation between the two scores (|r| < 0.06) and low overlap of their errors indicate that they carry complementary information. Because the unknown classes come from the same PlantVillage source, the results support a controlled open-set study rather than validated field deployment.